Dijkstra's Algorithm
Reference:
Example:
#include <limits.h>
#define SIZE 9
int w[SIZE][SIZE] = { { 0, 4, 0, 0, 0, 0, 0, 8, 0 }, // 0 : can't reach this vertex
{ 4, 0, 8, 0, 0, 0, 0, 11, 0 }, // >0 : cost of reach
{ 0, 8, 0, 7, 0, 4, 0, 0, 2 },
{ 0, 0, 7, 0, 9, 14, 0, 0, 0 },
{ 0, 0, 0, 9, 0, 10, 0, 0, 0 },
{ 0, 0, 4, 0, 10, 0, 2, 0, 0 },
{ 0, 0, 0, 14, 0, 2, 0, 1, 6 },
{ 8, 11, 0, 0, 0, 0, 1, 0, 7 },
{ 0, 0, 2, 0, 0, 0, 6, 7, 0 }};
int minDistance(int dist[], bool sptSet[])
{
int min = INT_MAX, min_index;
for (int v = 0; v < SIZE; v++)
if (!sptSet[v] && dist[v] <= min) {
min = dist[v];
min_index = v;
}
return min_index;
}
void find_path(int *parent, int x) // print all shortest paths from source vertex to x
{
if (x != parent[x]) { // recursive until find source vertex
find_path(parent, parent[x]);
printf(" -> ");
}
printf("%d", x);
}
void printSolution(int dist[], int *parent, int nSize, int src)
{
printf("Source Vertex\tTarget Vertex\tDistance from Source\tShortest Path\n");
for (int i = 0; i < nSize; i++) {
printf("%d\t\t%d\t\t%d\t\t\t", src, i, dist[i]);
find_path(parent, i);
printf("\n");
}
}
void dijkstra(int graph[SIZE][SIZE], int src)
{
int parent[SIZE]; //record shortest path
int dist[SIZE]; // The output array. dist[i] will hold the shortest distance from src to i
bool sptSet[SIZE]; // sptSet[i] will true if vertex i is included in shortest
// path tree or shortest distance from src to i is finalized
for (int i = 0; i < SIZE; i++) // Initialize all distances as INFINITE and stpSet[] as false
dist[i] = INT_MAX, sptSet[i] = false;
dist[src] = 0; //set dist of source vertex as zero, Distance of source vertex from itself is always 0
parent[src] = src; //set parent of source vertex as itself
// Find shortest path for all vertices
for (int count = 0; count < SIZE - 1; count++)
{
int u = minDistance(dist, sptSet); // Pick the minimum distance vertex from the set of vertices not
// yet processed. u is always equal to src in first iteration.
sptSet[u] = true; // Mark the picked vertex as processed
// Update dist value of the adjacent vertices of the picked vertex.
for (int v = 0; v < SIZE; v++) {
// Update dist[v] only if is not in sptSet, there is an edge from
// u to v, and total weight of path from src to v through u is
// smaller than current value of dist[v]
if (!sptSet[v] && graph[u][v] && dist[u] != INT_MAX
&& dist[u] + graph[u][v] < dist[v]) {
dist[v] = dist[u] + graph[u][v];
parent[v] = u;
}
}
}
// print the constructed distance array and shortest path
printSolution(dist, parent, SIZE, src);
}
int main()
{
int source;
source = 0;
dijkstra(w, source);
return 0;
}
output:
source vertex = 0
Source Vertex Target Vertex Distance from Source Shortest Path
0 0 0 0
0 1 4 0 -> 1
0 2 12 0 -> 1 -> 2
0 3 19 0 -> 1 -> 2 -> 3
0 4 21 0 -> 7 -> 6 -> 5 -> 4
0 5 11 0 -> 7 -> 6 -> 5
0 6 9 0 -> 7 -> 6
0 7 8 0 -> 7
0 8 14 0 -> 1 -> 2 -> 8
source vertex = 8
Source Vertex Target Vertex Distance from Source Shortest Path
8 0 14 8 -> 2 -> 1 -> 0
8 1 10 8 -> 2 -> 1
8 2 2 8 -> 2
8 3 9 8 -> 2 -> 3
8 4 16 8 -> 2 -> 5 -> 4
8 5 6 8 -> 2 -> 5
8 6 6 8 -> 6
8 7 7 8 -> 7
8 8 0 8