title

G-41. Bellman Ford Algorithm

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{'title': 'G-41. Bellman Ford Algorithm', 'heatmap': [], 'summary': "Covers the bellman ford algorithm for finding the shortest path in directed graphs, emphasizing its ability to handle negative edges and cycles, and its time complexity of o(v*e), making it an alternative to dijkstra's algorithm.", 'chapters': [{'end': 308.994, 'segs': [{'end': 105.665, 'src': 'embed', 'start': 25.262, 'weight': 0, 'content': [{'end': 33.005, 'text': 'It is the exact similar algorithm which will help you to find the shortest path from a source to all the other nodes.', 'start': 25.262, 'duration': 7.743}, {'end': 34.605, 'text': 'Yes, to all the other nodes.', 'start': 33.105, 'duration': 1.5}, {'end': 39.667, 'text': 'But the only difference is if you remember the video of the Dijkstra.', 'start': 35.105, 'duration': 4.562}, {'end': 46.33, 'text': 'The Dijkstra algorithm fails when the graph has negative edges.', 'start': 40.327, 'duration': 6.003}, {'end': 52.033, 'text': 'Please remember, if the graph has negative edges, the Dijkstra algorithm will fail.', 'start': 47.091, 'duration': 4.942}, {'end': 53.434, 'text': 'And there was another point.', 'start': 52.253, 'duration': 1.181}, {'end': 62.239, 'text': 'If the graph has negative cycle, the Dijkstra algorithm goes for a TLE, like it will keep on running.', 'start': 53.914, 'duration': 8.325}, {'end': 64.58, 'text': 'It will keep on running, keep on minimizing the resistance.', 'start': 62.279, 'duration': 2.301}, {'end': 65.9, 'text': 'It keeps on running forever.', 'start': 64.84, 'duration': 1.06}, {'end': 70.144, 'text': 'So Dijkstra does not help you to detect negative cycle.', 'start': 66.221, 'duration': 3.923}, {'end': 75.15, 'text': 'so bellman ford is an algorithm that helps you to detect.', 'start': 70.144, 'duration': 5.006}, {'end': 76.011, 'text': 'remember this.', 'start': 75.15, 'duration': 0.861}, {'end': 80.016, 'text': 'that helps you to detect negative cycles as well.', 'start': 76.011, 'duration': 4.005}, {'end': 89.388, 'text': "that's the specialty about bellman ford, and it is applicable, and it is applicable only in dg.", 'start': 82.398, 'duration': 6.99}, {'end': 91.651, 'text': 'what is dg directed graphs?', 'start': 89.388, 'duration': 2.263}, {'end': 97.859, 'text': "now you might be thinking what if it's an undirected graph, and how do you apply bellman ford algorithm to it?", 'start': 91.651, 'duration': 6.208}, {'end': 103.784, 'text': 'very simple, remember, this is how a directed edge looks like.', 'start': 97.859, 'duration': 5.925}, {'end': 105.665, 'text': 'so the edge weight will be five.', 'start': 103.784, 'duration': 1.881}], 'summary': 'Dijkstra fails with negative edges, bellman ford detects negative cycles.', 'duration': 80.403, 'max_score': 25.262, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc25262.jpg'}, {'end': 153.729, 'src': 'embed', 'start': 120.733, 'weight': 7, 'content': [{'end': 127.556, 'text': 'there is a directed edge from one to two, which will cost you five, and there is a directed edge from two to one, which will cost you five.', 'start': 120.733, 'duration': 6.823}, {'end': 136.38, 'text': 'so you just need to represent the undirected graph in form of a directed graph in order to implement the bellman ford algorithm.', 'start': 127.556, 'duration': 8.824}, {'end': 142.483, 'text': 'the bellman ford algorithm will only work if you are given a directed graph.', 'start': 136.38, 'duration': 6.103}, {'end': 143.003, 'text': 'remember this.', 'start': 142.483, 'duration': 0.52}, {'end': 153.729, 'text': 'so if you are given an undirected graph, just change it to a directed graph by having two side edges with the same edge weights.', 'start': 143.003, 'duration': 10.726}], 'summary': 'Implement bellman ford algorithm with directed graph representation of undirected graph.', 'duration': 32.996, 'max_score': 120.733, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc120733.jpg'}], 'start': 3.186, 'title': 'Bellman ford algorithm', 'summary': "Discusses the bellman ford algorithm for finding the shortest path in directed graphs, emphasizing its distinction from dijkstra's algorithm and its ability to handle negative edges and cycles, as well as its application and capability to detect negative cycles.", 'chapters': [{'end': 80.016, 'start': 3.186, 'title': 'Bellman ford algorithm: shortest path', 'summary': "Introduces the bellman ford algorithm for finding the shortest path from a source to all other nodes, highlighting its difference from dijkstra's algorithm, which fails on graphs with negative edges and cycles.", 'duration': 76.83, 'highlights': ['Bellman Ford algorithm is used to find the shortest path from a source to all other nodes, even on graphs with negative edges.', "Dijkstra's algorithm fails on graphs with negative edges and negative cycles, while Bellman Ford can detect negative cycles.", 'Dijkstra algorithm fails when the graph has negative edges and cannot detect negative cycles, while Bellman Ford algorithm can handle negative edges and detect negative cycles.']}, {'end': 189.67, 'start': 82.398, 'title': 'Bellman ford algorithm in directed graphs', 'summary': "Explains the application of the bellman ford algorithm in directed graphs, emphasizing the need to convert undirected graphs to directed graphs and the algorithm's capability to detect negative cycles.", 'duration': 107.272, 'highlights': ["The Bellman Ford algorithm is applicable only in directed graphs, and undirected graphs need to be converted to directed graphs for implementation. The algorithm's limitation to directed graphs requires conversion of undirected graphs to directed graphs for implementation.", "The Bellman Ford algorithm can be used to detect negative cycles in graphs, aiding in determining path weights. The algorithm's capability to detect negative cycles helps in determining path weights, providing a useful feature not found in Dijkstra's algorithm."]}, {'end': 308.994, 'start': 189.67, 'title': 'Bellman-ford algorithm', 'summary': 'Explains the bellman-ford algorithm for finding the shortest path in a graph, specifically designed to identify negative cycles, and demonstrates its implementation with a directed graph and edge relaxation.', 'duration': 119.324, 'highlights': ['The Bellman-Ford algorithm is designed to identify negative cycles in a graph by detecting any path weight less than zero.', 'It is a single source shortest path algorithm with a starting point at zero and the edges given in any order.', 'The order of edges in the directed graph is not significant, and the algorithm requires relaxing all the edges to find the shortest path.']}], 'duration': 305.808, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc3186.jpg', 'highlights': ["Bellman Ford algorithm can detect negative cycles, unlike Dijkstra's algorithm.", 'Bellman Ford algorithm can handle negative edges and detect negative cycles.', "The algorithm's capability to detect negative cycles helps in determining path weights.", 'The Bellman-Ford algorithm is designed to identify negative cycles in a graph.', 'The algorithm requires relaxing all the edges to find the shortest path.', 'Bellman Ford algorithm is used to find the shortest path from a source to all other nodes, even on graphs with negative edges.', 'The Bellman Ford algorithm is applicable only in directed graphs.', 'Undirected graphs need to be converted to directed graphs for implementation.']}, {'end': 897.065, 'segs': [{'end': 444.206, 'src': 'embed', 'start': 392.533, 'weight': 0, 'content': [{'end': 399.117, 'text': "So I'll be like distance v is equal to the new distance, which is distance u plus w.", 'start': 392.533, 'duration': 6.584}, {'end': 402.66, 'text': 'This is what I call as relaxation of edges.', 'start': 399.117, 'duration': 3.543}, {'end': 405.782, 'text': 'This will be done for n minus one times.', 'start': 403.08, 'duration': 2.702}, {'end': 407.583, 'text': 'What do you mean by n minus one times?', 'start': 406.082, 'duration': 1.501}, {'end': 418.539, 'text': 'If you go over here and look at the n, n over here is 6, because there are 0,, 1, 2, 3, 4, 5, like zero-based indexing nodes.', 'start': 407.903, 'duration': 10.636}, {'end': 420.779, 'text': 'So, thereby n is 6.', 'start': 418.879, 'duration': 1.9}, {'end': 423.4, 'text': 'So, you have to relax it for 5 times.', 'start': 420.779, 'duration': 2.621}, {'end': 426.141, 'text': '5 iteration of relaxations has to be done.', 'start': 423.42, 'duration': 2.721}, {'end': 428.681, 'text': "Now, how to do it? Let's understand that.", 'start': 426.501, 'duration': 2.18}, {'end': 436.343, 'text': 'But before that, since you are calculating shortest path, what do you require? You require a distance array with everything initialized to infinity.', 'start': 428.821, 'duration': 7.522}, {'end': 437.064, 'text': "So, let's do that.", 'start': 436.484, 'duration': 0.58}, {'end': 444.206, 'text': 'So, initially, when you initialize the distance array, the source will be marked as 0 and everything else will be marked as infinity,', 'start': 437.364, 'duration': 6.842}], 'summary': 'Algorithm involves relaxation of edges, done 5 times for calculating shortest path.', 'duration': 51.673, 'max_score': 392.533, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc392533.jpg'}, {'end': 897.065, 'src': 'embed', 'start': 870.696, 'weight': 2, 'content': [{'end': 882.915, 'text': 'your distance array will be giving you the shortest path from the source 0 to all other nodes remember this which will be stored in this distance array.', 'start': 870.696, 'duration': 12.219}, {'end': 884.656, 'text': 'Now, a couple of questions.', 'start': 883.495, 'duration': 1.161}, {'end': 889.019, 'text': "Why n-1 iterations? That's the first question.", 'start': 885.196, 'duration': 3.823}, {'end': 893.963, 'text': 'And the second question will be definitely how to detect negative cycles?', 'start': 889.58, 'duration': 4.383}, {'end': 895.744, 'text': 'What if the graph has negative cycles?', 'start': 894.123, 'duration': 1.621}, {'end': 897.065, 'text': 'How will I know about that?', 'start': 896.064, 'duration': 1.001}], 'summary': 'Algorithm calculates shortest path from source to all nodes, addressing iterations and negative cycles.', 'duration': 26.369, 'max_score': 870.696, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc870696.jpg'}], 'start': 308.994, 'title': 'Relaxation of edges in shortest path and distance relaxation in graphs', 'summary': "Explains the process of relaxing edges in the context of finding the shortest path and discusses distance relaxation in graphs using dijkstra's algorithm, emphasizing the need to relax all edges n minus 1 times sequentially and the relevance of value comparisons, with a focus on the number of iterations required to achieve the shortest path and the absence of negative cycles in the graph.", 'chapters': [{'end': 511.109, 'start': 308.994, 'title': 'Relaxation of edges in shortest path', 'summary': 'Explains the concept of relaxing edges in the context of finding the shortest path, emphasizing the need to relax all edges n minus 1 times sequentially, with n being the number of nodes, before initializing a distance array with the source marked as 0 and the rest as infinity.', 'duration': 202.115, 'highlights': ['Relaxing all edges n minus 1 times sequentially It is emphasized that all edges need to be relaxed n minus 1 times sequentially, with n being the number of nodes, to calculate the shortest path.', "Definition of relax in the context of distance array and edge weight The definition of relax states that if the distance to reach a node 'u' plus the edge weight is lesser than the distance of another node 'v', it indicates a better path, similar to Dijkstra's algorithm.", 'Initializing the distance array for calculating shortest path The process of initializing the distance array for calculating the shortest path involves marking the source as 0 and the rest of the nodes as infinity, indicating that they have not been reached yet.']}, {'end': 897.065, 'start': 511.109, 'title': 'Distance relaxation in graphs', 'summary': "Discusses the process of distance relaxation in graphs using dijkstra's algorithm, iterating through the edges and updating the distance values until the shortest path from the source node to all other nodes is obtained, with a focus on the relevance of value comparisons and the number of iterations required to achieve this. it also addresses the absence of negative cycles in the graph and the method for detecting them.", 'duration': 385.956, 'highlights': ["The process of distance relaxation in graphs involves iterating through the edges and updating the distance values until the shortest path from the source node to all other nodes is obtained, with comparisons between current and updated distance values determining the need for relaxation, exemplified by specific edge relaxations and their impact on the distance values (e.g., updating a node's distance to a new value after relaxation). The number of iterations required to achieve the shortest path is emphasized, with the concept of n-1 iterations explained as a key aspect of the algorithm's convergence.", "The absence of negative cycles in the graph is highlighted, emphasizing that while negative edges are allowed, the absence of negative cycles ensures the algorithm's efficacy in determining the shortest path from the source node to all other nodes. This information is crucial in understanding the reliability of the algorithm's output and the absence of infinite loops or ambiguous results.", "The method for detecting negative cycles in a graph is mentioned as a critical aspect, addressing the potential presence of negative cycles and the need to identify them to avoid erroneous results in determining the shortest path. This information provides a comprehensive understanding of the algorithm's limitations and the necessary precautions for handling graphs with negative cycles."]}], 'duration': 588.071, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc308994.jpg', 'highlights': ['Relaxing all edges n minus 1 times sequentially to calculate the shortest path.', 'The process of distance relaxation in graphs involves iterating through the edges and updating the distance values until the shortest path from the source node to all other nodes is obtained.', "The absence of negative cycles in the graph ensures the algorithm's efficacy in determining the shortest path from the source node to all other nodes."]}, {'end': 1220.502, 'segs': [{'end': 1053.933, 'src': 'embed', 'start': 998.587, 'weight': 2, 'content': [{'end': 1000.869, 'text': 'And eventually this 3 helped me to compute 4.', 'start': 998.587, 'duration': 2.282}, {'end': 1003.27, 'text': 'And so on, it will just go on on this loop.', 'start': 1000.869, 'duration': 2.401}, {'end': 1004.771, 'text': 'Thought process is clear.', 'start': 1003.811, 'duration': 0.96}, {'end': 1008.093, 'text': 'But y n minus 1 is still the question.', 'start': 1005.172, 'duration': 2.921}, {'end': 1011.255, 'text': "Let's understand this with this particular directed graph.", 'start': 1008.354, 'duration': 2.901}, {'end': 1018.6, 'text': 'So in this directed graph, if you remember, while explaining, I did tell you edges can be in any order.', 'start': 1011.676, 'duration': 6.924}, {'end': 1027.277, 'text': 'edges can be in any particular order is what i always stated right.', 'start': 1020.194, 'duration': 7.083}, {'end': 1031.638, 'text': 'so imagine i give you the edges in this particular order.', 'start': 1027.277, 'duration': 4.361}, {'end': 1034.22, 'text': 'so how many nodes are there?', 'start': 1031.638, 'duration': 2.582}, {'end': 1035.941, 'text': 'the number of nodes are five.', 'start': 1034.22, 'duration': 1.721}, {'end': 1038.061, 'text': 'so how many iterations will we have?', 'start': 1035.941, 'duration': 2.12}, {'end': 1045.527, 'text': 'we will have one, two, three and four iterations because edges are five.', 'start': 1038.061, 'duration': 7.466}, {'end': 1049.85, 'text': 'so i have to do n minus one, which is four iterations correct.', 'start': 1045.527, 'duration': 4.323}, {'end': 1053.933, 'text': "so now what i'll do is i will start off with the distance array.", 'start': 1049.85, 'duration': 4.083}], 'summary': 'Using a directed graph with 5 nodes and 5 edges, 4 iterations are needed to compute a distance array.', 'duration': 55.346, 'max_score': 998.587, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc998587.jpg'}, {'end': 1144.782, 'src': 'embed', 'start': 1110.748, 'weight': 1, 'content': [{'end': 1114.75, 'text': 'so one goes as one, so go and update one as one.', 'start': 1110.748, 'duration': 4.002}, {'end': 1121.585, 'text': 'perfect. so in one iteration, at the end of the day This one was updated.', 'start': 1114.75, 'duration': 6.835}, {'end': 1123.406, 'text': 'So first iteration, done.', 'start': 1121.705, 'duration': 1.701}, {'end': 1126.368, 'text': "Now let's talk about the next iteration.", 'start': 1124.607, 'duration': 1.761}, {'end': 1129.931, 'text': 'Next iteration, what is 3? Infinity.', 'start': 1127.189, 'duration': 2.742}, {'end': 1133.194, 'text': 'Next iteration, what is 2? Infinity.', 'start': 1130.672, 'duration': 2.522}, {'end': 1137.577, 'text': 'Next iteration, what is 1? 1.', 'start': 1133.714, 'duration': 3.863}, {'end': 1139.578, 'text': 'So 1 plus 1, 2.', 'start': 1137.577, 'duration': 2.001}, {'end': 1142.04, 'text': 'So this will be updated to 2.', 'start': 1139.578, 'duration': 2.462}, {'end': 1144.782, 'text': "So let's update it to 2.", 'start': 1142.04, 'duration': 2.742}], 'summary': 'In one iteration, the value was updated from 1 to 2.', 'duration': 34.034, 'max_score': 1110.748, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc1110748.jpg'}, {'end': 1202.799, 'src': 'embed', 'start': 1172.71, 'weight': 0, 'content': [{'end': 1179.205, 'text': "in the third iteration we don't have three, But the second iteration gave me 2..", 'start': 1172.71, 'duration': 6.495}, {'end': 1186.811, 'text': 'When I go to relax the next edge, this 2, who has a value of 2 plus 1, will go ahead and update 3.', 'start': 1179.205, 'duration': 7.606}, {'end': 1188.793, 'text': 'So 3 will be updated to 3.', 'start': 1186.811, 'duration': 1.982}, {'end': 1190.434, 'text': 'Perfect Amazing.', 'start': 1188.793, 'duration': 1.641}, {'end': 1192.256, 'text': 'So I see this is done.', 'start': 1190.975, 'duration': 1.281}, {'end': 1194.698, 'text': 'Next, no more updates, no more relaxation.', 'start': 1192.516, 'duration': 2.182}, {'end': 1196.079, 'text': 'Third iteration done.', 'start': 1195.318, 'duration': 0.761}, {'end': 1197.776, 'text': 'Third iteration.', 'start': 1197.216, 'duration': 0.56}, {'end': 1202.799, 'text': 'Now, what happened in the first? 0 updated 1.', 'start': 1198.397, 'duration': 4.402}], 'summary': 'In the third iteration, 3 was updated to 3. in the first iteration, 0 was updated to 1.', 'duration': 30.089, 'max_score': 1172.71, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc1172710.jpg'}], 'start': 897.666, 'title': 'Iterative value updates', 'summary': 'Discusses an optimization algorithm that iteratively updates values, with each value being updated n minus 1 times, resulting in overall updates for all values on each iteration. it also explains performing n-1 iterations in a directed graph, using a 5-node graph as an example, and how the values get updated in each iteration.', 'chapters': [{'end': 948.848, 'start': 897.666, 'title': 'Optimization algorithm overview', 'summary': 'Discusses an algorithm that iteratively updates values, with each value updated n minus 1 times, leading to overall updates for all values on each iteration.', 'duration': 51.182, 'highlights': ['The algorithm involves updating values iteratively, with each value being updated n minus 1 times, leading to overall updates for all values on each iteration.', 'The process involves updating values in a sequence, with each value updating the next, eventually resulting in updates for all values.', 'The reason for updating each value n minus 1 times is not explicitly stated, prompting the question of why this specific number of iterations is chosen.']}, {'end': 1220.502, 'start': 948.848, 'title': 'N-1 iterations in directed graph', 'summary': 'Explains the intuition behind performing n-1 iterations in a directed graph, with an example of a graph with 5 nodes requiring 4 iterations and how the values get updated in each iteration.', 'duration': 271.654, 'highlights': ['The chapter explains the intuition behind performing n-1 iterations in a directed graph The explanation focuses on understanding the rationale behind conducting n-1 iterations in the context of a directed graph.', 'Example of a graph with 5 nodes requiring 4 iterations An example is provided where a graph with 5 nodes necessitates 4 iterations, illustrating the practical application of n-1 iterations.', "Explanation of how the values get updated in each iteration The process of value updates in each iteration is detailed, demonstrating the progressive updating of values based on the previous iteration's results."]}], 'duration': 322.836, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc897666.jpg', 'highlights': ['The algorithm involves updating values iteratively, with each value being updated n minus 1 times, leading to overall updates for all values on each iteration.', 'The process involves updating values in a sequence, with each value updating the next, eventually resulting in updates for all values.', 'The chapter explains the intuition behind performing n-1 iterations in a directed graph The explanation focuses on understanding the rationale behind conducting n-1 iterations in the context of a directed graph.', 'Example of a graph with 5 nodes requiring 4 iterations An example is provided where a graph with 5 nodes necessitates 4 iterations, illustrating the practical application of n-1 iterations.']}, {'end': 1653.625, 'segs': [{'end': 1292.405, 'src': 'embed', 'start': 1265.045, 'weight': 0, 'content': [{'end': 1271.313, 'text': 'the thought process, the intuition and the clarity about an algorithm is very, very, very important.', 'start': 1265.045, 'duration': 6.268}, {'end': 1275.877, 'text': 'now the question is how to detect negative cycle again.', 'start': 1271.313, 'duration': 4.564}, {'end': 1284.181, 'text': 'thought process, since I knew negative cycle means if I keep on, because this will give you minus one again.', 'start': 1275.877, 'duration': 8.304}, {'end': 1286.442, 'text': 'if I rotate, it will give you another minus one.', 'start': 1284.181, 'duration': 2.261}, {'end': 1292.405, 'text': 'if I rotate another minus one on every rotation, you are decreasing the path value by minus one.', 'start': 1286.442, 'duration': 5.963}], 'summary': 'Understanding algorithm intuition is crucial. detecting negative cycle involves decreasing path value by -1 on rotation.', 'duration': 27.36, 'max_score': 1265.045, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc1265045.jpg'}, {'end': 1406.14, 'src': 'embed', 'start': 1374.738, 'weight': 1, 'content': [{'end': 1375.899, 'text': "Now it's time to code it up.", 'start': 1374.738, 'duration': 1.161}, {'end': 1383.044, 'text': "So as usual, I'll be coding the C++ on the right, and you can figure out the exact similar Java solution on the left.", 'start': 1375.959, 'duration': 7.085}, {'end': 1391.129, 'text': 'So given a weighted, directed, and a connected graph of V, vertices, and E edges, find the shortest distance of all the vertex from the source.', 'start': 1383.564, 'duration': 7.565}, {'end': 1392.39, 'text': "So they'll be giving you a source.", 'start': 1391.329, 'duration': 1.061}, {'end': 1398.854, 'text': 'If the graph contains a negative cycle, then return an array consisting of only minus one.', 'start': 1392.89, 'duration': 5.964}, {'end': 1406.14, 'text': "And I think they've also stated if you cannot reach anyone, you have to assign it with 1 e 8.", 'start': 1399.595, 'duration': 6.545}], 'summary': 'Code c++ to find shortest distance in a weighted, directed graph with v vertices, e edges. handle negative cycles and unreachable vertices.', 'duration': 31.402, 'max_score': 1374.738, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc1374738.jpg'}, {'end': 1634.208, 'src': 'embed', 'start': 1605.241, 'weight': 2, 'content': [{'end': 1609.484, 'text': 'if the graph has negative edges or the cycles, what will you do?', 'start': 1605.241, 'duration': 4.243}, {'end': 1611.705, 'text': 'so it might be a follow-up question on dextra.', 'start': 1609.484, 'duration': 2.221}, {'end': 1618.891, 'text': 'so very, very important, but i do not think the questions like you will find questions straightly related to bellman ford,', 'start': 1611.705, 'duration': 7.186}, {'end': 1623.958, 'text': "because most of the questions are solved using dykstra's algorithm in shortest path.", 'start': 1618.891, 'duration': 5.067}, {'end': 1625.701, 'text': 'so, guys, i hope you have understood everything.', 'start': 1623.958, 'duration': 1.743}, {'end': 1630.327, 'text': 'so, just in case you did, please, please, please make sure you like this video, and i was checking our statistics.', 'start': 1625.701, 'duration': 4.626}, {'end': 1634.208, 'text': 'half of our audience does not subscribes us.', 'start': 1631.385, 'duration': 2.823}], 'summary': "Emphasizes importance of dijkstra's algorithm for shortest path; encourages audience to subscribe.", 'duration': 28.967, 'max_score': 1605.241, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc1605241.jpg'}], 'start': 1220.502, 'title': 'Bellman-ford algorithm', 'summary': "Explains the bellman-ford algorithm, its intuition, implementation, and relevance in negative edge weights or cycles, with a time complexity of o(v*e) and space complexity of o(v), as an alternative to dijkstra's algorithm.", 'chapters': [{'end': 1653.625, 'start': 1220.502, 'title': 'Bellman-ford algorithm', 'summary': "Explains the bellman-ford algorithm, outlining its intuition, implementation, time complexity, and relevance in the presence of negative edge weights or cycles, with a time complexity of o(v*e) and space complexity of o(v), offering an alternative to dijkstra's algorithm in such scenarios.", 'duration': 433.123, 'highlights': ['The chapter explains the intuition behind the Bellman-Ford algorithm, emphasizing the importance of thought process, intuition, and clarity about the algorithm, and the significance of understanding why the number of iterations is n minus one. ', "The algorithm's implementation is detailed, covering the process of detecting negative cycles and the steps involved in finding the shortest distance of all vertices from the source in a weighted, directed, and connected graph. The process involves iterating v-1 times for relaxation and handling negative cycles.", "The time complexity of the Bellman-Ford algorithm is discussed, highlighting its time complexity of O(V*E) and its relevance when dealing with graphs containing negative edge weights or cycles, where Dijkstra's algorithm may not work. Time complexity: O(V*E)"]}], 'duration': 433.123, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/0vVofAhAYjc/pics/0vVofAhAYjc1220502.jpg', 'highlights': ['The chapter explains the intuition behind the Bellman-Ford algorithm, emphasizing the importance of thought process, intuition, and clarity about the algorithm, and the significance of understanding why the number of iterations is n minus one.', "The algorithm's implementation is detailed, covering the process of detecting negative cycles and the steps involved in finding the shortest distance of all vertices from the source in a weighted, directed, and connected graph. The process involves iterating v-1 times for relaxation and handling negative cycles.", "The time complexity of the Bellman-Ford algorithm is discussed, highlighting its time complexity of O(V*E) and its relevance when dealing with graphs containing negative edge weights or cycles, where Dijkstra's algorithm may not work. Time complexity: O(V*E)"]}], 'highlights': ["Bellman Ford algorithm can detect negative cycles, unlike Dijkstra's algorithm.", "The algorithm's capability to detect negative cycles helps in determining path weights.", 'The Bellman-Ford algorithm is designed to identify negative cycles in a graph.', 'The algorithm requires relaxing all the edges to find the shortest path.', 'Relaxing all edges n minus 1 times sequentially to calculate the shortest path.', 'The process of distance relaxation in graphs involves iterating through the edges and updating the distance values until the shortest path from the source node to all other nodes is obtained.', "The absence of negative cycles in the graph ensures the algorithm's efficacy in determining the shortest path from the source node to all other nodes.", 'The algorithm involves updating values iteratively, with each value being updated n minus 1 times, leading to overall updates for all values on each iteration.', 'The process involves updating values in a sequence, with each value updating the next, eventually resulting in updates for all values.', 'The chapter explains the intuition behind performing n-1 iterations in a directed graph The explanation focuses on understanding the rationale behind conducting n-1 iterations in the context of a directed graph.', 'Example of a graph with 5 nodes requiring 4 iterations An example is provided where a graph with 5 nodes necessitates 4 iterations, illustrating the practical application of n-1 iterations.', 'The chapter explains the intuition behind the Bellman-Ford algorithm, emphasizing the importance of thought process, intuition, and clarity about the algorithm, and the significance of understanding why the number of iterations is n minus one.', "The algorithm's implementation is detailed, covering the process of detecting negative cycles and the steps involved in finding the shortest distance of all vertices from the source in a weighted, directed, and connected graph. The process involves iterating v-1 times for relaxation and handling negative cycles.", "The time complexity of the Bellman-Ford algorithm is discussed, highlighting its time complexity of O(V*E) and its relevance when dealing with graphs containing negative edge weights or cycles, where Dijkstra's algorithm may not work. Time complexity: O(V*E)"]}