Depth First Search

A Bottom-up Programming algorithm for Path Finding. Uses a Stack

Algorithm

1. Base case is when S = D or S = NULL
2. Keep a list of nodes visited
3. If we are not the base case, then visit all Neighbors

Concepts

• DFS Ordering

Complexity

• Finding node:
  • Avg/Best/Worst: $O(V+E)$ where:
    • $V$ is the number of vertices
    • $E$ is the number of edges

DFS Program (Length of Path)

#include <stdio.h>
#include <stdlib.h>
 
int DFS(int adj_mat[5][5], int start_node, int end_node, int* marked){
  if (start_node == end_node){
    return 0;
  }
  marked[start_node] = 1;
  // perform BFS on all neighbours
  for (int i = 0; i < 5; i++){
    if (adj_mat[start_node][i] == 1){
      if (marked[i] == 0){
        return 1 + DFS(adj_mat, i, end_node, marked);
      }
    }
  }
  return 0;
  
}
 
int main(){
  // create adjacency matrix
  int adj_mat[5][5] = {
                      {0,1,0,1,1},
                      {1,0,1,1,1},
                      {1,1,0,0,0},
                      {1,1,0,0,0},
                      {0,1,0,0,0},
  };
  int adj_mat_2[5][5] = {
                      {0,1,1,1,0},
                      {1,0,0,1,0},
                      {1,0,0,1,0},
                      {1,1,1,0,1},
                      {0,0,0,1,0},
  };
 
  int marked[5] = {0,0,0,0,0};
  printf("DFS Length: %d\n", DFS(adj_mat_2, 0, 4, marked));
 
  return 0;
}