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G-32. Dijkstra's Algorithm - Using Priority Queue - C++ and Java - Part 1

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{'title': "G-32. Dijkstra's Algorithm - Using Priority Queue - C++ and Java - Part 1", 'heatmap': [{'end': 507.591, 'start': 475.637, 'weight': 0.721}, {'end': 535.629, 'start': 516.597, 'weight': 0.763}, {'end': 941.533, 'start': 884.771, 'weight': 0.751}, {'end': 1024.617, 'start': 979.201, 'weight': 0.72}], 'summary': "Series covers dijkstra's algorithm for finding the shortest path, utilizing priority queue, adjacency list, and minimum heap data structures, with specific examples and distances, discussing its limitations for negative weight cycles and single negative weight graphs. it also explains the time complexity of e log v.", 'chapters': [{'end': 235.34, 'segs': [{'end': 44.313, 'src': 'embed', 'start': 3.387, 'weight': 0, 'content': [{'end': 4.629, 'text': 'Hey everyone, welcome back to the channel.', 'start': 3.387, 'duration': 1.242}, {'end': 6.211, 'text': 'I hope you guys are doing extremely well.', 'start': 4.649, 'duration': 1.562}, {'end': 10.597, 'text': "So we will be starting off with Dijkstra's algorithm in this video.", 'start': 6.591, 'duration': 4.006}, {'end': 14.082, 'text': 'And this is one of the most important algorithms.', 'start': 10.697, 'duration': 3.385}, {'end': 18.508, 'text': "if you're solving problems related to shortest path.", 'start': 14.082, 'duration': 4.426}, {'end': 22.131, 'text': 'okay, now, what does this algorithm state?', 'start': 19.469, 'duration': 2.662}, {'end': 24.653, 'text': 'the algorithm is very simple and straightforward.', 'start': 22.131, 'duration': 2.522}, {'end': 26.835, 'text': "it states that you'll be given a source node.", 'start': 24.653, 'duration': 2.182}, {'end': 29.738, 'text': "assume, over here i'm saying that the source node is zero.", 'start': 26.835, 'duration': 2.903}, {'end': 31.259, 'text': 'what does the source node means?', 'start': 29.738, 'duration': 1.521}, {'end': 32.34, 'text': 'the starting point.', 'start': 31.259, 'duration': 1.081}, {'end': 34.161, 'text': "this is where you're going to start.", 'start': 32.34, 'duration': 1.821}, {'end': 37.484, 'text': "so i'll be like okay, the source node is zero.", 'start': 34.161, 'duration': 3.323}, {'end': 39.426, 'text': 'in order to reach zero.', 'start': 37.484, 'duration': 1.942}, {'end': 44.313, 'text': "what will be the distance that you'll take if like zero, from zero to zero?", 'start': 39.426, 'duration': 4.887}], 'summary': "Introducing dijkstra's algorithm, a key algorithm for solving shortest path problems, starting from source node zero.", 'duration': 40.926, 'max_score': 3.387, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l43387.jpg'}, {'end': 121.943, 'src': 'embed', 'start': 71.365, 'weight': 2, 'content': [{'end': 72.506, 'text': 'There can be multiple paths.', 'start': 71.365, 'duration': 1.141}, {'end': 77.13, 'text': 'One of the paths can be this which travels via 2.', 'start': 73.207, 'duration': 3.923}, {'end': 80.152, 'text': 'And if it travels via 2, there is a 4 and there is a 2 line.', 'start': 77.13, 'duration': 3.022}, {'end': 84.744, 'text': 'And that will give a total path weight of 6.', 'start': 80.833, 'duration': 3.911}, {'end': 91.569, 'text': "right. there can be other paths as well, where you decide that you're going to take an entire journey of the graph and then come,", 'start': 84.744, 'duration': 6.825}, {'end': 96.333, 'text': "that'll be more four plus three plus two plus three plus one plus two.", 'start': 91.569, 'duration': 4.764}, {'end': 100.056, 'text': 'but what i am concerned about is to find the shortest one.', 'start': 96.333, 'duration': 3.723}, {'end': 101.838, 'text': 'so can i say the shortest one is four.', 'start': 100.056, 'duration': 1.782}, {'end': 113.975, 'text': 'right, and if this would have been something like one, can i say the shortest would have been then this part, which is one plus two, three, right.', 'start': 102.725, 'duration': 11.25}, {'end': 115.877, 'text': 'so the task is very simple.', 'start': 113.975, 'duration': 1.902}, {'end': 121.943, 'text': 'given a source node, given a source node, from that source node to every every node.', 'start': 115.877, 'duration': 6.066}], 'summary': 'Finding the shortest path in a graph with source node and total path weight.', 'duration': 50.578, 'max_score': 71.365, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l471365.jpg'}, {'end': 189.161, 'src': 'embed', 'start': 142.871, 'weight': 3, 'content': [{'end': 148.839, 'text': 'I should know what distance will I take as the shortest one, because I need the shortest one.', 'start': 142.871, 'duration': 5.968}, {'end': 150.901, 'text': 'That is what you need to tell me.', 'start': 149.279, 'duration': 1.622}, {'end': 155.007, 'text': "And that is what the Dijkstra's algorithm will help us to find.", 'start': 151.182, 'duration': 3.825}, {'end': 159.36, 'text': "Now, Dijkstra's algorithm can be implemented by two methods.", 'start': 155.839, 'duration': 3.521}, {'end': 166.583, 'text': 'One of them is actually three, like you can go across to three, but one is priority queue.', 'start': 160.101, 'duration': 6.482}, {'end': 168.383, 'text': 'The other one is the set.', 'start': 167.423, 'duration': 0.96}, {'end': 170.424, 'text': 'So you can use the data structure priority queue.', 'start': 168.644, 'duration': 1.78}, {'end': 173.565, 'text': 'You can use the data structure set as well.', 'start': 171.244, 'duration': 2.321}, {'end': 180.992, 'text': 'You can also use the queue, which is the third one, but this will take more time.', 'start': 173.945, 'duration': 7.047}, {'end': 183.274, 'text': 'priority queue also takes a bit of time.', 'start': 180.992, 'duration': 2.282}, {'end': 184.916, 'text': 'set is the fastest.', 'start': 183.274, 'duration': 1.642}, {'end': 189.161, 'text': "so in this video i'll be telling you the priority queue approach.", 'start': 184.916, 'duration': 4.245}], 'summary': "Dijkstra's algorithm helps find shortest distance using priority queue and set as fastest.", 'duration': 46.29, 'max_score': 142.871, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4142871.jpg'}], 'start': 3.387, 'title': "Dijkstra's algorithm and data structures", 'summary': "Explains dijkstra's algorithm for finding the shortest path and covers the process of finding the shortest distance using dijkstra's algorithm, along with the usage of priority queue, set, and queue data structures.", 'chapters': [{'end': 96.333, 'start': 3.387, 'title': "Dijkstra's algorithm explained", 'summary': "Explains dijkstra's algorithm for finding the shortest path, highlighting the importance of the algorithm and the basic principles behind it, including the concept of source nodes and calculating path weights based on edge weights.", 'duration': 92.946, 'highlights': ['The algorithm emphasizes the importance of source nodes in determining the starting point for calculating distances and path weights.', 'It explains the concept of calculating path weights based on edge weights, demonstrating how different paths can result in varying total path weights.', "The chapter introduces Dijkstra's algorithm as a fundamental tool for solving problems related to finding the shortest path in a graph."]}, {'end': 168.383, 'start': 96.333, 'title': "Finding shortest distance with dijkstra's algorithm", 'summary': "Explores the process of finding the shortest distance using dijkstra's algorithm, which can be implemented through priority queue or set, in order to find the distance from a source node to every other node in a given graph.", 'duration': 72.05, 'highlights': ["Dijkstra's algorithm can be implemented through priority queue or set, offering different methods for finding the shortest distance.", 'The task involves finding the shortest distance from a source node to every other node in a given graph.', 'The algorithm aims to determine the shortest distance from the source node to all other nodes, such as from zero to one, two, three, four, and five.']}, {'end': 235.34, 'start': 168.644, 'title': 'Data structures for algorithm explanation', 'summary': 'Covers the usage of priority queue, set, and queue data structures in algorithm explanation, emphasizing the set as the fastest option and highlighting the upcoming coverage of priority queue approach and the importance of watching all videos for clear understanding.', 'duration': 66.696, 'highlights': ['The set data structure is the fastest among priority queue, set, and queue.', 'The upcoming video will cover the priority queue approach for algorithm explanation.', 'Emphasizing the importance of watching all videos for clear understanding of the algorithm concepts.']}], 'duration': 231.953, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l43387.jpg', 'highlights': ["The chapter introduces Dijkstra's algorithm as a fundamental tool for solving problems related to finding the shortest path in a graph.", 'The algorithm emphasizes the importance of source nodes in determining the starting point for calculating distances and path weights.', 'It explains the concept of calculating path weights based on edge weights, demonstrating how different paths can result in varying total path weights.', "Dijkstra's algorithm can be implemented through priority queue or set, offering different methods for finding the shortest distance.", 'The set data structure is the fastest among priority queue, set, and queue.', 'The task involves finding the shortest distance from a source node to every other node in a given graph.']}, {'end': 514.456, 'segs': [{'end': 263.434, 'src': 'embed', 'start': 235.34, 'weight': 0, 'content': [{'end': 242.546, 'text': "yes, we will be solving a bunch of problems, and at the end of the day you can solve any problem of dexter's algorithm that comes in your interviews.", 'start': 235.34, 'duration': 7.206}, {'end': 246.387, 'text': 'we will be implementing the dextrose algorithm using the priority queue,', 'start': 243.106, 'duration': 3.281}, {'end': 252.249, 'text': 'so the graph can be represented in an adjacency list and this time we will be storing pairs.', 'start': 246.387, 'duration': 5.862}, {'end': 256.531, 'text': "okay. so something like if zero zero's adjacents are one and two.", 'start': 252.249, 'duration': 4.282}, {'end': 263.434, 'text': 'so i store something like one, comma four, which is basically the node and the weight, The node and the weight of the edge.', 'start': 256.531, 'duration': 6.903}], 'summary': "Solve problems using dijkstra's algorithm, implementing it with a priority queue and storing graph as an adjacency list with pairs.", 'duration': 28.094, 'max_score': 235.34, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4235340.jpg'}, {'end': 345.252, 'src': 'embed', 'start': 303.82, 'weight': 1, 'content': [{'end': 307.462, 'text': 'remember this what is a minimum heap data structure?', 'start': 303.82, 'duration': 3.642}, {'end': 316.869, 'text': "so if you're storing anything in terms of distance and node, the shorter distance i repeat, the shorter distance will be at the top, right,", 'start': 307.462, 'duration': 9.407}, {'end': 323.133, 'text': 'and if there are equal shorter distance, the earlier node or the shorter node will be at the top.', 'start': 316.869, 'duration': 6.264}, {'end': 332.36, 'text': "you'll understand as we move, we will always have a distance array which will keep track of how much distance are we taking in a path?", 'start': 323.133, 'duration': 9.227}, {'end': 337.645, 'text': 'okay, and we will have the source node, And source node can be 0, can be 1, can be 2, can be anything.', 'start': 332.36, 'duration': 5.285}, {'end': 340.327, 'text': 'So, as of now, the source node is 0.', 'start': 338.045, 'duration': 2.282}, {'end': 345.252, 'text': 'So, the initial, the first step of the algorithm is very, very simple.', 'start': 340.327, 'duration': 4.925}], 'summary': 'Minimum heap stores distances and nodes, ensuring shorter distances are at the top and earlier nodes break ties. algorithm starts with source node 0.', 'duration': 41.432, 'max_score': 303.82, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4303820.jpg'}, {'end': 422.099, 'src': 'embed', 'start': 394.679, 'weight': 4, 'content': [{'end': 398.063, 'text': 'zero is like i can go to two and i can go to one.', 'start': 394.679, 'duration': 3.384}, {'end': 403.312, 'text': 'there are two, two ways in which you can proceed from zero.', 'start': 398.063, 'duration': 5.249}, {'end': 404.873, 'text': 'right, and how will you figure this?', 'start': 403.312, 'duration': 1.561}, {'end': 409.815, 'text': 'one and two, if you remember, adjacency list will tell you about that, right.', 'start': 404.873, 'duration': 4.942}, {'end': 411.895, 'text': 'so just figure the one and two from there.', 'start': 409.815, 'duration': 2.08}, {'end': 415.557, 'text': 'so i can actually move to something like node one.', 'start': 411.895, 'duration': 3.662}, {'end': 418.258, 'text': 'and how much distance will i take if this is taking plus four?', 'start': 415.557, 'duration': 2.701}, {'end': 419.858, 'text': 'this is going to take four.', 'start': 418.258, 'duration': 1.6}, {'end': 422.099, 'text': 'why? because previously i took zero.', 'start': 419.858, 'duration': 2.241}], 'summary': 'Two ways from node zero: to node one and node two, with a distance of four to node one.', 'duration': 27.42, 'max_score': 394.679, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4394679.jpg'}, {'end': 473.616, 'src': 'embed', 'start': 444.816, 'weight': 3, 'content': [{'end': 448.399, 'text': 'so go and just replace it with a node with a distance four.', 'start': 444.816, 'duration': 3.583}, {'end': 450.4, 'text': 'take the four and the node one.', 'start': 448.399, 'duration': 2.001}, {'end': 452.102, 'text': 'put it into the priority queue.', 'start': 450.4, 'duration': 1.702}, {'end': 457.886, 'text': 'so repeat, i repeat Every time you get a distance which is better than the previous distance?', 'start': 452.102, 'duration': 5.784}, {'end': 465.05, 'text': 'That means you discovered a new path and you take that distance and put it into the priority queue always.', 'start': 458.306, 'duration': 6.744}, {'end': 469.853, 'text': 'Okay What is the next thing? You can always go to the node 2, which is the next adjacent.', 'start': 465.45, 'duration': 4.403}, {'end': 473.616, 'text': 'If you carefully see, node 2 is the new adjacent, which you can go at a 4.', 'start': 469.873, 'duration': 3.743}], 'summary': 'Replace node with distance 4, prioritize better distances, move to node 2 at distance 4.', 'duration': 28.8, 'max_score': 444.816, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4444816.jpg'}, {'end': 507.591, 'src': 'heatmap', 'start': 475.637, 'weight': 0.721, 'content': [{'end': 477.698, 'text': 'So the new distance taken will be another 4.', 'start': 475.637, 'duration': 2.061}, {'end': 480, 'text': 'And 2 previously was infinite, 4.', 'start': 477.698, 'duration': 2.302}, {'end': 483.062, 'text': "So 4, 2 is what I'll put into the priority queue.", 'start': 480, 'duration': 3.062}, {'end': 487.063, 'text': 'first iteration done similar to vfs.', 'start': 483.502, 'duration': 3.561}, {'end': 491.545, 'text': 'next, who will be at the top of the minimum heap?', 'start': 487.063, 'duration': 4.482}, {'end': 495.286, 'text': 'can i see four comma one will be at the top of the minimum heap.', 'start': 491.545, 'duration': 3.741}, {'end': 500.248, 'text': 'i, four is equal in both of them, but one is smaller minimum heap.', 'start': 495.286, 'duration': 4.962}, {'end': 501.228, 'text': 'so four comma one.', 'start': 500.248, 'duration': 0.98}, {'end': 507.591, 'text': "yes, so i'm saying i'm taking a distance of one in order to reach the node.", 'start': 501.228, 'duration': 6.363}], 'summary': 'Updated distance is 4, priority queue iteration, minimum heap top is 4,1.', 'duration': 31.954, 'max_score': 475.637, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4475637.jpg'}], 'start': 235.34, 'title': "Dijkstra's algorithm", 'summary': "Covers implementing and explaining dijkstra's algorithm using a priority queue, adjacency list, and minimum heap data structure to solve interview problems. it also explains the process of finding the shortest path, with specific examples and distances.", 'chapters': [{'end': 323.133, 'start': 235.34, 'title': "Dijkstra's algorithm implementation", 'summary': "Covers implementing dijkstra's algorithm using a priority queue and storing the graph in an adjacency list with pairs, enabling the solving of any related interview problems, and utilizing a minimum heap data structure to store distances and nodes.", 'duration': 87.793, 'highlights': ["The chapter emphasizes implementing Dijkstra's algorithm using a priority queue and storing the graph in an adjacency list with pairs, enabling the solving of any related interview problems.", 'Utilizing a minimum heap data structure to store distances and nodes ensures that the shorter distance will be at the top and, in case of equal shorter distances, the earlier node or the shorter node will be at the top.', 'The adjacency list stores pairs of nodes and weights, facilitating the determination of adjacent nodes and their respective weights, such as determining the adjacent nodes of 4 as 2 and 5 with weights 1 and 3 respectively.']}, {'end': 394.679, 'start': 323.133, 'title': "Dijkstra's algorithm explanation", 'summary': "Explains dijkstra's algorithm for finding the shortest path in a graph, using a priority queue to track distances from the source node and iterating through the queue to update distances and explore neighboring nodes.", 'duration': 71.546, 'highlights': ["Dijkstra's algorithm uses a distance array to track the distance taken in a path and a priority queue to iterate through the nodes, similar to BFS. The algorithm utilizes a distance array to keep track of path distances and employs a priority queue for node iteration, resembling BFS.", 'The algorithm begins by setting the source node as 0 and initializing the distance array with a distance of 0 for the source node. The initial step involves setting the source node as 0 and adding a distance of 0 for the source node to the distance array.', 'Nodes are iterated through using the priority queue, updating distances and exploring neighboring nodes to find the shortest path. The algorithm iterates through nodes using the priority queue, updating distances and exploring neighboring nodes to determine the shortest path.']}, {'end': 514.456, 'start': 394.679, 'title': 'Shortest path algorithm explanation', 'summary': 'Explains the process of finding the shortest path using the example of reaching nodes 1 and 2 from node 0, where the distance to reach node 1 is 4 and to reach node 2 is also 4.', 'duration': 119.777, 'highlights': ['The process involves using an adjacency list to determine the possible paths from node 0 to nodes 1 and 2, with the distance to reach node 1 being 4 and node 2 also being 4.', 'The distances to reach nodes are updated as better paths are discovered, and the new distances are added to the priority queue, following a similar process to BFS.', 'The top of the minimum heap shows the next node and its distance, with node 1 being reachable with a distance of 4.']}], 'duration': 279.116, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4235340.jpg', 'highlights': ["The chapter emphasizes implementing Dijkstra's algorithm using a priority queue and storing the graph in an adjacency list with pairs, enabling the solving of any related interview problems.", 'Utilizing a minimum heap data structure to store distances and nodes ensures that the shorter distance will be at the top and, in case of equal shorter distances, the earlier node or the shorter node will be at the top.', 'The algorithm begins by setting the source node as 0 and initializing the distance array with a distance of 0 for the source node. The initial step involves setting the source node as 0 and adding a distance of 0 for the source node to the distance array.', 'Nodes are iterated through using the priority queue, updating distances and exploring neighboring nodes to find the shortest path. The algorithm iterates through nodes using the priority queue, updating distances and exploring neighboring nodes to determine the shortest path.', 'The process involves using an adjacency list to determine the possible paths from node 0 to nodes 1 and 2, with the distance to reach node 1 being 4 and node 2 also being 4.', 'The distances to reach nodes are updated as better paths are discovered, and the new distances are added to the priority queue, following a similar process to BFS.']}, {'end': 679.477, 'segs': [{'end': 541.487, 'src': 'heatmap', 'start': 516.597, 'weight': 0, 'content': [{'end': 519.739, 'text': 'it will say you can go to 0 and you can go to 2.', 'start': 516.597, 'duration': 3.142}, {'end': 520.679, 'text': 'correct, so go to 0.', 'start': 519.739, 'duration': 0.94}, {'end': 528.084, 'text': 'so you can go to 0 and that will take a distance of 4, which will make it a total distance of 8.', 'start': 520.679, 'duration': 7.405}, {'end': 529.565, 'text': 'will you consider this?', 'start': 528.084, 'duration': 1.481}, {'end': 534.448, 'text': 'no, why 0 is already reachable at 0 distance not to be considered.', 'start': 529.565, 'duration': 4.883}, {'end': 535.629, 'text': 'where can you go?', 'start': 534.448, 'duration': 1.181}, {'end': 541.487, 'text': 'you can also go to the node 2 by taking a distance of 2..', 'start': 535.629, 'duration': 5.858}], 'summary': 'Nodes 0 and 2 are reachable, with distances of 0 and 2 respectively.', 'duration': 27.031, 'max_score': 516.597, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4516597.jpg'}, {'end': 687.503, 'src': 'embed', 'start': 655.957, 'weight': 1, 'content': [{'end': 658.779, 'text': 'You got three guys that went into the priority queue.', 'start': 655.957, 'duration': 2.822}, {'end': 660.82, 'text': 'You got two guys that got discarded.', 'start': 658.959, 'duration': 1.861}, {'end': 662.361, 'text': 'So just omit this off.', 'start': 660.84, 'duration': 1.521}, {'end': 668.625, 'text': "What's the next step? Who is the topmost element in the priority queue or minimum heap? Get it out.", 'start': 663.642, 'duration': 4.983}, {'end': 671.226, 'text': "There's 5, there's 7, there's 10.", 'start': 669.065, 'duration': 2.161}, {'end': 672.067, 'text': 'The 5 comma will.', 'start': 671.226, 'duration': 0.841}, {'end': 674.453, 'text': '5, 4 will be at the top.', 'start': 673.252, 'duration': 1.201}, {'end': 678.156, 'text': 'So 5 of a node 4.', 'start': 674.473, 'duration': 3.683}, {'end': 679.477, 'text': '5 at a node 4.', 'start': 678.156, 'duration': 1.321}, {'end': 687.503, 'text': 'Where can node 4 go? It can go to node 2 and it can also go to node 5 you can observe.', 'start': 679.477, 'duration': 8.026}], 'summary': 'Three guys in priority queue, 2 discarded. 5 and 7 are top elements.', 'duration': 31.546, 'max_score': 655.957, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4655957.jpg'}], 'start': 514.456, 'title': "Dijkstra's algorithm implementation", 'summary': "Discusses the implementation of dijkstra's algorithm, covering the analysis of adjacency lists, determination of reachable nodes, consideration of distances, and utilization of priority queues to optimize path finding.", 'chapters': [{'end': 679.477, 'start': 514.456, 'title': "Dijkstra's algorithm implementation", 'summary': "Discusses the implementation of dijkstra's algorithm, where the process involves analyzing adjacency lists, determining reachable nodes, considering distances, and utilizing priority queues to optimize the path finding process.", 'duration': 165.021, 'highlights': ['Determining reachable nodes and considering distances, such as reaching node 2 from node 1 at a distance of 2, and analyzing the adjacency list to identify better alternatives.', 'Utilizing priority queues to store and retrieve nodes, with 3 nodes entering the priority queue while 2 are discarded, showcasing the optimization of the path finding process.', 'Analyzing adjacency lists to determine reachable nodes and their corresponding distances, such as finding the shortest path to node 4 with a total distance of 5, and prioritizing nodes based on their distances for efficient path finding.']}], 'duration': 165.021, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4514456.jpg', 'highlights': ['Analyzing adjacency lists to determine reachable nodes and their corresponding distances, such as finding the shortest path to node 4 with a total distance of 5, and prioritizing nodes based on their distances for efficient path finding.', 'Utilizing priority queues to store and retrieve nodes, with 3 nodes entering the priority queue while 2 are discarded, showcasing the optimization of the path finding process.', 'Determining reachable nodes and considering distances, such as reaching node 2 from node 1 at a distance of 2, and analyzing the adjacency list to identify better alternatives.']}, {'end': 867.976, 'segs': [{'end': 713.641, 'src': 'embed', 'start': 679.477, 'weight': 0, 'content': [{'end': 687.503, 'text': 'Where can node 4 go? It can go to node 2 and it can also go to node 5 you can observe.', 'start': 679.477, 'duration': 8.026}, {'end': 688.984, 'text': 'From 4 you can go to 2.', 'start': 687.923, 'duration': 1.061}, {'end': 691.385, 'text': 'You can go to 5.', 'start': 688.984, 'duration': 2.401}, {'end': 693.167, 'text': 'Easily figured out by the adjacency list.', 'start': 691.385, 'duration': 1.782}, {'end': 698.631, 'text': 'So from 4 to 2, distance of 1, 6 not to be considered.', 'start': 693.607, 'duration': 5.024}, {'end': 702.738, 'text': 'From 4 to 5, 3 distance of 8.', 'start': 699.151, 'duration': 3.587}, {'end': 704.438, 'text': 'Will you consider this? Yes.', 'start': 702.738, 'duration': 1.7}, {'end': 706.299, 'text': 'Because you got a better one.', 'start': 705.279, 'duration': 1.02}, {'end': 710.901, 'text': 'So, 8 comma 5 will be considered.', 'start': 706.799, 'duration': 4.102}, {'end': 713.641, 'text': '8 comma 5 will be considered.', 'start': 710.921, 'duration': 2.72}], 'summary': 'Node 4 can go to nodes 2 and 5, with distances of 1 and 8 respectively, based on the adjacency list.', 'duration': 34.164, 'max_score': 679.477, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4679477.jpg'}, {'end': 764.708, 'src': 'embed', 'start': 737.708, 'weight': 2, 'content': [{'end': 744.491, 'text': 'So it will try to go to node 2, take a distance of 3, make a total distance of 10, which is not to be considered.', 'start': 737.708, 'duration': 6.783}, {'end': 752.553, 'text': 'It can go to 5 by taking a distance of 2, which will make the total distance of 9 not to be considered because we have 8.', 'start': 744.951, 'duration': 7.602}, {'end': 753.554, 'text': 'We have 8.', 'start': 752.553, 'duration': 1.001}, {'end': 755.975, 'text': 'Got it? So no new results.', 'start': 753.554, 'duration': 2.421}, {'end': 757.015, 'text': 'How about this?', 'start': 756.595, 'duration': 0.42}, {'end': 762.306, 'text': "next we'll take the next element out.", 'start': 759.224, 'duration': 3.082}, {'end': 764.708, 'text': 'uh, which is so eight, comma five is done by the way.', 'start': 762.306, 'duration': 2.402}], 'summary': 'Total distance of 8, considering distances to nodes 2 and 5.', 'duration': 27, 'max_score': 737.708, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4737708.jpg'}, {'end': 867.976, 'src': 'embed', 'start': 822.45, 'weight': 3, 'content': [{'end': 824.212, 'text': "So apparently, we're done.", 'start': 822.45, 'duration': 1.762}, {'end': 832.161, 'text': "apparently we're done and once you're done you will see this distance array stores the minimum.", 'start': 825.157, 'duration': 7.004}, {'end': 836.944, 'text': 'if you see till five, it is saying eight, which is very much sensible.', 'start': 832.161, 'duration': 4.783}, {'end': 845.17, 'text': 'why? because if you carefully observe yes, if you carefully observe from zero you can go to two, which will take you a distance of four.', 'start': 836.944, 'duration': 8.226}, {'end': 847.191, 'text': 'then you can go to one, then you can go here.', 'start': 845.17, 'duration': 2.021}, {'end': 852.452, 'text': 'so in this way you can actually take four plus five plus three, which is eight.', 'start': 847.691, 'duration': 4.761}, {'end': 853.492, 'text': 'all the other parts.', 'start': 852.452, 'duration': 1.04}, {'end': 859.094, 'text': "if, even if you try to take this, it's gonna cost you nine, so all the other parts will cost you more.", 'start': 853.492, 'duration': 5.602}, {'end': 863.215, 'text': 'so you got your minimum distance stored in your distance array.', 'start': 859.094, 'duration': 4.121}, {'end': 867.976, 'text': 'if you return this distance array, this is what your particular answer will be.', 'start': 863.215, 'duration': 4.761}], 'summary': 'The algorithm found the minimum distance of 8, based on careful observation and analysis.', 'duration': 45.526, 'max_score': 822.45, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4822450.jpg'}], 'start': 679.477, 'title': 'Pathfinding and distance calculation', 'summary': 'Discusses pathfinding algorithms for finding the shortest path, considering distances and nodes, and identifies best routes. it also explains minimum distance calculation using a distance array, with the minimum distance being 8, obtained through specific routes.', 'chapters': [{'end': 821.488, 'start': 679.477, 'title': 'Pathfinding algorithm analysis', 'summary': 'Discusses the process of finding the shortest path using a pathfinding algorithm, considering distances and nodes, and identifies the best possible routes based on the data provided.', 'duration': 142.011, 'highlights': ['The algorithm evaluates the possible routes from node 4 to nodes 2 and 5, considering the distances and identifying the best option based on the adjacency list.', 'The process continues with the analysis of the next nodes, such as 7 and 8, examining their possible routes and determining the best options based on the given distances.', 'Detailed evaluation of the potential routes from node 5 to other nodes, considering the distances and identifying the best possible paths based on the given data.']}, {'end': 867.976, 'start': 822.45, 'title': 'Minimum distance calculation', 'summary': 'Explains the process of calculating minimum distance using a distance array, with the minimum distance being 8, obtained by going through specific routes, and returning the distance array as the final answer.', 'duration': 45.526, 'highlights': ['The minimum distance stored in the distance array is 8, achieved by carefully observing and calculating specific routes.', 'The distance array accurately reflects the minimum distance, as all other routes would cost more, such as 9.']}], 'duration': 188.499, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4679477.jpg', 'highlights': ['The algorithm evaluates the possible routes from node 4 to nodes 2 and 5, considering the distances and identifying the best option based on the adjacency list.', 'Detailed evaluation of the potential routes from node 5 to other nodes, considering the distances and identifying the best possible paths based on the given data.', 'The process continues with the analysis of the next nodes, such as 7 and 8, examining their possible routes and determining the best options based on the given distances.', 'The minimum distance stored in the distance array is 8, achieved by carefully observing and calculating specific routes.', 'The distance array accurately reflects the minimum distance, as all other routes would cost more, such as 9.']}, {'end': 1054.26, 'segs': [{'end': 946.062, 'src': 'heatmap', 'start': 869.278, 'weight': 0, 'content': [{'end': 872.801, 'text': 'guys, i hope you have understood the algorithmic explanation of dextrose algorithm.', 'start': 869.278, 'duration': 3.523}, {'end': 874.022, 'text': "now it's time to code it up.", 'start': 872.801, 'duration': 1.221}, {'end': 880.547, 'text': "i'll be coding the c plus plus on the right and you can figure out the exact similar java code on the left if you have syntax issues.", 'start': 874.022, 'duration': 6.525}, {'end': 884.771, 'text': 'so it states the graph does not contain any negative weight cycle.', 'start': 880.547, 'duration': 4.224}, {'end': 888.554, 'text': 'remember, dextrose is not applicable to graphs with negative weight cycle.', 'start': 884.771, 'duration': 3.783}, {'end': 891.816, 'text': "i'll be discussing that right after coding this up.", 'start': 888.554, 'duration': 3.262}, {'end': 896.433, 'text': 'okay, so if you carefully see, we are given the uh number of nodes.', 'start': 891.816, 'duration': 4.617}, {'end': 899.234, 'text': 'we are also given the adjacency list and the source.', 'start': 896.433, 'duration': 2.801}, {'end': 902.475, 'text': "so usually it's a list of int.", 'start': 899.234, 'duration': 3.241}, {'end': 903.676, 'text': 'so we are given a vector of int.', 'start': 902.475, 'duration': 1.201}, {'end': 908.177, 'text': 'why? because we are storing a node that is a node and the weight as well.', 'start': 903.676, 'duration': 4.501}, {'end': 912.419, 'text': 'so instead of a pair, we are storing it in terms of a list.', 'start': 908.177, 'duration': 4.242}, {'end': 914.86, 'text': 'okay, so what is the thing that we took?', 'start': 912.419, 'duration': 2.441}, {'end': 916.581, 'text': 'we took a minimum heap.', 'start': 914.86, 'duration': 1.721}, {'end': 919.562, 'text': 'this is how, in c plus plus, you declare a minimum heap.', 'start': 916.581, 'duration': 2.981}, {'end': 921.023, 'text': 'then what is the next thing we did?', 'start': 919.562, 'duration': 1.461}, {'end': 928.706, 'text': 'we always, uh, had a distance array of same size done and everything is, if you remember, marked as infinite.', 'start': 921.023, 'duration': 7.683}, {'end': 932.148, 'text': 'so make sure you mark everything as infinite.', 'start': 928.706, 'duration': 3.442}, {'end': 935.99, 'text': 'in our case, we can mark infinite as a very, very big value.', 'start': 932.148, 'duration': 3.842}, {'end': 938.311, 'text': 'now, what is the initial configuration?', 'start': 935.99, 'duration': 2.321}, {'end': 941.533, 'text': 'we know that the source from source to source it is always zero.', 'start': 938.311, 'duration': 3.222}, {'end': 946.062, 'text': 'So we say, okay, from source to source, it is always zero.', 'start': 942.54, 'duration': 3.522}], 'summary': 'Explaining dijkstra algorithm, coding in c++, using adjacency list and minimum heap, marking distances as infinite.', 'duration': 76.784, 'max_score': 869.278, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4869278.jpg'}, {'end': 975.557, 'src': 'embed', 'start': 935.99, 'weight': 3, 'content': [{'end': 938.311, 'text': 'now, what is the initial configuration?', 'start': 935.99, 'duration': 2.321}, {'end': 941.533, 'text': 'we know that the source from source to source it is always zero.', 'start': 938.311, 'duration': 3.222}, {'end': 946.062, 'text': 'So we say, okay, from source to source, it is always zero.', 'start': 942.54, 'duration': 3.522}, {'end': 947.182, 'text': 'So we will do this.', 'start': 946.402, 'duration': 0.78}, {'end': 950.044, 'text': "I'll say distance comma source is what the priority queue will have.", 'start': 947.583, 'duration': 2.461}, {'end': 952.045, 'text': 'Now we will iterate in the priority queue.', 'start': 950.504, 'duration': 1.541}, {'end': 952.765, 'text': 'Pretty simple.', 'start': 952.265, 'duration': 0.5}, {'end': 956.867, 'text': 'And we will be iterating in the priority queue.', 'start': 954.046, 'duration': 2.821}, {'end': 960.069, 'text': "And what I'll say is, I'll get the top element.", 'start': 956.967, 'duration': 3.102}, {'end': 962.49, 'text': "And in the top element, first I'll get the distance.", 'start': 960.569, 'duration': 1.921}, {'end': 975.557, 'text': "right what it has taken till now and that will be stored at pq dot, top dot first, and then i'll take the node which will be pq dot, top dot second.", 'start': 963.783, 'duration': 11.774}], 'summary': 'Initial configuration sets source to zero. iterates priority queue for distance and node.', 'duration': 39.567, 'max_score': 935.99, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4935990.jpg'}, {'end': 1024.617, 'src': 'heatmap', 'start': 979.201, 'weight': 0.72, 'content': [{'end': 983.302, 'text': "perfect, now it's time to travel for the adjacent node.", 'start': 979.201, 'duration': 4.101}, {'end': 984.723, 'text': "so this is how i'll travel.", 'start': 983.302, 'duration': 1.421}, {'end': 992.685, 'text': 'now i know this auto of it this time is not an integer because it is storing two elements in form of a vector or a list.', 'start': 984.723, 'duration': 7.962}, {'end': 998.667, 'text': "so i'll be like okay, let me get the new edge weight and it will be very simple.", 'start': 992.685, 'duration': 5.982}, {'end': 1006.273, 'text': "it of one because it's stored at the second place and can i see the adjacent node will be id of zero.", 'start': 998.667, 'duration': 7.606}, {'end': 1009.574, 'text': 'make sure in interviews you name the variables like this.', 'start': 1006.273, 'duration': 3.301}, {'end': 1014.977, 'text': "now can i say if, if the current is this like, they'll reach the node.", 'start': 1009.574, 'duration': 5.403}, {'end': 1024.617, 'text': "you have taken this and now you'll travel for the adjacent weight if that's lesser than what you will require,", 'start': 1014.977, 'duration': 9.64}], 'summary': 'Traverse adjacent nodes, update edge weights, and check conditions for interview preparation.', 'duration': 45.416, 'max_score': 979.201, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4979201.jpg'}], 'start': 869.278, 'title': 'Graph algorithms', 'summary': "Covers dextrose algorithm for graphs, unsuitable for negative weight cycles, and provides c++ coding demo. it also explains dijkstra's algorithm for finding shortest paths, using priority queue, and initializing distances.", 'chapters': [{'end': 912.419, 'start': 869.278, 'title': 'Dextrose algorithm coding explanation', 'summary': 'Explains the dextrose algorithm for graphs, stating that it is not applicable to graphs with negative weight cycles, and provides a coding demonstration in c++.', 'duration': 43.141, 'highlights': ['The Dextrose algorithm is not applicable to graphs with negative weight cycles.', 'The chapter provides a coding demonstration in C++ for the Dextrose algorithm.', 'The algorithm requires the number of nodes, adjacency list, and source as inputs, and uses a vector to store nodes and their weights.']}, {'end': 1054.26, 'start': 912.419, 'title': "Dijkstra's algorithm explained", 'summary': "Explains the dijkstra's algorithm for finding the shortest path in a graph, emphasizing the use of priority queue and updating distances, with an initial configuration of marking all distances as infinite and starting from the source with a distance of 0.", 'duration': 141.841, 'highlights': ["The chapter explains the Dijkstra's algorithm for finding the shortest path in a graph. It provides an overview of the topic and sets the context for the subsequent details.", 'Emphasizing the use of priority queue and updating distances. It highlights the key data structure and the crucial step of updating distances to find the shortest path efficiently.', "Starting from the source with a distance of 0. It underlines the initial configuration for the algorithm, setting the source's distance as 0 to initiate the process."]}], 'duration': 184.982, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l4869278.jpg', 'highlights': ["The chapter explains Dijkstra's algorithm for finding the shortest path in a graph.", 'The Dextrose algorithm is not applicable to graphs with negative weight cycles.', 'The chapter provides a coding demonstration in C++ for the Dextrose algorithm.', 'Emphasizing the use of priority queue and updating distances.', 'Starting from the source with a distance of 0.']}, {'end': 1353.016, 'segs': [{'end': 1100.693, 'src': 'embed', 'start': 1073.811, 'weight': 0, 'content': [{'end': 1079.055, 'text': "But in this video, I'll be telling you why a Dijkstra's algorithm will not work for negative weight cycle.", 'start': 1073.811, 'duration': 5.244}, {'end': 1080.376, 'text': "So let's go and understand that.", 'start': 1079.195, 'duration': 1.181}, {'end': 1087.77, 'text': "So, Dijkstra doesn't work in any of the graphs that has a single negative weight.", 'start': 1081.448, 'duration': 6.322}, {'end': 1093.551, 'text': "It also doesn't work if there's a cycle which ends up having a negative weight.", 'start': 1088.39, 'duration': 5.161}, {'end': 1095.572, 'text': 'So, no negative cycles as well.', 'start': 1093.691, 'duration': 1.881}, {'end': 1100.693, 'text': 'So, the whole reason lies around negative weight.', 'start': 1096.072, 'duration': 4.621}], 'summary': "Dijkstra's algorithm fails for negative weight cycles in graphs.", 'duration': 26.882, 'max_score': 1073.811, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l41073811.jpg'}, {'end': 1282.384, 'src': 'embed', 'start': 1253.309, 'weight': 4, 'content': [{'end': 1255.17, 'text': "that's how the paths are computed right.", 'start': 1253.309, 'duration': 1.861}, {'end': 1262.986, 'text': "that is why The Dijkstra's algorithm is only applicable for graphs with positive weights.", 'start': 1255.17, 'duration': 7.816}, {'end': 1273.755, 'text': "So what are the time complexity of this particular algorithm? It's nothing but E log V, where E is the total number of edges in the entire graph.", 'start': 1263.747, 'duration': 10.008}, {'end': 1275.957, 'text': 'V is the number of nodes.', 'start': 1274.235, 'duration': 1.722}, {'end': 1282.384, 'text': "there is a very, very critical, uh derivation of this, which i'll be doing in the next video.", 'start': 1276.317, 'duration': 6.067}], 'summary': "Dijkstra's algorithm applicable for graphs with positive weights. time complexity: e log v.", 'duration': 29.075, 'max_score': 1253.309, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l41253309.jpg'}], 'start': 1054.26, 'title': "Limitations of dijkstra's algorithm", 'summary': "Discusses the limitations of dijkstra's algorithm for negative weight cycles, single negative weight graphs, and the use of priority queues and distance arrays. it also explains why the algorithm is only applicable for graphs with positive weights and its time complexity of e log v.", 'chapters': [{'end': 1207.231, 'start': 1054.26, 'title': "Dijkstra's algorithm limitations", 'summary': "Discusses why dijkstra's algorithm will not work for negative weight cycles, highlighting that it fails in graphs with a single negative weight and in the presence of cycles with negative weights, due to the use of priority queues and distance arrays.", 'duration': 152.971, 'highlights': ["Dijkstra's algorithm fails in graphs with a single negative weight and in the presence of cycles with negative weights, due to the use of priority queues and distance arrays.", "The algorithm doesn't work for negative weight cycles, as it results in distance reduction on every traversal, leading to incorrect distances being calculated.", 'The explanation focuses on the use of priority queues and distance arrays in the algorithm, demonstrating how negative weight cycles lead to incorrect distance calculations.']}, {'end': 1282.384, 'start': 1207.231, 'title': "Negative weights and dijkstra's algorithm", 'summary': "Explains why graphs with negative weights cannot implement dijkstra's algorithm as it will fall into an infinite loop due to the concept of shortest path requiring positive weights. dijkstra's algorithm is only applicable for graphs with positive weights, and its time complexity is e log v, where e is the total number of edges and v is the number of nodes.", 'duration': 75.153, 'highlights': ["The Dijkstra's algorithm is only applicable for graphs with positive weights The chapter emphasizes that Dijkstra's algorithm can only be applied to graphs with positive weights to avoid falling into an infinite loop, as it is practically impossible to compute paths with negative weights.", "Time complexity of Dijkstra's algorithm is E log V The time complexity of Dijkstra's algorithm is quantified as E log V, with E representing the total number of edges and V denoting the number of nodes in the graph.", "Explanation of why graphs with negative weights cannot implement Dijkstra's algorithm The chapter explains the impracticality of using Dijkstra's algorithm for graphs with negative weights, as it would result in an infinite loop due to the concept that shortest paths require positive weights."]}, {'end': 1353.016, 'start': 1282.384, 'title': 'Using priority queue in data structures', 'summary': 'Discusses the usage of priority queue and set data structures in algorithms, and highlights the practical implementation, emphasizing that replacing priority queue with a queue data structure still yields correct results.', 'duration': 70.632, 'highlights': ['The importance of priority queue and set data structures in algorithms and their practical implementation will be explicitly explained in the upcoming videos.', 'Emphasizing that replacing priority queue with a queue data structure will still provide correct answers, encouraging viewers to try it out for themselves.', 'Encouraging viewers to like the video, subscribe to the channel, and explore related content in the description.']}], 'duration': 298.756, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/V6H1qAeB-l4/pics/V6H1qAeB-l41054260.jpg', 'highlights': ["Dijkstra's algorithm fails in graphs with a single negative weight and in the presence of cycles with negative weights, due to the use of priority queues and distance arrays.", "The algorithm doesn't work for negative weight cycles, as it results in distance reduction on every traversal, leading to incorrect distances being calculated.", 'The explanation focuses on the use of priority queues and distance arrays in the algorithm, demonstrating how negative weight cycles lead to incorrect distance calculations.', "The Dijkstra's algorithm is only applicable for graphs with positive weights The chapter emphasizes that Dijkstra's algorithm can only be applied to graphs with positive weights to avoid falling into an infinite loop, as it is practically impossible to compute paths with negative weights.", "Time complexity of Dijkstra's algorithm is E log V The time complexity of Dijkstra's algorithm is quantified as E log V, with E representing the total number of edges and V denoting the number of nodes in the graph.", "Explanation of why graphs with negative weights cannot implement Dijkstra's algorithm The chapter explains the impracticality of using Dijkstra's algorithm for graphs with negative weights, as it would result in an infinite loop due to the concept that shortest paths require positive weights."]}], 'highlights': ['The algorithm emphasizes the importance of source nodes in determining the starting point for calculating distances and path weights.', "The chapter introduces Dijkstra's algorithm as a fundamental tool for solving problems related to finding the shortest path in a graph.", 'The algorithm begins by setting the source node as 0 and initializing the distance array with a distance of 0 for the source node. The initial step involves setting the source node as 0 and adding a distance of 0 for the source node to the distance array.', 'The task involves finding the shortest distance from a source node to every other node in a given graph.', 'Utilizing a minimum heap data structure to store distances and nodes ensures that the shorter distance will be at the top and, in case of equal shorter distances, the earlier node or the shorter node will be at the top.', "The chapter emphasizes implementing Dijkstra's algorithm using a priority queue and storing the graph in an adjacency list with pairs, enabling the solving of any related interview problems.", 'The distances to reach nodes are updated as better paths are discovered, and the new distances are added to the priority queue, following a similar process to BFS.', 'The process involves using an adjacency list to determine the possible paths from node 0 to nodes 1 and 2, with the distance to reach node 1 being 4 and node 2 also being 4.', 'The algorithm evaluates the possible routes from node 4 to nodes 2 and 5, considering the distances and identifying the best option based on the adjacency list.', 'The minimum distance stored in the distance array is 8, achieved by carefully observing and calculating specific routes.', "The chapter explains Dijkstra's algorithm for finding the shortest path in a graph.", 'The Dextrose algorithm is not applicable to graphs with negative weight cycles.', 'The chapter provides a coding demonstration in C++ for the Dextrose algorithm.', "The algorithm doesn't work for negative weight cycles, as it results in distance reduction on every traversal, leading to incorrect distances being calculated.", "The Dijkstra's algorithm is only applicable for graphs with positive weights The chapter emphasizes that Dijkstra's algorithm can only be applied to graphs with positive weights to avoid falling into an infinite loop, as it is practically impossible to compute paths with negative weights.", "Time complexity of Dijkstra's algorithm is E log V The time complexity of Dijkstra's algorithm is quantified as E log V, with E representing the total number of edges and V denoting the number of nodes in the graph."]}