title

5.18 Red Black Tree Deletion | DSA Tutorials for Beginners

description

In this lecture, I have explained all the cases of deletion in red black tree with example.
@8:05: Case 1(if red node, just delete it)
@16:05:- All the cases when we delete a black node who is having black children
@45:47:- example of red black tree deletion(all the cases with the help of one example)
***********************************************************
DSA Full Course: https: https://www.youtube.com/playlist?list=PLdo5W4Nhv31bbKJzrsKfMpo_grxuLl8LU
******************************************
See Complete Playlists:
C Programming Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31a8UcMN9-35ghv8qyFWD9_S
C++ Programming: https://www.youtube.com/playlist?list=PLdo5W4Nhv31YU5Wx1dopka58teWP9aCee
Python Full Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31bZSiqiOL5ta39vSnBxpOPT
Printing Pattern in C: https://www.youtube.com/playlist?list=PLdo5W4Nhv31Yu1igxTE2x0aeShbKtVcCy
DAA Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31ZTn2P9vF02bkb3SC8uiUUn
Placement Series: https://www.youtube.com/playlist?list=PLdo5W4Nhv31YvlDpJhvOYbM9Ap8UypgEy
Dynamic Programming: https://www.youtube.com/playlist?list=PLdo5W4Nhv31aBrJE1WS4MR9LRfbmZrAQu
Operating Systems: //www.youtube.com/playlist?list=PLdo5W4Nhv31a5ucW_S1K3-x6ztBRD-PNa
DBMS: https://www.youtube.com/playlist?list=PLdo5W4Nhv31b33kF46f9aFjoJPOkdlsRc
*****************************************************
Connect & Contact Me:
Facebook: https://www.facebook.com/Jennys-Lectures-CSIT-Netjrf-316814368950701/
Quora: https://www.quora.com/profile/Jayanti-Khatri-Lamba
Instagram: https://www.instagram.com/jayantikhatrilamba/
#redblacktree #dsa #jennyslectures

detail

{'title': '5.18 Red Black Tree Deletion | DSA Tutorials for Beginners', 'heatmap': [{'end': 1024.012, 'start': 981.442, 'weight': 0.853}, {'end': 2273.35, 'start': 2159.944, 'weight': 0.801}, {'end': 2537.825, 'start': 2497.774, 'weight': 0.768}, {'end': 2615.11, 'start': 2573.054, 'weight': 0.708}, {'end': 2725.763, 'start': 2687.665, 'weight': 1}, {'end': 3446.734, 'start': 3403.103, 'weight': 0.79}], 'summary': "Covers deletion in red-black trees, addressing the process, potential violations, handling cases of nodes with no, one, and two children, resolving double black nodes, and maintaining the tree's properties, as well as the application of case 6 for node deletion, resulting in a balanced red-black tree.", 'chapters': [{'end': 157.992, 'segs': [{'end': 53.54, 'src': 'embed', 'start': 22.617, 'weight': 0, 'content': [{'end': 23.698, 'text': 'what is that black tree?', 'start': 22.617, 'duration': 1.081}, {'end': 30.483, 'text': 'it is a binary search tree, or you can say it is a self balancing binary search tree with some extra properties.', 'start': 23.698, 'duration': 6.785}, {'end': 31.563, 'text': 'what are those properties?', 'start': 30.483, 'duration': 1.08}, {'end': 33.004, 'text': 'root would be black.', 'start': 31.563, 'duration': 1.441}, {'end': 35.947, 'text': 'second property was what there should not be.', 'start': 33.004, 'duration': 2.943}, {'end': 42.892, 'text': 'any two adjacent red nodes means if parent is red then its children should be black.', 'start': 35.947, 'duration': 6.945}, {'end': 53.54, 'text': 'third property was what that in each path from any node to its descendant nil node there should be same number of black nodes.', 'start': 42.892, 'duration': 10.648}], 'summary': 'The black tree is a self-balancing binary search tree with specific properties including black root, no adjacent red nodes, and consistent black nodes on paths.', 'duration': 30.923, 'max_score': 22.617, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ22617.jpg'}, {'end': 89.921, 'src': 'embed', 'start': 64.059, 'weight': 1, 'content': [{'end': 76.431, 'text': 'we simply follow the rules of binary search tree insertion right and if tree is empty then we create a black node and we will simply insert that node in the tree.', 'start': 64.059, 'duration': 12.372}, {'end': 79.273, 'text': 'if tree is not empty, then what you will do?', 'start': 76.431, 'duration': 2.842}, {'end': 86.439, 'text': 'we always create a node in red color and we will insert as a leaf node.', 'start': 79.273, 'duration': 7.166}, {'end': 89.921, 'text': 'then in that case which property is going to be violated?', 'start': 86.439, 'duration': 3.482}], 'summary': 'Binary search tree insertion follows rules; creates black node if tree is empty, red node as leaf if not; violating property is unclear.', 'duration': 25.862, 'max_score': 64.059, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ64059.jpg'}, {'end': 135.459, 'src': 'embed', 'start': 109.873, 'weight': 2, 'content': [{'end': 117.931, 'text': 'fine now here in deletion out of these three important properties of red black tree, which property is going to be violated?', 'start': 109.873, 'duration': 8.058}, {'end': 125.115, 'text': 'right, see, you are going to delete a red node, then there would not be any problem.', 'start': 117.931, 'duration': 7.184}, {'end': 129.676, 'text': 'just delete that node and exit right.', 'start': 125.115, 'duration': 4.561}, {'end': 135.459, 'text': 'but if you delete a black node, in that case which property is going to be violated?', 'start': 129.676, 'duration': 5.783}], 'summary': 'Red black tree: deleting black node violates a property.', 'duration': 25.586, 'max_score': 109.873, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ109873.jpg'}], 'start': 0.389, 'title': 'Deletion in red black trees', 'summary': 'Explains the properties of red black trees, the process of insertion, and the potential violations during deletion.', 'chapters': [{'end': 157.992, 'start': 0.389, 'title': 'Deletion in red black trees', 'summary': 'Explains the properties of red black trees, the process of insertion, and the potential violations of properties during deletion in red black trees.', 'duration': 157.603, 'highlights': ['Red black tree is a self balancing binary search tree with properties such as root being black, no adjacent red nodes, and equal number of black nodes in each path to descendant nil node. Explains the properties of red black trees, emphasizing the importance of root being black, no adjacent red nodes, and equal number of black nodes in each path to descendant nil node.', 'The process of insertion in red black trees involves creating a node in red color and inserting it as a leaf node, which can lead to a violation of the red red conflict property. Describes the process of insertion in red black trees, highlighting the creation of a node in red color and the potential violation of the red red conflict property.', 'Deletion in red black trees can lead to a violation of the property that ensures the same number of black nodes in each path from any node to its descendant nil node. Explains how deletion in red black trees can result in a violation of the property ensuring the same number of black nodes in each path from any node to its descendant nil node.']}], 'duration': 157.603, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ389.jpg', 'highlights': ['Red black tree is a self balancing binary search tree with specific properties.', 'The process of insertion in red black trees involves creating a node in red color.', 'Deletion in red black trees can lead to a violation of the property ensuring the same number of black nodes.']}, {'end': 599.401, 'segs': [{'end': 266.96, 'src': 'embed', 'start': 237.835, 'weight': 2, 'content': [{'end': 239.997, 'text': "i'm just taking a case of binary search tree.", 'start': 237.835, 'duration': 2.162}, {'end': 243.961, 'text': "i'm not taking red black tree here right, so simply delete it.", 'start': 239.997, 'duration': 3.964}, {'end': 246.631, 'text': 'no need to do anything right now.', 'start': 244.73, 'duration': 1.901}, {'end': 252.393, 'text': 'second case was if the node you want to delete is having only one child, suppose i want to delete this 7.', 'start': 246.631, 'duration': 5.762}, {'end': 254.474, 'text': 'first of all, search the 7 right.', 'start': 252.393, 'duration': 2.081}, {'end': 256.935, 'text': 'compare with this 10 less than 10.', 'start': 254.474, 'duration': 2.461}, {'end': 260.197, 'text': 'so we are going to to the left of this 10.', 'start': 256.935, 'duration': 3.262}, {'end': 261.156, 'text': 'now. here you got 7.', 'start': 260.197, 'duration': 0.959}, {'end': 263.198, 'text': 'now 7 is having only one child.', 'start': 261.156, 'duration': 2.042}, {'end': 266.96, 'text': 'no problem, what you will do see now.', 'start': 263.198, 'duration': 3.762}], 'summary': 'Explaining deletion in a binary search tree, handling cases of no child and one child.', 'duration': 29.125, 'max_score': 237.835, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ237835.jpg'}, {'end': 358.552, 'src': 'embed', 'start': 313.833, 'weight': 1, 'content': [{'end': 323.432, 'text': "internal nodes we are not going to delete, only we will delete the leaf nodes, internal nodes is going to be replaced with it's children.", 'start': 313.833, 'duration': 9.599}, {'end': 328.154, 'text': 'right, with which child you need to take care of that thing now?', 'start': 323.432, 'duration': 4.722}, {'end': 332.837, 'text': 'third case was if, suppose i want to delete, suppose, this 10.', 'start': 328.154, 'duration': 4.683}, {'end': 336.119, 'text': 'now 10 is having two children.', 'start': 332.837, 'duration': 3.282}, {'end': 338, 'text': 'now we will replace this 10.', 'start': 336.119, 'duration': 1.881}, {'end': 343.953, 'text': 'with which children with 9 or 15 or with what this thing you need to take care now.', 'start': 338, 'duration': 5.953}, {'end': 345.615, 'text': 'here two cases are there.', 'start': 343.953, 'duration': 1.662}, {'end': 351.242, 'text': 'either you can replace it with its in order predecessor or in order successor.', 'start': 345.615, 'duration': 5.627}, {'end': 353.105, 'text': 'two cases are there.', 'start': 351.242, 'duration': 1.863}, {'end': 354.747, 'text': 'so these two approaches are there.', 'start': 353.105, 'duration': 1.642}, {'end': 358.552, 'text': 'suppose i am replacing the stand with its in order predecessor.', 'start': 354.747, 'duration': 3.805}], 'summary': 'Deleting leaf nodes and replacing internal nodes with children, considering in order predecessor or successor.', 'duration': 44.719, 'max_score': 313.833, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ313833.jpg'}, {'end': 470.654, 'src': 'embed', 'start': 423.302, 'weight': 0, 'content': [{'end': 430.247, 'text': 'first step is in this in this, deletion in red black pre is what simply perform standard bst deletion right.', 'start': 423.302, 'duration': 6.945}, {'end': 435.25, 'text': 'the same rules here we have discussed these rules would be followed after that.', 'start': 430.247, 'duration': 5.003}, {'end': 440.194, 'text': 'you need to take care of that property, that is, that red black property of this tree.', 'start': 435.25, 'duration': 4.944}, {'end': 448.616, 'text': 'So now we will see all the cases one by one, with the help of example, and at last we will also discuss that.', 'start': 441.024, 'duration': 7.592}, {'end': 455.988, 'text': 'we will take example of one red black pre and we will apply the deletion operation and we will discuss all the cases in one example.', 'start': 448.616, 'duration': 7.372}, {'end': 457.368, 'text': 'right now.', 'start': 456.368, 'duration': 1}, {'end': 460.15, 'text': 'first step is simply perform bst deletion.', 'start': 457.368, 'duration': 2.782}, {'end': 463.211, 'text': 'so you should know how to perform bst deletion, right?', 'start': 460.15, 'duration': 3.061}, {'end': 466.052, 'text': "suppose i'm taking this is a red black tree.", 'start': 463.211, 'duration': 2.841}, {'end': 469.013, 'text': 'now you can see this is a red black tree because this is a binary search tree.', 'start': 466.052, 'duration': 2.961}, {'end': 470.654, 'text': 'first of all, root is black.', 'start': 469.013, 'duration': 1.641}], 'summary': 'The transcript discusses deletion in a red-black tree, emphasizing the importance of preserving the red-black property and covering various cases with examples.', 'duration': 47.352, 'max_score': 423.302, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ423302.jpg'}, {'end': 575.899, 'src': 'embed', 'start': 552.063, 'weight': 4, 'content': [{'end': 559.299, 'text': 'so here somewhere it is also written that when you delete it, then simply replace it with this either of its nil children.', 'start': 552.063, 'duration': 7.236}, {'end': 564.91, 'text': 'so here you can write nil and this is also in black in color.', 'start': 559.299, 'duration': 5.611}, {'end': 568.393, 'text': 'so you can see it is still a red black tree.', 'start': 564.91, 'duration': 3.483}, {'end': 570.815, 'text': 'right root is black in every path.', 'start': 568.393, 'duration': 2.422}, {'end': 571.195, 'text': 'see, here.', 'start': 570.815, 'duration': 0.38}, {'end': 573.657, 'text': 'you can see, here we have one and two black node, one and two.', 'start': 571.195, 'duration': 2.462}, {'end': 575.899, 'text': 'here also one and two and one and two.', 'start': 573.657, 'duration': 2.242}], 'summary': 'Explanation of red-black tree properties with visual examples.', 'duration': 23.836, 'max_score': 552.063, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ552063.jpg'}], 'start': 157.992, 'title': 'Tree node deletion', 'summary': "Covers the deletion process in binary search trees and red-black trees, addressing cases of nodes with no, one, and two children, and the approaches for maintaining the tree's properties. it also provides examples for illustration.", 'chapters': [{'end': 338, 'start': 157.992, 'title': 'Deletion in binary search tree', 'summary': 'Discusses the process of deleting nodes in a binary search tree, covering cases of deleting nodes with no children, one child, and two children, emphasizing the need to replace internal nodes with their children and illustrating the process through examples.', 'duration': 180.008, 'highlights': ['The chapter discusses the process of deleting nodes in a binary search tree The chapter provides an overview of the process of deleting nodes in a binary search tree, emphasizing the different cases and scenarios involved in the deletion process.', 'Replacing internal nodes with their children and illustrating the process through examples Emphasizes the need to replace internal nodes with their children and illustrates the process of deletion through practical examples, providing a clear understanding of the concept.', 'Cases of deleting nodes with no children, one child, and two children Covers the different scenarios of deleting nodes in a binary search tree, including cases where nodes have no children, one child, or two children, providing a comprehensive understanding of the deletion process.']}, {'end': 599.401, 'start': 338, 'title': 'Red black tree deletion', 'summary': 'Discusses the process of deleting nodes in a red black tree, including the two approaches of replacing a node with its in order predecessor or successor and the steps for maintaining the red black property of the tree after deletion.', 'duration': 261.401, 'highlights': ['The two approaches for replacing a node are either with its in order predecessor or in order successor, where the predecessor is the largest element from the left subtree and the successor is the smallest element from the right subtree, demonstrated by examples (relevant for understanding the deletion process)', 'The step-by-step process for maintaining the red black property after deletion by performing standard BST deletion and then addressing the red black property is explained with an example, including the case of deleting a red node and replacing it with its nil child (relevant for understanding the red black tree maintenance)', 'The simplest case in deletion is when the node to be deleted is red, where it can be directly deleted and replaced with either of its nil children, ensuring the red black tree properties are maintained (relevant for understanding the deletion process)']}], 'duration': 441.409, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ157992.jpg', 'highlights': ['Covers the deletion process in binary search trees, emphasizing different cases and scenarios involved.', 'Emphasizes the need to replace internal nodes with their children and illustrates the process through practical examples.', 'Covers the different scenarios of deleting nodes in a binary search tree, including cases where nodes have no children, one child, or two children.', 'Explains the two approaches for replacing a node with its in order predecessor or in order successor, demonstrated by examples.', 'Explains the step-by-step process for maintaining the red-black property after deletion, including the case of deleting a red node and replacing it with its nil child.', 'Describes the simplest case in deletion when the node to be deleted is red, ensuring the red-black tree properties are maintained.']}, {'end': 1016.409, 'segs': [{'end': 662.15, 'src': 'embed', 'start': 630.124, 'weight': 0, 'content': [{'end': 633.146, 'text': 'so you cannot delete this 20.', 'start': 630.124, 'duration': 3.022}, {'end': 635.028, 'text': 'internal. we cannot delete internal nodes.', 'start': 633.146, 'duration': 1.882}, {'end': 637.37, 'text': 'we can replace those nodes.', 'start': 635.028, 'duration': 2.342}, {'end': 642.415, 'text': 'so now with which node you are going to replace this 20?', 'start': 637.37, 'duration': 5.045}, {'end': 645.398, 'text': 'because it is having only one child.', 'start': 642.415, 'duration': 2.983}, {'end': 648.883, 'text': 'so just follow the rules of BST deletion.', 'start': 645.398, 'duration': 3.485}, {'end': 651.646, 'text': 'we are going to replace this 20 with this 30.', 'start': 648.883, 'duration': 2.763}, {'end': 655.291, 'text': 'now. here I am writing 30.', 'start': 651.646, 'duration': 3.645}, {'end': 659.647, 'text': 'now 30 is read, but here I am not recoloring it.', 'start': 655.291, 'duration': 4.356}, {'end': 660.889, 'text': 'this is still black.', 'start': 659.647, 'duration': 1.242}, {'end': 662.15, 'text': 'why so?', 'start': 660.889, 'duration': 1.261}], 'summary': 'Bst node 20 replaced with 30, maintaining black color.', 'duration': 32.026, 'max_score': 630.124, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ630124.jpg'}, {'end': 771.539, 'src': 'embed', 'start': 719.391, 'weight': 1, 'content': [{'end': 722.691, 'text': 'so if the node to be deleted is red, this is leaf node now.', 'start': 719.391, 'duration': 3.3}, {'end': 724.392, 'text': 'so we can simply delete it.', 'start': 722.691, 'duration': 1.701}, {'end': 726.272, 'text': 'right, we can delete leaf node.', 'start': 724.392, 'duration': 1.88}, {'end': 728.173, 'text': 'we cannot delete internal nodes.', 'start': 726.272, 'duration': 1.901}, {'end': 729.213, 'text': 'so simply delete it.', 'start': 728.173, 'duration': 1.04}, {'end': 736.52, 'text': 'I am not replacing this with its nil, children, or you can do it something like this here nil, nil, nil and nil.', 'start': 730.239, 'duration': 6.281}, {'end': 742.43, 'text': 'so here what you can write if the node to be deleted is red, then just delete it.', 'start': 737.409, 'duration': 5.021}, {'end': 749.512, 'text': 'and if the node you want to delete is black with one child in color red,', 'start': 742.43, 'duration': 7.082}, {'end': 756.934, 'text': 'then simply replace that node with its child right and delete that child because child is red.', 'start': 749.512, 'duration': 7.422}, {'end': 765.496, 'text': 'so simply you can delete that and that node would be having its own color because we are not going to change its color right now.', 'start': 756.934, 'duration': 8.562}, {'end': 768.297, 'text': 'let us take few more example of this case.', 'start': 765.496, 'duration': 2.801}, {'end': 771.539, 'text': 'so here in this example i want to delete, suppose 30.', 'start': 768.297, 'duration': 3.242}], 'summary': 'Deleting red leaf nodes, replacing black nodes with red child, and not changing the color of the node being deleted.', 'duration': 52.148, 'max_score': 719.391, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ719391.jpg'}, {'end': 816.581, 'src': 'embed', 'start': 789.446, 'weight': 3, 'content': [{'end': 795.509, 'text': 'here i am following the approach where i am going to select in order successor right now.', 'start': 789.446, 'duration': 6.063}, {'end': 797.43, 'text': 'see this 30 is internal node.', 'start': 795.509, 'duration': 1.921}, {'end': 798.63, 'text': 'so we cannot delete it.', 'start': 797.43, 'duration': 1.2}, {'end': 800.331, 'text': 'you can only replace it.', 'start': 798.63, 'duration': 1.701}, {'end': 802.213, 'text': 'we will delete the leaf node.', 'start': 800.331, 'duration': 1.882}, {'end': 803.433, 'text': 'this point is very important.', 'start': 802.213, 'duration': 1.22}, {'end': 805.415, 'text': 'you need to take care of this point.', 'start': 803.433, 'duration': 1.982}, {'end': 813.239, 'text': 'so now the in order successor would be what the smallest element from the right subtree of that node, because i want to delete this 30.', 'start': 805.415, 'duration': 7.824}, {'end': 816.581, 'text': 'so the right subtree of this node is this one smallest element is 38.', 'start': 813.239, 'duration': 3.342}], 'summary': 'Select in-order successor to replace and delete nodes, smallest element is 38.', 'duration': 27.135, 'max_score': 789.446, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ789446.jpg'}, {'end': 996.019, 'src': 'embed', 'start': 971.215, 'weight': 4, 'content': [{'end': 981.442, 'text': 'so there a double black situation will arise and the main task here is what you need to convert that double black into single black,', 'start': 971.215, 'duration': 10.227}, {'end': 984.804, 'text': 'and for that you need to have some cases.', 'start': 981.442, 'duration': 3.362}, {'end': 987.526, 'text': "so we'll discuss all the cases with the help of example.", 'start': 984.804, 'duration': 2.722}, {'end': 991.697, 'text': 'now now, suppose, here i want to delete this 20 right.', 'start': 987.526, 'duration': 4.171}, {'end': 996.019, 'text': 'first of all, search where is 20 to the right of this 10 it is having two children.', 'start': 991.697, 'duration': 4.322}], 'summary': 'Task: convert double black to single black in given cases.', 'duration': 24.804, 'max_score': 971.215, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ971215.jpg'}], 'start': 599.401, 'title': 'Red-black tree node deletion', 'summary': 'Covers the process of deleting nodes in a red-black tree, including rules for replacing nodes, handling red leaf nodes, replacing black nodes with red children, and resolving double-black nodes, with specific examples and emphasis on maintaining tree properties.', 'chapters': [{'end': 742.43, 'start': 599.401, 'title': 'Bst deletion and node replacement', 'summary': 'Discusses the process of deleting nodes in a binary search tree, emphasizing the rules for replacing internal nodes and preserving their colors, and highlights the ability to delete red leaf nodes in the deletion process.', 'duration': 143.029, 'highlights': ["The process of replacing internal nodes in a Binary Search Tree (BST) is detailed, emphasizing the preservation of the node's color, whether black or red, when the node is not deleted. The rule ensures that the color of an internal node remains unchanged if it is not deleted.", 'The ability to delete red leaf nodes in a BST is highlighted, indicating that red leaf nodes can be deleted during the deletion process, distinguishing them from internal nodes, which cannot be deleted directly.', 'The chapter explains the process of deleting nodes in a BST, including the scenario of replacing an internal node with a single child according to the rules of BST deletion, demonstrating the replacement of a node with its in-order successor and the ability to delete a red leaf node.']}, {'end': 853.396, 'start': 742.43, 'title': 'Deleting a node in red-black tree', 'summary': 'Explains the process of deleting a node in a red-black tree, including the scenario of replacing a black node with a red child and the selection of in-order successor or predecessor, using a specific example of deleting the node 30 and the subsequent replacement with the in-order successor 38.', 'duration': 110.966, 'highlights': ['The process of replacing a black node with a red child involves simply replacing the node with its child and deleting the child, as the child is red.', 'The selection of in-order successor or predecessor is crucial when deleting an internal node, and in this example, the in-order successor 38 is selected to replace the node 30.', 'The in-order successor is the smallest element from the right subtree of the node being deleted, and in this case, the in-order successor 38 replaces the node 30, maintaining its color as red and demonstrating that the internal node will retain its own color even after replacement.', 'The concept of replacing an internal node with its in-order successor and the subsequent recursive call to delete the in-order successor.']}, {'end': 1016.409, 'start': 853.396, 'title': 'Red black tree deletion', 'summary': 'Explains the process of deleting nodes in a red-black tree, ensuring the tree properties are maintained, including the resolution of double-black nodes and the replacement of deleted nodes with their in-order successors.', 'duration': 163.013, 'highlights': ['When deleting a black node with black children in a red-black tree, a double black situation arises, and the task is to convert the double black into single black, which requires specific cases to be handled.', 'Replacing a node with its in-order successor ensures the maintenance of the red-black tree properties, such as color preservation and structural integrity.', "In the process of deleting nodes in a red-black tree, the in-order successor is identified from the right subtree, ensuring the replacement maintains the tree's properties."]}], 'duration': 417.008, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ599401.jpg', 'highlights': ["The process of deleting nodes in a red-black tree involves replacing internal nodes in a Binary Search Tree (BST) while preserving the node's color.", 'Red leaf nodes can be deleted during the deletion process in a BST, distinguishing them from internal nodes.', 'Replacing a black node with a red child involves simply replacing the node with its child and deleting the child.', 'The selection of in-order successor or predecessor is crucial when deleting an internal node in a red-black tree.', 'When deleting a black node with black children in a red-black tree, a double black situation arises, and specific cases need to be handled.']}, {'end': 1823.563, 'segs': [{'end': 1089.086, 'src': 'embed', 'start': 1063.371, 'weight': 1, 'content': [{'end': 1072.859, 'text': 'so if you delete this and you will replace it with its nil, so its own color was black and the children color is also black.', 'start': 1063.371, 'duration': 9.488}, {'end': 1076.542, 'text': 'so it is now double black.', 'start': 1072.859, 'duration': 3.683}, {'end': 1082.362, 'text': 'this is the case now, or you can say it is now db double black node.', 'start': 1076.542, 'duration': 5.82}, {'end': 1084.503, 'text': 'you need to take care of this node now.', 'start': 1082.362, 'duration': 2.141}, {'end': 1086.865, 'text': 'this is the main problem in deletion in red black trade.', 'start': 1084.503, 'duration': 2.362}, {'end': 1089.086, 'text': 'now you need to convert it into single black.', 'start': 1086.865, 'duration': 2.221}], 'summary': 'After deletion, the node becomes double black, a main problem in red-black trees, requiring conversion to single black.', 'duration': 25.715, 'max_score': 1063.371, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ1063371.jpg'}, {'end': 1165.475, 'src': 'embed', 'start': 1110.143, 'weight': 0, 'content': [{'end': 1120.892, 'text': 'so the main property which is violated here is what, because of deletion of black node in this path we have one less black node.', 'start': 1110.143, 'duration': 10.749}, {'end': 1123.955, 'text': 'so it has affected the black height.', 'start': 1120.892, 'duration': 3.063}, {'end': 1125.796, 'text': 'now you need to take care of this thing now.', 'start': 1123.955, 'duration': 1.841}, {'end': 1129.639, 'text': 'so here we have multiple cases right now.', 'start': 1125.796, 'duration': 3.843}, {'end': 1139.195, 'text': 'see, first case is simple if the root is double black, so simply remove double black, right.', 'start': 1129.639, 'duration': 9.556}, {'end': 1146.981, 'text': 'suppose, because of some situations you got double black at the root right.', 'start': 1139.195, 'duration': 7.786}, {'end': 1148.242, 'text': 'this is root.', 'start': 1146.981, 'duration': 1.261}, {'end': 1154.686, 'text': 'this is double black and here we have left subtree and here we have right subtree, right.', 'start': 1148.242, 'duration': 6.444}, {'end': 1156.408, 'text': 'no need to do anything.', 'start': 1154.686, 'duration': 1.722}, {'end': 1160.431, 'text': 'simply remove this double black and make it single black, right.', 'start': 1156.408, 'duration': 4.023}, {'end': 1162.332, 'text': 'this situation we will discuss with the help of example.', 'start': 1160.431, 'duration': 1.901}, {'end': 1165.475, 'text': 'this is the simplest case in this scenario, right.', 'start': 1162.332, 'duration': 3.143}], 'summary': 'Deletion of black node reduced black height, affecting tree structure. handling double black root involves simple case of making it single black.', 'duration': 55.332, 'max_score': 1110.143, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ1110143.jpg'}, {'end': 1486.69, 'src': 'embed', 'start': 1457.279, 'weight': 2, 'content': [{'end': 1461.401, 'text': 'this was double black node to its parent right now.', 'start': 1457.279, 'duration': 4.122}, {'end': 1468.665, 'text': 'here also, two situations can be there if the parent is already black, then it will become double black, and if the parent is red,', 'start': 1461.401, 'duration': 7.264}, {'end': 1470.046, 'text': 'then it will become single black.', 'start': 1468.665, 'duration': 1.381}, {'end': 1471.907, 'text': 'here the parent was red.', 'start': 1470.046, 'duration': 1.861}, {'end': 1474.208, 'text': 'so here also two situations are there.', 'start': 1471.907, 'duration': 2.301}, {'end': 1482.544, 'text': 'if, rather than parent I am writing P, P is red now.', 'start': 1474.208, 'duration': 8.336}, {'end': 1484.046, 'text': 'next thing, what we have done.', 'start': 1482.544, 'duration': 1.502}, {'end': 1486.69, 'text': 'the sibling becomes now red.', 'start': 1484.046, 'duration': 2.644}], 'summary': 'Node becomes double black when parent is red, sibling becomes red.', 'duration': 29.411, 'max_score': 1457.279, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ1457279.jpg'}, {'end': 1564.93, 'src': 'embed', 'start': 1539.212, 'weight': 4, 'content': [{'end': 1544.396, 'text': 'right now, if the parent was red, sorry, the parent is black, so it would become double black.', 'start': 1539.212, 'duration': 5.184}, {'end': 1547.498, 'text': 'and here still the double black situation is there.', 'start': 1544.396, 'duration': 3.102}, {'end': 1549.359, 'text': 'so we will apply some other cases.', 'start': 1547.498, 'duration': 1.861}, {'end': 1551.28, 'text': 'right, that thing also we will discuss.', 'start': 1549.359, 'duration': 1.921}, {'end': 1553.342, 'text': 'i hope you got these points.', 'start': 1551.28, 'duration': 2.062}, {'end': 1555.603, 'text': 'so now here let us discuss this case.', 'start': 1553.342, 'duration': 2.261}, {'end': 1558.225, 'text': 'that parent is already black, so it will become double black.', 'start': 1555.603, 'duration': 2.622}, {'end': 1560.046, 'text': 'see, let us take this case.', 'start': 1558.225, 'duration': 1.821}, {'end': 1561.387, 'text': 'this is a red black tree.', 'start': 1560.046, 'duration': 1.341}, {'end': 1563.769, 'text': 'perfect binary tree is there and all the nodes are black.', 'start': 1561.387, 'duration': 2.382}, {'end': 1564.93, 'text': 'so this is a red black tree.', 'start': 1563.769, 'duration': 1.161}], 'summary': 'Discussing red black tree cases and situations', 'duration': 25.718, 'max_score': 1539.212, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ1539212.jpg'}, {'end': 1682.862, 'src': 'embed', 'start': 1655.476, 'weight': 3, 'content': [{'end': 1664.278, 'text': "it will ask to its obviously parent right, because if children is in problem, so he'll go to its, he'll go to his parent right.", 'start': 1655.476, 'duration': 8.802}, {'end': 1670.523, 'text': "so now he'll go to his parent and give its extra black or give its problem to its parent.", 'start': 1664.278, 'duration': 6.245}, {'end': 1673.326, 'text': 'so now parent becomes double black.', 'start': 1670.523, 'duration': 2.803}, {'end': 1673.786, 'text': 'why so?', 'start': 1673.326, 'duration': 0.46}, {'end': 1676.049, 'text': 'because parent is already black.', 'start': 1673.786, 'duration': 2.263}, {'end': 1679.273, 'text': 'so it means it become double black and it becomes now single black.', 'start': 1676.049, 'duration': 3.224}, {'end': 1682.862, 'text': 'Now sibling becomes red.', 'start': 1680.62, 'duration': 2.242}], 'summary': "Children's problem passed to parent, turning it double black, then single black. sibling turns red.", 'duration': 27.386, 'max_score': 1655.476, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ1655476.jpg'}], 'start': 1016.409, 'title': 'Red-black tree node handling', 'summary': 'Explains how to handle double black nodes in red-black trees, covering the process of redistributing the black color and resolving double black situations through various cases and steps.', 'chapters': [{'end': 1359.569, 'start': 1016.409, 'title': 'Handling double black nodes in red-black trees', 'summary': "Discusses the handling of double black nodes in red-black trees, including the situation of double black nodes and the resolution of conflicts by checking the sibling and children's colors.", 'duration': 343.16, 'highlights': ['When deleting a black node in a red-black tree, a double black node may be created, leading to a violation of the black height property, which needs to be resolved to maintain balance.', 'The main problem in deletion in red-black trees arises from the situation of double black nodes, which need to be converted into single black through various resolution cases.', "In the case where the double black node's sibling is black and both its children are black, a specific resolution case is applied to address the imbalance and restore the tree's properties."]}, {'end': 1823.563, 'start': 1359.569, 'title': 'Red-black tree node handling', 'summary': 'Explains the handling of double black nodes in a red-black tree, including the process of redistributing the black color and resolving double black situations through various cases and steps.', 'duration': 463.994, 'highlights': ['The sibling of a double black node cannot receive the extra black, so the node will pass its problem to its parent, turning the parent red and resolving the double black situation. When a double black node cannot distribute its extra black to its sibling or children, it passes the problem to its parent, turning the parent red and resolving the double black situation.', 'After passing the problem to the parent, the sibling becomes red, indicating the resolution of the double black situation. Upon passing the problem to the parent, the sibling of the double black node becomes red, signifying the resolution of the double black situation.', 'If the parent is already black, the double black node becomes double black, and further cases need to be applied to resolve the situation. When the parent of the double black node is already black, the node becomes double black, necessitating the application of additional cases to resolve the situation.', 'In case of a root being double black, removing the double black results in a single black node, resolving the situation. When the root of the red-black tree becomes double black, removing the double black results in a single black node, effectively resolving the situation.']}], 'duration': 807.154, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ1016409.jpg', 'highlights': ['When deleting a black node in a red-black tree, a double black node may be created, leading to a violation of the black height property, which needs to be resolved to maintain balance.', 'The main problem in deletion in red-black trees arises from the situation of double black nodes, which need to be converted into single black through various resolution cases.', 'The sibling of a double black node cannot receive the extra black, so the node will pass its problem to its parent, turning the parent red and resolving the double black situation.', 'After passing the problem to the parent, the sibling becomes red, indicating the resolution of the double black situation.', 'If the parent is already black, the double black node becomes double black, and further cases need to be applied to resolve the situation.', 'In case of a root being double black, removing the double black results in a single black node, resolving the situation.']}, {'end': 2379.177, 'segs': [{'end': 1957.14, 'src': 'embed', 'start': 1902.848, 'weight': 0, 'content': [{'end': 1915.238, 'text': 'when the parent will go and tell him to calm down, then it will become black, right, but in that process the parent will become angry.', 'start': 1902.848, 'duration': 12.39}, {'end': 1924.666, 'text': 'so parent will become red because generally it happens when you are angry and your parent comes to calm you down, to cool you down.', 'start': 1915.238, 'duration': 9.428}, {'end': 1931.423, 'text': 'then they will become angry and then after that you will be like silent.', 'start': 1924.666, 'duration': 6.757}, {'end': 1935.145, 'text': 'so now we are going to swap the colors.', 'start': 1931.423, 'duration': 3.722}, {'end': 1940.987, 'text': 'now the sibling becomes red to black, but parents become from black to red.', 'start': 1935.145, 'duration': 5.842}, {'end': 1944.848, 'text': 'first step is this one right, but still the problems is there.', 'start': 1940.987, 'duration': 3.861}, {'end': 1945.888, 'text': 'db problem is there.', 'start': 1944.848, 'duration': 1.04}, {'end': 1947.749, 'text': 'double black problem is there now.', 'start': 1945.888, 'duration': 1.861}, {'end': 1957.14, 'text': 'second step is what the parent will rotate in the double black node direction.', 'start': 1947.749, 'duration': 9.391}], 'summary': 'Parent tries to calm child, ends up angry, color swap happens, double black problem arises, parent rotates in double black node direction.', 'duration': 54.292, 'max_score': 1902.848, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ1902848.jpg'}, {'end': 2273.35, 'src': 'heatmap', 'start': 2159.944, 'weight': 0.801, 'content': [{'end': 2166.09, 'text': 'after deleting this 15, and as you can see, this is now a red black tree from here.', 'start': 2159.944, 'duration': 6.146}, {'end': 2166.751, 'text': 'this is null.', 'start': 2166.09, 'duration': 0.661}, {'end': 2169.468, 'text': 'so you can delete it Now.', 'start': 2166.751, 'duration': 2.717}, {'end': 2170.789, 'text': 'what can be the next case?', 'start': 2169.468, 'duration': 1.321}, {'end': 2173.21, 'text': 'So now we will discuss the case five.', 'start': 2171.309, 'duration': 1.901}, {'end': 2178.893, 'text': 'Let us take this example, right? This is a red black tree and from here I want to delete this one.', 'start': 2173.37, 'duration': 5.523}, {'end': 2184.875, 'text': 'In one example I want to discuss more than this one case, two or three cases I will discuss.', 'start': 2179.173, 'duration': 5.702}, {'end': 2187.317, 'text': 'Now see if you delete this one.', 'start': 2184.956, 'duration': 2.361}, {'end': 2190.679, 'text': 'right. first of all, search where is one.', 'start': 2188.217, 'duration': 2.462}, {'end': 2191.56, 'text': 'this is black.', 'start': 2190.679, 'duration': 0.881}, {'end': 2196.725, 'text': 'so we will replace it with its null nil node and it will become double black.', 'start': 2191.56, 'duration': 5.165}, {'end': 2199.107, 'text': 'now, right, so here we have the problem.', 'start': 2196.725, 'duration': 2.382}, {'end': 2202.831, 'text': 'now find out which case you need to apply to find out this thing.', 'start': 2199.107, 'duration': 3.724}, {'end': 2204.973, 'text': 'just check the sibling of double black.', 'start': 2202.831, 'duration': 2.142}, {'end': 2207.074, 'text': 'sibling is what black.', 'start': 2204.973, 'duration': 2.101}, {'end': 2210.595, 'text': 'now. children of the sibling say this is also black.', 'start': 2207.074, 'duration': 3.521}, {'end': 2213.396, 'text': 'this is also black because these are nil.', 'start': 2210.595, 'duration': 2.801}, {'end': 2215.196, 'text': 'so now this case you will apply.', 'start': 2213.396, 'duration': 1.8}, {'end': 2215.977, 'text': 'first of all.', 'start': 2215.196, 'duration': 0.781}, {'end': 2220.258, 'text': "right, so now he'll give its problem to its parent.", 'start': 2215.977, 'duration': 4.281}, {'end': 2222.058, 'text': 'so now remove this double black.', 'start': 2220.258, 'duration': 1.8}, {'end': 2223.519, 'text': 'this would become single black.', 'start': 2222.058, 'duration': 1.461}, {'end': 2226.44, 'text': 'now null, and the parent is black, already black.', 'start': 2223.519, 'duration': 2.921}, {'end': 2227.92, 'text': 'so it would become now double black.', 'start': 2226.44, 'duration': 1.48}, {'end': 2232.774, 'text': 'right now, still, problem of double black exists.', 'start': 2228.991, 'duration': 3.783}, {'end': 2234.316, 'text': 'now. reapply cases.', 'start': 2232.774, 'duration': 1.542}, {'end': 2237.499, 'text': 'now. find out which case you need to apply.', 'start': 2234.316, 'duration': 3.183}, {'end': 2239.781, 'text': 'now. this is the node which is having problem.', 'start': 2237.499, 'duration': 2.282}, {'end': 2245.386, 'text': 'now check out the sibling of this node, that is 30, which is black right now.', 'start': 2239.781, 'duration': 5.605}, {'end': 2247.227, 'text': 'check out this node.', 'start': 2245.386, 'duration': 1.841}, {'end': 2251.91, 'text': 'sorry, this, children of sibling see it is having two children.', 'start': 2247.227, 'duration': 4.683}, {'end': 2258.595, 'text': 'which children is near to this double black node, this one, and which is far from this, this one.', 'start': 2251.91, 'duration': 6.685}, {'end': 2260.296, 'text': 'so first you will check sibling.', 'start': 2258.595, 'duration': 1.701}, {'end': 2261.177, 'text': 'this is black.', 'start': 2260.296, 'duration': 0.881}, {'end': 2271.189, 'text': 'now the child who is far from double black, this situation siblings child who is far from double black.', 'start': 2261.177, 'duration': 10.012}, {'end': 2273.35, 'text': 'this child is far from double black.', 'start': 2271.189, 'duration': 2.161}], 'summary': 'Discussion of red black tree deletion cases and problem-solving', 'duration': 113.406, 'max_score': 2159.944, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ2159944.jpg'}], 'start': 1823.563, 'title': 'Red black tree operations', 'summary': 'Explains the steps to resolve the double black (db) problem in a red black tree, involving color swapping, rotations, and specific cases, leading to the final transformation of the tree into a balanced state with no double black nodes.', 'chapters': [{'end': 1935.145, 'start': 1823.563, 'title': 'Handling sibling of double black node', 'summary': 'Discusses the cases when handling the sibling of a double black node in a tree, highlighting the process of calming down the sibling from being red to black through a parent intervention and color swapping.', 'duration': 111.582, 'highlights': ['The sibling of double black is red, requiring the intervention of a parent to calm it down, which involves a color swap, resulting in the parent turning red and then the sibling becoming black.', 'Explains the scenario when the sibling and its children were black, indicating the need to discuss other cases involving a red sibling and subsequent actions for calming it down.', "Describes the process akin to siblings where one is angry and the other seeks the parent's intervention to calm the angry sibling down, resulting in color changes and ultimately calming the red sibling down."]}, {'end': 2379.177, 'start': 1935.145, 'title': 'Red black tree operations', 'summary': 'Explains the steps to resolve the double black (db) problem in a red black tree, involving color swapping, rotations, and application of specific cases, leading to the final transformation of the tree into a balanced state with no double black nodes.', 'duration': 444.032, 'highlights': ['The final transformation of the tree into a balanced state with no double black nodes. After a series of operations including color swapping, rotations, and application of specific cases, the tree is transformed into a balanced state with no double black nodes, resolving the DB problem.', 'The steps to resolve the double black (DB) problem in a Red Black tree involving color swapping, rotations, and application of specific cases. The chapter details the specific steps to resolve the double black (DB) problem in a Red Black tree, including color swapping, rotations, and application of specific cases, emphasizing the process to eliminate the DB problem.', 'Color swapping, rotations, and application of specific cases to eliminate the DB problem. The process involves color swapping, rotations, and application of specific cases to eliminate the double black (DB) problem, ensuring the balanced state of the Red Black tree.']}], 'duration': 555.614, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ1823563.jpg', 'highlights': ['The steps to resolve the double black (DB) problem in a Red Black tree involving color swapping, rotations, and application of specific cases. The chapter details the specific steps to resolve the double black (DB) problem in a Red Black tree, including color swapping, rotations, and application of specific cases, emphasizing the process to eliminate the DB problem.', 'The final transformation of the tree into a balanced state with no double black nodes. After a series of operations including color swapping, rotations, and application of specific cases, the tree is transformed into a balanced state with no double black nodes, resolving the DB problem.', 'The sibling of double black is red, requiring the intervention of a parent to calm it down, which involves a color swap, resulting in the parent turning red and then the sibling becoming black.']}, {'end': 2859.773, 'segs': [{'end': 2537.825, 'src': 'heatmap', 'start': 2458.944, 'weight': 0, 'content': [{'end': 2460.265, 'text': 'First of all what we have done.', 'start': 2458.944, 'duration': 1.321}, {'end': 2463.648, 'text': 'We simply swap color of.', 'start': 2460.926, 'duration': 2.722}, {'end': 2466.349, 'text': 'See this one and this one.', 'start': 2464.608, 'duration': 1.741}, {'end': 2469.912, 'text': "Right Means color of db's sibling.", 'start': 2466.85, 'duration': 3.062}, {'end': 2477.769, 'text': "With it's child who is near to db.", 'start': 2470.692, 'duration': 7.077}, {'end': 2479.951, 'text': 'now, after swapping the colors, what we have done?', 'start': 2477.769, 'duration': 2.182}, {'end': 2486.154, 'text': 'we have rotate the sibling of this db in opposite direction to db, not in the direction of db.', 'start': 2479.951, 'duration': 6.203}, {'end': 2492.158, 'text': 'so now and now still the double black problem exists and definitely you need to apply case 6.', 'start': 2486.154, 'duration': 6.004}, {'end': 2497.774, 'text': 'so here you can write down apply case 6 right now.', 'start': 2492.158, 'duration': 5.616}, {'end': 2499.195, 'text': 'what is case 6?', 'start': 2497.774, 'duration': 1.421}, {'end': 2502.397, 'text': 'see, so now we will discuss case 6.', 'start': 2499.195, 'duration': 3.202}, {'end': 2505.7, 'text': 'after applying case 5 this would become this thing.', 'start': 2502.397, 'duration': 3.303}, {'end': 2509.363, 'text': 'i guess this would be red.', 'start': 2505.7, 'duration': 3.663}, {'end': 2515.408, 'text': 'right, because when you will this double black, this node will give its extra black to parent.', 'start': 2509.363, 'duration': 6.045}, {'end': 2519.031, 'text': 'then the sibling becomes angry or you can say it becomes red.', 'start': 2515.408, 'duration': 3.623}, {'end': 2519.751, 'text': 'now this is nil.', 'start': 2519.031, 'duration': 0.72}, {'end': 2520.892, 'text': 'so you can delete it.', 'start': 2519.751, 'duration': 1.141}, {'end': 2522.333, 'text': 'so now this is the tree now.', 'start': 2520.892, 'duration': 1.441}, {'end': 2524.275, 'text': 'here what is case 6.', 'start': 2522.333, 'duration': 1.942}, {'end': 2525.235, 'text': 'now we will discuss.', 'start': 2524.275, 'duration': 0.96}, {'end': 2530.199, 'text': 'see, this is node having double black situation now, check out the sibling of double black.', 'start': 2525.235, 'duration': 4.964}, {'end': 2532.06, 'text': 'this is black now.', 'start': 2530.199, 'duration': 1.861}, {'end': 2533.401, 'text': 'this is having two children.', 'start': 2532.06, 'duration': 1.341}, {'end': 2537.825, 'text': 'so first of all you will check the child who is far from double black.', 'start': 2533.401, 'duration': 4.424}], 'summary': 'Swapping colors and applying cases to resolve double black problem in a tree structure.', 'duration': 61.948, 'max_score': 2458.944, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ2458944.jpg'}, {'end': 2615.11, 'src': 'heatmap', 'start': 2573.054, 'weight': 0.708, 'content': [{'end': 2579.86, 'text': "Now this is the far child, so he'll ask to its parent to go and calm down his children.", 'start': 2573.054, 'duration': 6.806}, {'end': 2588.385, 'text': 'now, if the parent will go, in that case we will swap the parent and siblings color.', 'start': 2581.161, 'duration': 7.224}, {'end': 2592.547, 'text': "here both are having black and black, so swapping doesn't affect anything.", 'start': 2588.385, 'duration': 4.162}, {'end': 2598.45, 'text': 'now, if situation is something like this, if this is red and this is obviously black, in that case this would become black.', 'start': 2592.547, 'duration': 5.903}, {'end': 2601.792, 'text': 'this would become red, but here this is not the case.', 'start': 2598.45, 'duration': 3.342}, {'end': 2615.11, 'text': "both are black, so no swapping would be there right now again, next step is what now he'll rotate towards db direction, because in this case 10,", 'start': 2601.792, 'duration': 13.318}], 'summary': 'Discussion on swapping colors and rotating towards db direction in a tree scenario.', 'duration': 42.056, 'max_score': 2573.054, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ2573054.jpg'}, {'end': 2725.763, 'src': 'heatmap', 'start': 2687.665, 'weight': 1, 'content': [{'end': 2691.468, 'text': 'now, next step is what this remove this double black.', 'start': 2687.665, 'duration': 3.803}, {'end': 2691.808, 'text': 'why so?', 'start': 2691.468, 'duration': 0.34}, {'end': 2699.774, 'text': 'because see, this double black node can push his double black problem upwards, not downwards.', 'start': 2691.808, 'duration': 7.966}, {'end': 2706.459, 'text': 'now the problem was the far child was red, so he will give its extra black to 30.', 'start': 2699.774, 'duration': 6.685}, {'end': 2711.063, 'text': 'so the 30 would become now black and this would become single black.', 'start': 2706.459, 'duration': 4.604}, {'end': 2714.513, 'text': "and that's it.", 'start': 2713.772, 'duration': 0.741}, {'end': 2719.217, 'text': 'now you can see, this is a red black tree right after applying case 6.', 'start': 2714.513, 'duration': 4.704}, {'end': 2725.763, 'text': 'so now these are all the cases and these cases are having its mirror image also like this.', 'start': 2719.217, 'duration': 6.546}], 'summary': 'Applying case 6 resolves double black node, yielding single black node.', 'duration': 38.098, 'max_score': 2687.665, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ2687665.jpg'}], 'start': 2381.437, 'title': 'Red-black tree node deletion', 'summary': 'Discusses the application of case 6 in red-black tree node deletion, including the steps involved and the necessity to apply case 6 after case 5, with a reference to the previous application of case 3. it also explains the process of deleting nodes in a red-black tree, detailing the steps and cases, including the application of case 6 to resolve the double black problem, resulting in a balanced red-black tree.', 'chapters': [{'end': 2458.224, 'start': 2381.437, 'title': 'Red-black tree node deletion', 'summary': 'Discusses the application of case 6 in red-black tree node deletion, including the steps involved and the necessity to apply case 6 after case 5, with a reference to the previous application of case 3.', 'duration': 76.787, 'highlights': ['The necessity to apply case 6 after case 5 in red-black tree node deletion, as indicated by the previous application of case 3 and case 5.', 'Explanation of the steps involved in case 6, emphasizing the simplicity of deleting a red node.', 'The presence of a double black situation in the tree, prompting the need to find the appropriate case to apply for resolution.']}, {'end': 2859.773, 'start': 2458.944, 'title': 'Red black tree deletion', 'summary': 'Explains the process of deleting nodes in a red black tree, detailing the steps and cases, including the application of case 6 to resolve the double black problem, resulting in a balanced red black tree.', 'duration': 400.829, 'highlights': ['The chapter explains the process of applying case 6 to resolve the double black problem in a red black tree. The application of case 6 resolves the double black problem by pushing the extra black upwards, resulting in a balanced red black tree.', 'The chapter discusses the rotation and color swapping involved in resolving the double black problem, ensuring the red black tree remains balanced. The process involves rotating the parent towards the child with the problem and swapping colors, ensuring the tree remains balanced and the double black problem is resolved.', 'The chapter emphasizes the need to apply the same rules in the mirror image cases for maintaining balance in the red black tree. Emphasizes the importance of applying the same rules in mirror image cases to maintain balance in the red black tree, ensuring consistency in resolving double black problems.']}], 'duration': 478.336, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ2381437.jpg', 'highlights': ['The necessity to apply case 6 after case 5 in red-black tree node deletion, as indicated by the previous application of case 3 and case 5.', 'The chapter explains the process of applying case 6 to resolve the double black problem in a red black tree. The application of case 6 resolves the double black problem by pushing the extra black upwards, resulting in a balanced red black tree.', 'The chapter discusses the rotation and color swapping involved in resolving the double black problem, ensuring the red black tree remains balanced. The process involves rotating the parent towards the child with the problem and swapping colors, ensuring the tree remains balanced and the double black problem is resolved.']}, {'end': 3192.415, 'segs': [{'end': 3011.6, 'src': 'embed', 'start': 2985.048, 'weight': 2, 'content': [{'end': 2991.499, 'text': 'so we will replace this 30 with this 35 right and we are going to replace it.', 'start': 2985.048, 'duration': 6.451}, {'end': 2993.261, 'text': 'we are not going to delete the internal load.', 'start': 2991.499, 'duration': 1.762}, {'end': 2996.464, 'text': 'that is why it will having its own color, that is black.', 'start': 2993.261, 'duration': 3.203}, {'end': 2997.425, 'text': 'only now.', 'start': 2996.464, 'duration': 0.961}, {'end': 2999.427, 'text': '35, 35, 235 are there.', 'start': 2997.425, 'duration': 2.002}, {'end': 3004.232, 'text': 'so now we recursively call delete on this in order successor right.', 'start': 2999.427, 'duration': 4.805}, {'end': 3007.255, 'text': 'so we cannot directly delete it because it is already black.', 'start': 3004.232, 'duration': 3.023}, {'end': 3011.6, 'text': 'so now we will replace it with nil and it would become now double black.', 'start': 3007.255, 'duration': 4.345}], 'summary': 'Replacing 30 with 35, maintaining internal load, resulting in 35, 35, 235. recursively calling delete on inorder successor to handle double black node.', 'duration': 26.552, 'max_score': 2985.048, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ2985048.jpg'}, {'end': 3113.521, 'src': 'embed', 'start': 3086.106, 'weight': 0, 'content': [{'end': 3091.675, 'text': 'so that is why it will become red right now.', 'start': 3086.106, 'duration': 5.569}, {'end': 3093.155, 'text': 'still the problem occurs now.', 'start': 3091.675, 'duration': 1.48}, {'end': 3096.076, 'text': 'double black problem is here now again.', 'start': 3093.155, 'duration': 2.921}, {'end': 3097.877, 'text': 'check out which case you need to apply now.', 'start': 3096.076, 'duration': 1.801}, {'end': 3099.057, 'text': 'check out the sibling of this.', 'start': 3097.877, 'duration': 1.18}, {'end': 3102.218, 'text': 'one sibling is black right now.', 'start': 3099.057, 'duration': 3.161}, {'end': 3105.259, 'text': 'check out the far child from this double black.', 'start': 3102.218, 'duration': 3.041}, {'end': 3106.559, 'text': 'this is also black now.', 'start': 3105.259, 'duration': 1.3}, {'end': 3107.559, 'text': 'check out the near child.', 'start': 3106.559, 'duration': 1}, {'end': 3113.521, 'text': 'this is also black now again, you will apply this case only right now.', 'start': 3107.559, 'duration': 5.962}], 'summary': 'Addressing a recurring problem with double black cases in a system, applying specific checks and actions to resolve it.', 'duration': 27.415, 'max_score': 3086.106, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ3086106.jpg'}, {'end': 3166.576, 'src': 'embed', 'start': 3140.21, 'weight': 3, 'content': [{'end': 3144.834, 'text': 'so in that case you will do what simply remove double black, right.', 'start': 3140.21, 'duration': 4.624}, {'end': 3149.157, 'text': 'so simply remove it double black and 50 is become single black now.', 'start': 3144.834, 'duration': 4.323}, {'end': 3154.528, 'text': 'so now this is the tree after deleting 30.', 'start': 3151.226, 'duration': 3.302}, {'end': 3156.71, 'text': "so this is, you can see, it's a red black tree.", 'start': 3154.528, 'duration': 2.182}, {'end': 3160.612, 'text': 'now, from here, delete 90, where is 90?', 'start': 3156.71, 'duration': 3.902}, {'end': 3161.613, 'text': 'here we have 90.', 'start': 3160.612, 'duration': 1.001}, {'end': 3166.576, 'text': 'see now the node you want to delete is red, so you can simply delete it.', 'start': 3161.613, 'duration': 4.963}], 'summary': 'Deleting nodes from a red-black tree, resulting in a single black node and a red-black tree.', 'duration': 26.366, 'max_score': 3140.21, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ3140210.jpg'}], 'start': 2859.954, 'title': 'Red black tree deletion', 'summary': 'Discusses the process of deleting nodes in a red-black tree, including applying case 4, case 3, and addressing the extra black problem, leading to the final structure of the red-black tree after deletion. it also addresses the cases of double black nodes and their siblings, resulting in the transformation of nodes from double black to single black, maintaining the properties of a red-black tree.', 'chapters': [{'end': 3007.255, 'start': 2859.954, 'title': 'Red black tree deletion', 'summary': 'Discusses the process of deleting nodes in a red-black tree, including applying case 4, case 3, and addressing the extra black problem, leading to the final structure of the red-black tree after deletion.', 'duration': 147.301, 'highlights': ['Applying case 4 to resolve the double black problem The process involves swapping the parent color and its sibling, rotating the parent in the direction of the double black, and reapplying the deletion cases.', 'Applying case 3 to handle the extra black problem After checking the black sibling and distant children nodes, the extra black is pushed upwards to the parent, adjusting the colors accordingly.', 'Replacing the deleted node with its in-order successor and recursively calling delete When deleting a node with two children, it is replaced by its in-order successor, and the deletion process is recursively called on the successor to maintain the red-black tree properties.']}, {'end': 3192.415, 'start': 3007.255, 'title': 'Red black tree deletion process', 'summary': 'Discusses the process of deleting nodes from a red black tree, addressing the cases of double black nodes and their siblings, resulting in the transformation of nodes from double black to single black, maintaining the properties of a red black tree.', 'duration': 185.16, 'highlights': ['The chapter explains the process of handling double black nodes in a red black tree, involving the redistribution of black nodes and transformation of double black nodes to single black, ensuring the maintenance of the red black tree properties.', 'It describes the specific cases and steps involved in handling double black nodes and their siblings, resulting in the transformation of the double black nodes and their siblings to maintain the red black tree properties.', 'The example highlights the deletion process of nodes in a red black tree, including the handling of a double black node by redistributing the black nodes and transforming them to single black, ensuring the preservation of the red black tree properties.']}], 'duration': 332.461, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ2859954.jpg', 'highlights': ['Applying case 4 to resolve the double black problem The process involves swapping the parent color and its sibling, rotating the parent in the direction of the double black, and reapplying the deletion cases.', 'Applying case 3 to handle the extra black problem After checking the black sibling and distant children nodes, the extra black is pushed upwards to the parent, adjusting the colors accordingly.', 'Replacing the deleted node with its in-order successor and recursively calling delete When deleting a node with two children, it is replaced by its in-order successor, and the deletion process is recursively called on the successor to maintain the red-black tree properties.', 'The chapter explains the process of handling double black nodes in a red black tree, involving the redistribution of black nodes and transformation of double black nodes to single black, ensuring the maintenance of the red black tree properties.', 'It describes the specific cases and steps involved in handling double black nodes and their siblings, resulting in the transformation of the double black nodes and their siblings to maintain the red black tree properties.', 'The example highlights the deletion process of nodes in a red black tree, including the handling of a double black node by redistributing the black nodes and transforming them to single black, ensuring the preservation of the red black tree properties.']}, {'end': 3784.789, 'segs': [{'end': 3224.359, 'src': 'embed', 'start': 3192.415, 'weight': 2, 'content': [{'end': 3194.776, 'text': 'you want to delete, but this is already black node.', 'start': 3192.415, 'duration': 2.361}, {'end': 3197.258, 'text': 'so you cannot simply delete it right.', 'start': 3194.776, 'duration': 2.482}, {'end': 3202.042, 'text': 'we will replace it with its nil and it would become now double black.', 'start': 3197.258, 'duration': 4.784}, {'end': 3204.588, 'text': 'now, here the problem exists.', 'start': 3202.867, 'duration': 1.721}, {'end': 3208.31, 'text': 'now you need to convert it into single black right now.', 'start': 3204.588, 'duration': 3.722}, {'end': 3209.911, 'text': 'check out the sibling of double black.', 'start': 3208.31, 'duration': 1.601}, {'end': 3211.352, 'text': 'that is 65.', 'start': 3209.911, 'duration': 1.441}, {'end': 3212.472, 'text': 'is the sibling?', 'start': 3211.352, 'duration': 1.12}, {'end': 3214.173, 'text': 'sibling is black in color.', 'start': 3212.472, 'duration': 1.701}, {'end': 3219.896, 'text': 'right after that, check out the child of the sibling, which is far from double black.', 'start': 3214.173, 'duration': 5.723}, {'end': 3224.359, 'text': 'so this child is far from double black and this is nil and this is black.', 'start': 3219.896, 'duration': 4.463}], 'summary': 'Replace black node, resolve double black, ensure sibling is black.', 'duration': 31.944, 'max_score': 3192.415, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ3192415.jpg'}, {'end': 3446.734, 'src': 'heatmap', 'start': 3403.103, 'weight': 0.79, 'content': [{'end': 3407.726, 'text': 'so now, after rotation, tree would be something like this 70 would go downward.', 'start': 3403.103, 'duration': 4.623}, {'end': 3409.007, 'text': '68 would go upward.', 'start': 3407.726, 'duration': 1.281}, {'end': 3410.989, 'text': '68 is now red.', 'start': 3409.007, 'duration': 1.982}, {'end': 3412.93, 'text': 'now, after rotation, remove db.', 'start': 3410.989, 'duration': 1.941}, {'end': 3413.851, 'text': 'so db is this one.', 'start': 3412.93, 'duration': 0.921}, {'end': 3414.811, 'text': 'so remove this thing.', 'start': 3413.851, 'duration': 0.96}, {'end': 3416.573, 'text': 'this would become only null.', 'start': 3414.811, 'duration': 1.762}, {'end': 3421.316, 'text': 'that is one black and change the color of red child.', 'start': 3416.573, 'duration': 4.743}, {'end': 3428.282, 'text': 'see, the red child was this one because because of the 65 was red right.', 'start': 3421.316, 'duration': 6.966}, {'end': 3431.905, 'text': 'so 65, the far child was red, so it would become now black.', 'start': 3428.282, 'duration': 3.623}, {'end': 3434.767, 'text': 'so 65 now becomes black.', 'start': 3431.905, 'duration': 2.862}, {'end': 3438.229, 'text': 'see, now it will push its problem upward right.', 'start': 3434.767, 'duration': 3.462}, {'end': 3446.734, 'text': 'so 65 is one level up from this, so he can give one extra black to 65 now, right so now this is only null, so you can remove it.', 'start': 3438.229, 'duration': 8.505}], 'summary': 'After rotation and removal, 70 goes downward, 68 goes upward, and 65 becomes black.', 'duration': 43.631, 'max_score': 3403.103, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ3403103.jpg'}, {'end': 3490.108, 'src': 'embed', 'start': 3460.586, 'weight': 3, 'content': [{'end': 3463.749, 'text': 'Inorder successor is what? From the right subtree find out the smallest.', 'start': 3460.586, 'duration': 3.163}, {'end': 3465.992, 'text': 'Smallest is 65.', 'start': 3463.91, 'duration': 2.082}, {'end': 3467.333, 'text': 'So here you will write 65.', 'start': 3465.992, 'duration': 1.341}, {'end': 3469.055, 'text': 'We are not deleting this.', 'start': 3467.333, 'duration': 1.722}, {'end': 3470.456, 'text': 'We are replacing the value only.', 'start': 3469.095, 'duration': 1.361}, {'end': 3475.542, 'text': 'So it would become, it would remain, it would, you know, retain its color, right? That is black.', 'start': 3470.516, 'duration': 5.026}, {'end': 3478.345, 'text': 'now 265 are there.', 'start': 3476.385, 'duration': 1.96}, {'end': 3481.846, 'text': 'so we will call recursively the delete function on this in order successor.', 'start': 3478.345, 'duration': 3.501}, {'end': 3482.966, 'text': 'so we will delete this one.', 'start': 3481.846, 'duration': 1.12}, {'end': 3483.767, 'text': 'but this is black.', 'start': 3482.966, 'duration': 0.801}, {'end': 3485.287, 'text': 'so you cannot directly delete it.', 'start': 3483.767, 'duration': 1.52}, {'end': 3490.108, 'text': 'so it would become now double black, right.', 'start': 3485.287, 'duration': 4.821}], 'summary': 'In a deletion operation, the in-order successor is found from the right subtree, and the smallest value (65) is used. the value is replaced, not deleted, and the node retains its color.', 'duration': 29.522, 'max_score': 3460.586, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ3460586.jpg'}, {'end': 3784.789, 'src': 'embed', 'start': 3759.498, 'weight': 0, 'content': [{'end': 3761.399, 'text': 'the change the color would be same.', 'start': 3759.498, 'duration': 1.901}, {'end': 3764.121, 'text': 'internal node will be retain its own color.', 'start': 3761.399, 'duration': 2.722}, {'end': 3767.143, 'text': 'right now we delete this one.', 'start': 3764.121, 'duration': 3.022}, {'end': 3767.843, 'text': 'so this is red.', 'start': 3767.143, 'duration': 0.7}, {'end': 3769.985, 'text': 'so you can simply delete it right.', 'start': 3767.843, 'duration': 2.142}, {'end': 3774.919, 'text': 'So this is how we are going to perform delete operation in red black tree.', 'start': 3771.516, 'duration': 3.403}, {'end': 3778.263, 'text': 'I hope I have discussed all the cases with the help of an example.', 'start': 3775.18, 'duration': 3.083}, {'end': 3783.748, 'text': "If you have any problem, then you can write me down in the comment box, right? So now I'll see you in the next video.", 'start': 3778.443, 'duration': 5.305}, {'end': 3784.388, 'text': 'Till then, bye-bye.', 'start': 3783.768, 'duration': 0.62}, {'end': 3784.789, 'text': 'Take care.', 'start': 3784.428, 'duration': 0.361}], 'summary': 'Explanation of red black tree delete operation with examples.', 'duration': 25.291, 'max_score': 3759.498, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ3759498.jpg'}], 'start': 3192.415, 'title': 'Red black tree deletion', 'summary': "Explains the process of deleting nodes in a red-black tree, covering the steps to handle the double black problem, the application of case 6, and the replacement of a node with its inorder successor while retaining the tree's properties.", 'chapters': [{'end': 3481.846, 'start': 3192.415, 'title': 'Red black tree deletion', 'summary': "Explains the process of deleting a node from a red-black tree, including the steps to handle the double black problem and the application of case 6, ultimately resulting in a balanced red-black tree. it also covers the replacement of a node with its inorder successor while retaining the tree's properties.", 'duration': 289.431, 'highlights': ['The chapter explains the process of deleting a node from a red-black tree, including the steps to handle the double black problem and the application of case 6, ultimately resulting in a balanced red-black tree. It covers the steps to handle the double black problem and the application of case 6, ultimately resulting in a balanced red-black tree.', "The replacement of a node with its inorder successor while retaining the tree's properties is also discussed. It discusses the replacement of a node with its inorder successor while retaining the tree's properties."]}, {'end': 3784.789, 'start': 3481.846, 'title': 'Red black tree delete operation', 'summary': 'Explains the process of deleting nodes in a red-black tree, covering cases such as replacing nodes with their children, handling double black nodes, and resolving imbalance by pushing the problem to the parent or sibling.', 'duration': 302.943, 'highlights': ['Nodes are replaced with their children while retaining the same color, simplifying the deletion process.', 'Handling double black nodes involves pushing the problem to the parent or sibling, resulting in the adjustment of colors and removal of the double black node.', 'Explanation of cases such as sibling becoming red, resolving imbalance by pushing the problem to the parent, and the process of removing double black nodes provides a comprehensive understanding of the red-black tree deletion operation.']}], 'duration': 592.374, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/w5cvkTXY0vQ/pics/w5cvkTXY0vQ3192415.jpg', 'highlights': ['The chapter explains the process of deleting a node from a red-black tree, including the steps to handle the double black problem and the application of case 6, ultimately resulting in a balanced red-black tree.', 'Nodes are replaced with their children while retaining the same color, simplifying the deletion process.', 'Handling double black nodes involves pushing the problem to the parent or sibling, resulting in the adjustment of colors and removal of the double black node.', "The replacement of a node with its inorder successor while retaining the tree's properties is also discussed."]}], 'highlights': ["Covers deletion in red-black trees, addressing the process, potential violations, handling cases of nodes with no, one, and two children, resolving double black nodes, and maintaining the tree's properties, as well as the application of case 6 for node deletion, resulting in a balanced red-black tree.", "The process of deleting nodes in a red-black tree involves replacing internal nodes in a Binary Search Tree (BST) while preserving the node's color.", 'The steps to resolve the double black (DB) problem in a Red Black tree involving color swapping, rotations, and application of specific cases. The chapter details the specific steps to resolve the double black (DB) problem in a Red Black tree, including color swapping, rotations, and application of specific cases, emphasizing the process to eliminate the DB problem.', 'The necessity to apply case 6 after case 5 in red-black tree node deletion, as indicated by the previous application of case 3 and case 5.', 'The chapter explains the process of applying case 6 to resolve the double black problem in a red black tree. The application of case 6 resolves the double black problem by pushing the extra black upwards, resulting in a balanced red black tree.', 'The chapter discusses the rotation and color swapping involved in resolving the double black problem, ensuring the red black tree remains balanced. The process involves rotating the parent towards the child with the problem and swapping colors, ensuring the tree remains balanced and the double black problem is resolved.', 'Applying case 4 to resolve the double black problem The process involves swapping the parent color and its sibling, rotating the parent in the direction of the double black, and reapplying the deletion cases.', 'Replacing the deleted node with its in-order successor and recursively calling delete When deleting a node with two children, it is replaced by its in-order successor, and the deletion process is recursively called on the successor to maintain the red-black tree properties.']}