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C++ Program to Find SSSP (Single Source Shortest Path) in DAG (Directed Acyclic Graphs)
This is a C++ program to find SSSP (Single Source Shortest Path) in DAG (Directed Acyclic Graphs) using Dijkstra Algorithm to find out from the first node in graph to every other node with the shortest path length showed beside each pair of vertices.
Algorithm
Begin Take the elements of the graph as input. function shortestpath(): Initialize the variables a[i] = 1 d[i] = 0 s[i].from = 0 Initialize a loop for i = 0 to 3 do if b[0][i] == 0 continue else d[i] = b[0][i] s[i].from = 0 done done Initialize a loop while (c < 4) initialize min = INFINITY for i = 0 to 3 do if min <= d[i] or d[i] == 0 or a[i] == 1 continue else if min > d[i] min = d[i] done for loop int k = 0 to 3 do if (min == d[k]) t = k break else continue done Initialize a[t] = 1 for j = 0 to 3 if a[j] == 1 or b[t][j] == 0 continue else if a[j] != 1 if d[j] > (d[t] + b[t][j]) d[j] = d[t] + b[t][j] s[i].from = t done Increment c done For loop i = 0 to 3 Print minimum cost from node1 to node2. done End
Example
#include <iostream> using namespace std; #define INFINITY 9999 struct node { int from; } s[4]; int c = 0; void djikstras(int *a, int b[][4], int *d) { int i = 0, j, min, t; a[i] = 1; d[i] = 0; s[i].from = 0; for (i = 0; i < 4;i++) { if (b[0][i] == 0) { continue; } else { d[i] = b[0][i]; s[i].from = 0; } } while (c < 4) { min = INFINITY; for (i = 0; i < 4; i++) { if (min <= d[i] || d[i] == 0 || a[i] == 1) { continue; } else if (min > d[i]) { min = d[i]; } } for (int k = 0; k < 4; k++) { if (min == d[k]) { t = k; break; } else { continue; } } a[t] = 1; for (j = 0; j < 4; j++) { if (a[j] == 1 || b[t][j] == 0) { continue; } else if (a[j] != 1) { if (d[j] > (d[t] + b[t][j])) { d[j] = d[t] + b[t][j]; s[i].from = t; } } } c++; } for (int i = 0; i < 4; i++) { cout<<"from node "<<s[i].from<<" cost is:"<<d[i]<<endl; } } int main() { int a[4]; int d[4]; for(int k = 0; k < 4; k++) { d[k] = INFINITY; } for (int i = 0; i < 4; i++) { a[i] = 0; } int b[4][4]; for (int i = 0;i < 4;i++) { cout<<"enter values for "<<(i+1)<<" row"<<endl; for(int j = 0;j < 4;j++) { cin>>b[i][j]; } } djikstras(a,b,d); }
Output
enter values for 1 row 0 1 3 2 enter values for 2 row 2 1 3 0 enter values for 3 row 2 3 0 1 enter values for 4 row 1 3 2 0 from node 0 cost is:0 from node 0 cost is:1 from node 0 cost is:3 from node 0 cost is:2
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