Concepts158
Bellman-Ford Algorithm
Bellman–Ford finds single-source shortest paths even when some edge weights are negative.
Dijkstra - Variations and Applications
Dijkstra’s algorithm can be adapted to track the second shortest path by keeping the best and second-best distances per vertex.
Topological Sort - DP on DAG
Topological sort orders vertices of a directed acyclic graph (DAG) so every edge goes from earlier to later, which is perfect for dynamic programming (DP).
Breadth-First Search (BFS)
Breadth-First Search (BFS) explores a graph level by level, visiting all vertices at distance d from the source before any at distance d+1.
Multi-Source BFS
Multi-source BFS explores an unweighted graph starting from several sources at once to compute the minimum distance to any source for every vertex.
0-1 BFS
0-1 BFS is a shortest path algorithm specialized for graphs whose edge weights are only 0 or 1.
Depth-First Search (DFS)
Depth-First Search (DFS) explores a graph by going as deep as possible along each path before backtracking.
2D Prefix Sum
A 2D prefix sum (also called an integral image) lets you compute the sum of any axis-aligned sub-rectangle in constant time after O(nm) preprocessing.
Prefix Sum and Difference Array
Prefix sums precompute running totals so any range sum [l, r] can be answered in O(1) time as prefix[r] - prefix[l-1].
Sorting Algorithms
Sorting arranges items into a chosen order so that searching, grouping, and further algorithms become faster and simpler.
Greedy Algorithms
Greedy algorithms build a solution step by step by always taking the best local choice available.
Ternary Search
Ternary search finds the maximum or minimum of a unimodal function on a line by probing two interior points and discarding one third of the interval each step.