Chapter 4

1. Chapter 4 • 4 Basic Algorithms • Binary Search • Depth-First Search • Breadth-First Search • Topological Sort

2. Advanced Algorithms • DFS  Testing Whether a Graph is Connected • BFS  Finding the shorted path • BFS or DFS  Solving a maze.

3. Binary Search int bsearch(L, i , j, key) { while (i <= j) { k = (i+j)/2; if (key == L[k]) return k; // Found if (key < L[k]) j = k-1; else i = k+1; } return –1 // Not found } key = 31 i k j 57 i j k 57

4. adj is an arry of linked lists: adj[0]  2  3  null adj[1]  1  4  null adj[2]  1  4  ... trav is a linked list dfs (adj, start) { n = adj.size(); for i = 0 to n-1 visit[i] = false; dfs_rec(adj, start); } dfs_rec (adj, cur) { print(cur); visit[cur] = true; trav = adj[cur]; while (trav != null) { v = trav.vertex(); if (!visit[v]) dfs_rec(adj, v); trav = trav.next(); } } DFS

5. q is an initially empty queue adj is an array of linked lists trav is a linked list visit is an array of bool bfs (adj, start) { n = adj.size(); for i = 0 to n-1 { visit[i] = false; print(start); visit[start] = true; q.push(start); while (!q.empty()) { cur = q.pop(); trav = adj[cur]; while (trav != null) { v = trav.vertex(); if (!visit[v]) { print(v) visit[v] = true; q.push(v); } trav = trav.next(); } } } BFS

6. Maze Problem S F

7. Maze Problem S B C A D E G L I H M K J N W X O V Y Z U P Q T R F

8. Maze Problem S A B C D E G L I H M K J N W X Y O V Z U P Q R T F

9. Maze Problem S A B C D E G L I H M K J N W X Y O V Z U P Q R T F

10. Maze Problem S A B C D E G L I H M K J N W X Y O V Z U P Q R T F

11. ts is a stack; topsort (adj, ts) { n = adj.size(); k = n; for i = 0 to n-1 visit[i] = false; for i = 0 to n-1 if (!visit[i]) tsr(adj,i,ts); } tsr (adj, cur, ts) { visit[cur] = true; trav = adj[cur]; while (trav != null) { v = trav.vertex(); if (!visit[v]) tsr(adj, v, ts); trav = trav.next(); } ts.push(cur); } Topological Sort