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Computer Science

965Introduction to Single-Source Shortest Path Problems
966Dijkstra's Algorithm Overview and Intuition
967The Relaxation Operation
968Algorithm Initialization and Data Structures
969Dijkstra's Algorithm Step-by-Step Execution
970Correctness of Dijkstra's Algorithm
971Why Negative Edges Break Dijkstra's Algorithm
972Dijkstra's with Array-Based Priority Queue
973Dijkstra's with Binary Heap Priority Queue
974Dijkstra's with Fibonacci Heap
975Path Reconstruction from Predecessor Array
976Dijkstra's on Dense vs Sparse Graphs
977Early Termination for Single Target Queries
978Bidirectional Dijkstra's Algorithm
979Practical Applications of Dijkstra's Algorithm
980Bellman-Ford Overview and Motivation
981Bellman-Ford Algorithm Structure
982Edge Relaxation in Bellman-Ford
983The V-1 Iterations Principle
984Bellman-Ford Implementation
985Detecting Negative Weight Cycles
986Bellman-Ford Time Complexity
987Bellman-Ford vs Dijkstra Comparison
988SPFA: Shortest Path Faster Algorithm
989Bellman-Ford Applications
990All-Pairs Shortest Paths Problem
991Floyd-Warshall Core Idea
992Floyd-Warshall Dynamic Programming Formulation
993Floyd-Warshall Algorithm Implementation
994Floyd-Warshall Time and Space Complexity
995Handling Negative Edge Weights
996Detecting Negative Cycles
997Path Reconstruction in Floyd-Warshall
998Transitive Closure with Floyd-Warshall
999Floyd-Warshall vs Repeated Dijkstra
1000Introduction to A* Search

Computer Science

965Introduction to Single-Source Shortest Path Problems
966Dijkstra's Algorithm Overview and Intuition
967The Relaxation Operation
968Algorithm Initialization and Data Structures
969Dijkstra's Algorithm Step-by-Step Execution
970Correctness of Dijkstra's Algorithm
971Why Negative Edges Break Dijkstra's Algorithm
972Dijkstra's with Array-Based Priority Queue
973Dijkstra's with Binary Heap Priority Queue
974Dijkstra's with Fibonacci Heap
975Path Reconstruction from Predecessor Array
976Dijkstra's on Dense vs Sparse Graphs
977Early Termination for Single Target Queries
978Bidirectional Dijkstra's Algorithm
979Practical Applications of Dijkstra's Algorithm
980Bellman-Ford Overview and Motivation
981Bellman-Ford Algorithm Structure
982Edge Relaxation in Bellman-Ford
983The V-1 Iterations Principle
984Bellman-Ford Implementation
985Detecting Negative Weight Cycles
986Bellman-Ford Time Complexity
987Bellman-Ford vs Dijkstra Comparison
988SPFA: Shortest Path Faster Algorithm
989Bellman-Ford Applications
990All-Pairs Shortest Paths Problem
991Floyd-Warshall Core Idea
992Floyd-Warshall Dynamic Programming Formulation
993Floyd-Warshall Algorithm Implementation
994Floyd-Warshall Time and Space Complexity
995Handling Negative Edge Weights
996Detecting Negative Cycles
997Path Reconstruction in Floyd-Warshall
998Transitive Closure with Floyd-Warshall
999Floyd-Warshall vs Repeated Dijkstra
1000Introduction to A* Search

← Computer Science

Lesson 983 of 2,872·23. Shortest Path AlgorithmsPro lesson

The V-1 Iterations Principle

Why exactly V-1 iterations of edge relaxation guarantee shortest paths in graphs without negative cycles.

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