Always enjoyed the 3 body problem. I feel it points to a lack of parallelism built-in to numerical analysis, which is mitigated by computation somewhat but it’s not native.
All-Pairs Shortest Paths – Floyd Warshall Algorithm is still the gold standard for shortest-path for all pairs.
But there are others which help us move closer to complete solutions – a nice list on the next link.
Insertion sort or Selection sort or Bubble sort
Merge Sort, Quicksort
Breadth First Search (BFS)
Depth First Search (DFS)
Lee algorithm | Shortest path in a Maze
Flood fill Algorithm
Inorder, Preorder, Postorder Tree Traversals
Floyd’s Cycle Detection Algorithm
Longest Increasing Subsequence
Topological Sorting in a DAG
Disjoint-Set Data Structure (Union-Find Algorithm)
Kruskal’s Algorithm for finding Minimum Spanning Tree
Single-Source Shortest Paths – Dijkstra’s Algorithm
All-Pairs Shortest Paths – Floyd Warshall Algorithm