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G-12. Detect a Cycle in an Undirected Graph using DFS | C++ | Java

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{'title': 'G-12. Detect a Cycle in an Undirected Graph using DFS | C++ | Java', 'heatmap': [{'end': 452.182, 'start': 423.644, 'weight': 0.781}, {'end': 1023.799, 'start': 1009.66, 'weight': 1}], 'summary': 'Content focuses on detecting cycles in undirected graphs using the depth-first search (dfs) algorithm, providing detailed explanations on cycle detection, marking visited nodes, identifying graph cycles, and emphasizing the utilization of dfs for cycle detection.', 'chapters': [{'end': 422.804, 'segs': [{'end': 37.178, 'src': 'embed', 'start': 3.336, 'weight': 2, 'content': [{'end': 4.677, 'text': 'hey, everyone, welcome back to the channel.', 'start': 3.336, 'duration': 1.341}, {'end': 6.618, 'text': 'i hope you guys are doing extremely well.', 'start': 4.677, 'duration': 1.941}, {'end': 13.281, 'text': 'so in this video we are going to, uh, solve something like cycle detection in an undirected graph using dfs.', 'start': 6.618, 'duration': 6.663}, {'end': 16.503, 'text': 'so if you have not seen the previous video, go back and watch it.', 'start': 13.281, 'duration': 3.222}, {'end': 21.125, 'text': 'we have solved how to detect the cycle using bfs.', 'start': 16.503, 'duration': 4.622}, {'end': 25.887, 'text': 'but over here we will be using the depth first search algorithm.', 'start': 21.125, 'duration': 4.762}, {'end': 27.868, 'text': 'so you know what is the cycle.', 'start': 25.887, 'duration': 1.981}, {'end': 37.178, 'text': "it's very simple you start from a node and you come back to that node via any path without breaking any edge.", 'start': 27.868, 'duration': 9.31}], 'summary': 'Solving cycle detection in an undirected graph using dfs.', 'duration': 33.842, 'max_score': 3.336, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX43336.jpg'}, {'end': 94.638, 'src': 'embed', 'start': 68.778, 'weight': 0, 'content': [{'end': 73.482, 'text': 'then tries to go here, then probably tries to go here, then has no way,', 'start': 68.778, 'duration': 4.704}, {'end': 82.832, 'text': 'goes back and tries to go one and if it reaches back to somewhere which is previously visited.', 'start': 73.482, 'duration': 9.35}, {'end': 90.015, 'text': "because, you need to understand, you started from one in this direction and if you're again coming back to one via dfs,", 'start': 82.832, 'duration': 7.183}, {'end': 92.557, 'text': 'it means you definitely have a cycle.', 'start': 90.015, 'duration': 2.542}, {'end': 94.638, 'text': 'that is for sure right.', 'start': 92.557, 'duration': 2.081}], 'summary': 'Dfs algorithm detects cycles by revisiting a previously visited node.', 'duration': 25.86, 'max_score': 68.778, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX468778.jpg'}, {'end': 248.635, 'src': 'embed', 'start': 217.488, 'weight': 1, 'content': [{'end': 218.669, 'text': 'basically it came from one.', 'start': 217.488, 'duration': 1.181}, {'end': 221.152, 'text': 'that is what it, what you need to carry first.', 'start': 218.669, 'duration': 2.483}, {'end': 224.915, 'text': 'the call for two will be made once the dfs is done.', 'start': 221.152, 'duration': 3.763}, {'end': 226.577, 'text': 'then we will go for three.', 'start': 224.915, 'duration': 1.662}, {'end': 228.298, 'text': 'right, that is how the dfs works.', 'start': 226.577, 'duration': 1.721}, {'end': 229.94, 'text': 'so we can keep it as dotted.', 'start': 228.298, 'duration': 1.642}, {'end': 236.265, 'text': 'now, remember over here dotted means We will do this call after this particular call is over.', 'start': 229.94, 'duration': 6.325}, {'end': 238.587, 'text': 'So we have DFS of 2.', 'start': 236.545, 'duration': 2.042}, {'end': 243.111, 'text': "So if we have a DFS of 2, this is where you'll understand the concept of parent.", 'start': 238.587, 'duration': 4.524}, {'end': 248.635, 'text': 'For 2, the moment you reach 2, obviously, first and foremost thing, done.', 'start': 243.571, 'duration': 5.064}], 'summary': 'The process involves steps 1, 2, and 3, with a focus on dfs and the concept of parent.', 'duration': 31.147, 'max_score': 217.488, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX4217488.jpg'}], 'start': 3.336, 'title': 'Detecting cycles in graphs with dfs', 'summary': 'Covers cycle detection in undirected graphs using the depth-first search (dfs) algorithm, explaining the concept of a cycle and providing insights into how dfs identifies previously visited nodes within the path. it also explains the dfs algorithm in detail, including marking visited nodes, carrying parent nodes, and identifying graph cycles.', 'chapters': [{'end': 116.498, 'start': 3.336, 'title': 'Cycle detection in undirected graph using dfs', 'summary': 'Discusses how to detect a cycle in an undirected graph using the depth first search algorithm, explaining the concept of a cycle and the intuition behind dfs, with a focus on identifying previously visited nodes within the path.', 'duration': 113.162, 'highlights': ['The algorithm focuses on identifying previously visited nodes within the path to detect a cycle using the depth first search algorithm.', 'Explanation of the concept of a cycle in a graph is provided, emphasizing the idea of starting from a node and returning to it via any path without breaking any edge.', 'Emphasizing the importance of understanding the intuition behind DFS, particularly in detecting cycles by recognizing previously visited nodes in the path.']}, {'end': 422.804, 'start': 117.299, 'title': 'Dfs algorithm explained', 'summary': 'Explains the depth-first search (dfs) algorithm, detailing the process of marking visited nodes, carrying parent nodes, and identifying cycles in a graph using dfs.', 'duration': 305.505, 'highlights': ['DFS algorithm explained with a focus on marking visited nodes and carrying parent nodes for cycle detection.', 'Illustration of DFS process through an example of traversing nodes 1, 2, 3, 5, 7, 6, and 4.', 'Explanation of identifying cycles in the graph by analyzing the parent-child relationships in the DFS algorithm.']}], 'duration': 419.468, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX43336.jpg', 'highlights': ['The algorithm focuses on identifying previously visited nodes within the path to detect a cycle using the depth first search algorithm.', 'DFS algorithm explained with a focus on marking visited nodes and carrying parent nodes for cycle detection.', 'Explanation of the concept of a cycle in a graph is provided, emphasizing the idea of starting from a node and returning to it via any path without breaking any edge.', 'Explanation of identifying cycles in the graph by analyzing the parent-child relationships in the DFS algorithm.', 'Emphasizing the importance of understanding the intuition behind DFS, particularly in detecting cycles by recognizing previously visited nodes in the path.', 'Illustration of DFS process through an example of traversing nodes 1, 2, 3, 5, 7, 6, and 4.']}, {'end': 714.395, 'segs': [{'end': 453.382, 'src': 'heatmap', 'start': 423.644, 'weight': 1, 'content': [{'end': 428.246, 'text': 'But will it call for DFS of 1,3? Will it call for DFS of 1,3? No.', 'start': 423.644, 'duration': 4.602}, {'end': 433.448, 'text': 'Why? Because this 1, if you see, is visited over here.', 'start': 428.586, 'duration': 4.862}, {'end': 435.389, 'text': "And it's not the parent.", 'start': 434.189, 'duration': 1.2}, {'end': 443.458, 'text': 'How did it How did it mark itself? Because it was previously in the path.', 'start': 436.33, 'duration': 7.128}, {'end': 445.719, 'text': 'It was previously in the path here.', 'start': 444.158, 'duration': 1.561}, {'end': 447.78, 'text': 'That is why it was marked in the visited.', 'start': 445.839, 'duration': 1.941}, {'end': 452.182, 'text': "So I say, hey, for this one, don't call it.", 'start': 448.14, 'duration': 4.042}, {'end': 453.382, 'text': 'Do not call it.', 'start': 452.642, 'duration': 0.74}], 'summary': 'Dfs of 1,3 is not called as 1 is already visited and not the parent.', 'duration': 29.738, 'max_score': 423.644, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX4423644.jpg'}, {'end': 503.835, 'src': 'embed', 'start': 475.436, 'weight': 3, 'content': [{'end': 477.617, 'text': 'this guy says you are returning me a true.', 'start': 475.436, 'duration': 2.181}, {'end': 478.638, 'text': "i'll also return true.", 'start': 477.617, 'duration': 1.021}, {'end': 481.14, 'text': 'now this guy says i got it true.', 'start': 478.638, 'duration': 2.502}, {'end': 485.322, 'text': 'Should I go and have my brains on 3-1?', 'start': 482, 'duration': 3.322}, {'end': 487.303, 'text': "I don't need to do any further calls.", 'start': 485.862, 'duration': 1.441}, {'end': 488.143, 'text': 'I got it true.', 'start': 487.483, 'duration': 0.66}, {'end': 491.785, 'text': "If I'm getting it true, there's no need to do DFS for further calls.", 'start': 488.584, 'duration': 3.201}, {'end': 493.726, 'text': 'And I say, true.', 'start': 492.206, 'duration': 1.52}, {'end': 498.149, 'text': 'For the source node starting with 1, I got someone as.', 'start': 494.427, 'duration': 3.722}, {'end': 500.693, 'text': 'True, which means I have a cycle.', 'start': 499.312, 'duration': 1.381}, {'end': 502.294, 'text': 'Which means I have a cycle.', 'start': 501.193, 'duration': 1.101}, {'end': 503.835, 'text': "Does that make sense? That's true.", 'start': 502.714, 'duration': 1.121}], 'summary': "The transcript discusses the process of identifying a cycle, with multiple affirmations of 'true' and a reference to the source node starting with 1.", 'duration': 28.399, 'max_score': 475.436, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX4475436.jpg'}, {'end': 587.044, 'src': 'embed', 'start': 552.975, 'weight': 2, 'content': [{'end': 554.815, 'text': "So if you're calling for IT, this will be the parent.", 'start': 552.975, 'duration': 1.84}, {'end': 556.055, 'text': "So you'll call for it.", 'start': 555.235, 'duration': 0.82}, {'end': 561.741, 'text': 'But if you remember this, This call was made DFS a 4-3 and it returned a false.', 'start': 556.796, 'duration': 4.945}, {'end': 563.201, 'text': 'You did not do anything.', 'start': 562.401, 'duration': 0.8}, {'end': 572.783, 'text': 'But when you made a call for 3-6, when you made a call for 3-6, it found out one was already visited.', 'start': 563.841, 'duration': 8.942}, {'end': 573.883, 'text': 'So it returned a true.', 'start': 572.843, 'duration': 1.04}, {'end': 577.983, 'text': 'So if any of the DFS calls is returning a true, you keep on returning true.', 'start': 574.363, 'duration': 3.62}, {'end': 580.304, 'text': "So this is a DFS call that you're making.", 'start': 578.304, 'duration': 2}, {'end': 587.044, 'text': 'So if it by chance returns a true, remember this, if it by chance returns a true, Not a false.', 'start': 580.864, 'duration': 6.18}], 'summary': 'In a dfs call, 3-6 returned true, indicating one was visited, while a 4-3 call returned false, resulting in no action taken.', 'duration': 34.069, 'max_score': 552.975, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX4552975.jpg'}, {'end': 668.71, 'src': 'embed', 'start': 637.91, 'weight': 0, 'content': [{'end': 640.191, 'text': 'It has to be non-parent.', 'start': 637.91, 'duration': 2.281}, {'end': 642.511, 'text': 'Then only I can call it as a cycle.', 'start': 641.091, 'duration': 1.42}, {'end': 648.172, 'text': "So I'll be like, if this guy is visited, if it comes to else, means visited.", 'start': 642.851, 'duration': 5.321}, {'end': 656.413, 'text': 'And if it is not a parent, if it is not a parent, dude, how did it visit itself? That means it is a cycle.', 'start': 649.092, 'duration': 7.321}, {'end': 659.394, 'text': 'That means this is the point where I encounter a cycle.', 'start': 656.793, 'duration': 2.601}, {'end': 660.903, 'text': 'Something like this.', 'start': 660.222, 'duration': 0.681}, {'end': 664.786, 'text': 'When I was trying for 3, I got 1.', 'start': 661.543, 'duration': 3.243}, {'end': 668.71, 'text': 'How did you get 1? 1 was visited but it was not apparent.', 'start': 664.786, 'duration': 3.924}], 'summary': 'Encountered a cycle while traversing, 1 was visited but not a parent.', 'duration': 30.8, 'max_score': 637.91, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX4637910.jpg'}], 'start': 423.644, 'title': 'Cycle detection in dfs', 'summary': "Explains the process of cycle detection in a graph using dfs, highlighting the algorithm's utilization of marking visited nodes and returning true for cycles, along with a recommendation for multiple graph dry runs for better understanding.", 'chapters': [{'end': 475.436, 'start': 423.644, 'title': 'Cycle detection in dfs', 'summary': 'Explains the process of cycle detection in a graph using dfs, where the algorithm utilizes the concept of marking visited nodes and returning true for cycles, exemplified by the repetition of returning true in the function calls.', 'duration': 51.792, 'highlights': ['The algorithm marks visited nodes and returns true for cycles, as demonstrated by the repeated return of true in the function calls.', 'The presence of a cycle is determined by the repeated return of true in the function calls.']}, {'end': 714.395, 'start': 475.436, 'title': 'Dfs cycle detection pseudo code', 'summary': 'Explains the dfs algorithm for cycle detection, highlighting the process of marking nodes, checking for visited and non-parent nodes, and returning true if a cycle is found, with a recommendation to do multiple graph dry runs for better understanding.', 'duration': 238.959, 'highlights': ['The algorithm involves marking nodes, checking for visited and non-parent nodes, and returning true if a cycle is found.', 'The DFS call returns true if any of its calls return true, and false if all adjacent nodes are visited without encountering a cycle.', 'The pseudo code for DFS cycle detection involves marking nodes, checking for visited and non-parent nodes, and returning true if a cycle is found, and false if no cycle is encountered after traversing all adjacent nodes.']}], 'duration': 290.751, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX4423644.jpg', 'highlights': ['The algorithm marks visited nodes and returns true for cycles, as demonstrated by the repeated return of true in the function calls.', 'The presence of a cycle is determined by the repeated return of true in the function calls.', 'The DFS call returns true if any of its calls return true, and false if all adjacent nodes are visited without encountering a cycle.', 'The pseudo code for DFS cycle detection involves marking nodes, checking for visited and non-parent nodes, and returning true if a cycle is found, and false if no cycle is encountered after traversing all adjacent nodes.']}, {'end': 1139.945, 'segs': [{'end': 897.153, 'src': 'embed', 'start': 872.832, 'weight': 1, 'content': [{'end': 880.474, 'text': 'so if you just call for dfs of one, it will go and it will visit these guys and it will never find a cycle.', 'start': 872.832, 'duration': 7.642}, {'end': 885.682, 'text': 'in order to find a cycle, you have to actually call dfs of seven, right.', 'start': 880.474, 'duration': 5.208}, {'end': 886.983, 'text': 'so how will you do this?', 'start': 885.682, 'duration': 1.301}, {'end': 897.153, 'text': 'this is why what you do is you always call something like i equal to one till nine, and you say if these guys are not visited,', 'start': 886.983, 'duration': 10.17}], 'summary': 'Dfs algorithm can find cycles by calling dfs of seven, and iterating through i from 1 to 9.', 'duration': 24.321, 'max_score': 872.832, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX4872832.jpg'}, {'end': 954.795, 'src': 'embed', 'start': 925.841, 'weight': 4, 'content': [{'end': 927.642, 'text': 'Next, it will be 3.', 'start': 925.841, 'duration': 1.801}, {'end': 928.522, 'text': 'Again, find visited.', 'start': 927.642, 'duration': 0.88}, {'end': 929.342, 'text': 'No DFS calls.', 'start': 928.702, 'duration': 0.64}, {'end': 930.523, 'text': 'Next, it will be 4.', 'start': 929.903, 'duration': 0.62}, {'end': 933.044, 'text': 'It will find already visited.', 'start': 930.523, 'duration': 2.521}, {'end': 934.165, 'text': 'No DFS calls.', 'start': 933.565, 'duration': 0.6}, {'end': 936.887, 'text': 'Next, it will be 5, non-visited.', 'start': 934.745, 'duration': 2.142}, {'end': 939.308, 'text': 'So, it goes and calls the DFS for 5 now.', 'start': 936.907, 'duration': 2.401}, {'end': 942.289, 'text': 'So, first, a DFS call for 1 was made.', 'start': 939.788, 'duration': 2.501}, {'end': 944.25, 'text': 'Next, the DFS call of 5 was made.', 'start': 942.77, 'duration': 1.48}, {'end': 950.634, 'text': '5 will make sure 5 is visited, 6 is visited, right? So now the DFS of 5 will be called.', 'start': 944.27, 'duration': 6.364}, {'end': 953.355, 'text': 'And 5 will go and mark these guys.', 'start': 951.374, 'duration': 1.981}, {'end': 954.795, 'text': 'And again it will not get a cycle.', 'start': 953.535, 'duration': 1.26}], 'summary': 'Dfs calls made for nodes 1, 5, marking visited nodes without creating cycles.', 'duration': 28.954, 'max_score': 925.841, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX4925841.jpg'}, {'end': 1074.193, 'src': 'heatmap', 'start': 1009.66, 'weight': 3, 'content': [{'end': 1016.606, 'text': 'you return a true or else at the end of the day, if you none of them gave a cycle, you return a false.', 'start': 1009.66, 'duration': 6.946}, {'end': 1018.588, 'text': 'so you can just compile that and check it out.', 'start': 1016.606, 'duration': 1.982}, {'end': 1020.898, 'text': 'It is running absolutely fine.', 'start': 1019.537, 'duration': 1.361}, {'end': 1023.799, 'text': "So it's time to discuss the space complexity.", 'start': 1021.278, 'duration': 2.521}, {'end': 1026.641, 'text': 'Are we using the space complexity? We are.', 'start': 1024.56, 'duration': 2.081}, {'end': 1032.003, 'text': "We're using something like recursion stack space, which can be B go of N at the worst case.", 'start': 1027.001, 'duration': 5.002}, {'end': 1033.625, 'text': 'Assume all the nodes are connected.', 'start': 1032.144, 'duration': 1.481}, {'end': 1035.406, 'text': "It'll be a recursion.", 'start': 1033.704, 'duration': 1.702}, {'end': 1037.487, 'text': 'Assume you get a graph, something like this.', 'start': 1035.705, 'duration': 1.782}, {'end': 1041.991, 'text': 'Then the recursion will go here, then here, then here, then here.', 'start': 1039.209, 'duration': 2.782}, {'end': 1044.071, 'text': 'So complete recursion stack space.', 'start': 1042.031, 'duration': 2.04}, {'end': 1046.214, 'text': "We're using something like a visited array.", 'start': 1044.613, 'duration': 1.601}, {'end': 1049.016, 'text': 'So you can just sum it up to b go of n.', 'start': 1046.973, 'duration': 2.043}, {'end': 1052.618, 'text': "I'm not adding the adjacency list into a column.", 'start': 1049.016, 'duration': 3.602}, {'end': 1055.981, 'text': "What about the time complexity? We're using a DFS traversal.", 'start': 1053.119, 'duration': 2.862}, {'end': 1058.623, 'text': 'And we know the DFS traversal is n plus 2e.', 'start': 1056.301, 'duration': 2.322}, {'end': 1063.526, 'text': 'Because for every node, you visit all the degrees or all the adjacent nodes.', 'start': 1059.223, 'duration': 4.303}, {'end': 1065.628, 'text': 'And the summation of adjacent nodes is.', 'start': 1063.886, 'duration': 1.742}, {'end': 1069.43, 'text': '2e. so n plus 2e plus b.', 'start': 1066.588, 'duration': 2.842}, {'end': 1074.193, 'text': "go of n because you're running a for loop, you're running a for loop.", 'start': 1069.43, 'duration': 4.763}], 'summary': 'Using dfs traversal with time complexity of n+2e+b and space complexity of bgo of n.', 'duration': 67.696, 'max_score': 1009.66, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX41009660.jpg'}, {'end': 1139.945, 'src': 'embed', 'start': 1138.924, 'weight': 0, 'content': [{'end': 1139.465, 'text': 'Till then, bye-bye.', 'start': 1138.924, 'duration': 0.541}, {'end': 1139.945, 'text': 'Take care.', 'start': 1139.485, 'duration': 0.46}], 'summary': "Short farewell: 'till then, bye-bye. take care.'", 'duration': 1.021, 'max_score': 1138.924, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX41138924.jpg'}], 'start': 714.395, 'title': 'Graph cycle detection', 'summary': 'Explains a depth-first search algorithm for detecting cycles in a graph, emphasizing recursion and iterative checks for visited nodes, resulting in the identification of cycles. it also provides insights into the time and space complexity of dfs traversal.', 'chapters': [{'end': 849.672, 'start': 714.395, 'title': 'Graph cycle detection', 'summary': 'Explains a depth-first search algorithm for detecting cycles in a graph, emphasizing the importance of recursion and the process of identifying repeated nodes in the path cycle.', 'duration': 135.277, 'highlights': ['The importance of strong recursion is emphasized to efficiently implement the algorithm.', 'The algorithm involves checking for cycles in a graph through a depth-first search, with a focus on identifying repeated nodes in the path cycle.', 'The process involves calling the depth-first search for adjacent nodes and identifying the presence of cycles by checking the return value of the function.']}, {'end': 977.167, 'start': 849.672, 'title': 'Detecting cycles in a graph', 'summary': 'Explains the process of detecting cycles in a graph using depth-first search (dfs) algorithm, involving multiple components and iterative checks for visited nodes, resulting in the identification of cycles in the graph.', 'duration': 127.495, 'highlights': ['The process involves using depth-first search (DFS) to iterate through the graph components and identify cycles by checking for visited nodes and making iterative DFS calls for unvisited nodes.', 'By iterating through the graph components and making iterative DFS calls for unvisited nodes, the algorithm effectively identifies cycles, as demonstrated by the example provided in the transcript.', 'An essential step in the process involves declaring a visited array to ensure that multiple DFS calls for different nodes are made in an organized manner, preventing redundant calls and ensuring accurate cycle detection.']}, {'end': 1139.945, 'start': 977.167, 'title': 'Dfs time and space complexity analysis', 'summary': 'Explains the time complexity of dfs traversal as n+2e+bgo(n) and the space complexity as bgo(n), while emphasizing the importance of visiting nine nodes in total and providing insights into the recursive stack space and adjacency list.', 'duration': 162.778, 'highlights': ['The time complexity of DFS traversal is n+2e+bgo(n), with the emphasis on visiting nine nodes in total and the impact of the for loop on the overall time complexity.', 'The space complexity involves the use of recursion stack space, which can be bgo(n) at worst case, and a visited array, contributing to the overall space complexity.', 'The importance of visiting nine nodes in total is highlighted, with the explanation of how the for loop ensures the DFS visits them nine times, impacting the overall time complexity.']}], 'duration': 425.55, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zQ3zgFypzX4/pics/zQ3zgFypzX4714395.jpg', 'highlights': ['The algorithm involves checking for cycles in a graph through a depth-first search, with a focus on identifying repeated nodes in the path cycle.', 'By iterating through the graph components and making iterative DFS calls for unvisited nodes, the algorithm effectively identifies cycles, as demonstrated by the example provided in the transcript.', 'The process involves using depth-first search (DFS) to iterate through the graph components and identify cycles by checking for visited nodes and making iterative DFS calls for unvisited nodes.', 'The importance of strong recursion is emphasized to efficiently implement the algorithm.', 'An essential step in the process involves declaring a visited array to ensure that multiple DFS calls for different nodes are made in an organized manner, preventing redundant calls and ensuring accurate cycle detection.', 'The time complexity of DFS traversal is n+2e+bgo(n), with the emphasis on visiting nine nodes in total and the impact of the for loop on the overall time complexity.', 'The space complexity involves the use of recursion stack space, which can be bgo(n) at worst case, and a visited array, contributing to the overall space complexity.', 'The importance of visiting nine nodes in total is highlighted, with the explanation of how the for loop ensures the DFS visits them nine times, impacting the overall time complexity.', 'The process involves calling the depth-first search for adjacent nodes and identifying the presence of cycles by checking the return value of the function.']}], 'highlights': ['The time complexity of DFS traversal is n+2e+bgo(n), with the emphasis on visiting nine nodes in total and the impact of the for loop on the overall time complexity.', 'The space complexity involves the use of recursion stack space, which can be bgo(n) at worst case, and a visited array, contributing to the overall space complexity.', 'The process involves using depth-first search (DFS) to iterate through the graph components and identify cycles by checking for visited nodes and making iterative DFS calls for unvisited nodes.', 'The algorithm involves checking for cycles in a graph through a depth-first search, with a focus on identifying repeated nodes in the path cycle.', 'The importance of strong recursion is emphasized to efficiently implement the algorithm.', 'An essential step in the process involves declaring a visited array to ensure that multiple DFS calls for different nodes are made in an organized manner, preventing redundant calls and ensuring accurate cycle detection.', 'The presence of a cycle is determined by the repeated return of true in the function calls.', 'The algorithm marks visited nodes and returns true for cycles, as demonstrated by the repeated return of true in the function calls.', 'The pseudo code for DFS cycle detection involves marking nodes, checking for visited and non-parent nodes, and returning true if a cycle is found, and false if no cycle is encountered after traversing all adjacent nodes.', 'The process involves calling the depth-first search for adjacent nodes and identifying the presence of cycles by checking the return value of the function.', 'DFS algorithm explained with a focus on marking visited nodes and carrying parent nodes for cycle detection.', 'Explanation of identifying cycles in the graph by analyzing the parent-child relationships in the DFS algorithm.', 'The algorithm focuses on identifying previously visited nodes within the path to detect a cycle using the depth first search algorithm.', 'Explanation of the concept of a cycle in a graph is provided, emphasizing the idea of starting from a node and returning to it via any path without breaking any edge.', 'Emphasizing the importance of understanding the intuition behind DFS, particularly in detecting cycles by recognizing previously visited nodes in the path.', 'Illustration of DFS process through an example of traversing nodes 1, 2, 3, 5, 7, 6, and 4.', 'By iterating through the graph components and making iterative DFS calls for unvisited nodes, the algorithm effectively identifies cycles, as demonstrated by the example provided in the transcript.']}