@pankajyd/

Least distance in Graph

This code prints least distance between two vertices v1 and v2 in a weighted graph.

Files
• main.c
main.c
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```
```/*
Input:
First line contains number of vertices(nv) and number of edges(ne)

Next 'ne' lines contains edge between v1 and v2 and the weight of the edge.

Last line contains vertices between distance is to be found.

e.g.
5 8
0 1 4
0 2 2
1 2 3
2 1 1
1 3 2
2 4 5
4 2 5
1 4 3
0 4

number of vertices nv = 5; number of edges ne = 8;
0 1 4: edge is from v1 to v2 with weight w = 4;

last line: v1 = 0; v2 = 4;
find least distance between v1 and v2;
*/

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>

typedef struct vertex{
int v;
int color;
int parent;
int d;
}vertex;

typedef struct list{
int v;
int w;
struct list* next;
}list;

typedef struct Heap{
vertex **A;
int size;
}Heap;

void swap(Heap *H, int i, int j){
vertex* tmp;
tmp = H->A[i];
H->A[i] = H->A[j];
H->A[j] = tmp;
}

void Heapify(Heap *H, int i){
int min_index = i;

if(2*i + 1 >= H->size){
return;
}
else{
if(H->A[i]->d > H->A[2*i + 1]->d){
min_index = 2*i + 1;
}
if(2*i + 2 < H->size && H->A[2*i + 2]->d < H->A[min_index]->d){
min_index = 2*i + 2;
}
if(min_index != i){
swap(H, i, min_index);
Heapify(H, min_index);
}
}
}

void Build_min_Heap(Heap *H){
int n = H->size;
for(int i = n/2; i >= 0; i--){
Heapify(H, i);
}
}

vertex* Extract_min(Heap* H){
vertex* min = H->A[0];
H->A[0] = H->A[H->size - 1];
H->size--;
Heapify(H, 0);
return min;
}

void Decrease_key(Heap *H, int i, int key){
H->A[i]->d = key;
while(i >0 && H->A[i]->d < H->A[(i-1)/2]->d){
H->A[i] = H->A[(i-1)/2];
i = (i-1)/2;
}
H->A[i]->d = key;
}

void BFS(vertex* V, vertex **pv, int v1, int v2, int nv){
//printf("\nIn BFS:\n");
////////////////////
V[v1].d = 0;
V[v1].parent = -1;
///////////////////

//////////////////////////////////////
Heap* H = (Heap*)malloc(sizeof(Heap));
H->A = pv;
H->size = nv;
Build_min_Heap(H);
//////////////////////////////////////
// printf("\nPrinting Min heap at start:\n");
// for(int i = 0; i < nv; i++){
// 	printf("(v = %d, d = %d)\n", pv[i]->v, pv[i]->d);
// }
//printf("\nHeap Size: %d.\n", H->size);
// vertex* u = Extract_min(H);
// printf("\nExtracted v = %d with d = %d", u->v, u->d);

while(H->size > 0){
vertex* u = Extract_min(H);
//printf("\nExtracted %d with d = %d", u->v, u->d);
u->color = 2;
}
}
if(H->size > 0){
Build_min_Heap(H);
}
}
}

int main(){
int t = 1;

vertex *V;
int v1, v2, w;
int nv, ne; //Number of vertices and edges
list *tmp;

vertex G[2500];
vertex* pv[2500];
V = G;

while(t--){
scanf("%d %d", &nv, &ne);

for(int i = 0; i < nv; i++){
V[i].v = i;
V[i].color = 0;
V[i].parent = -1;
V[i].d = 2147483647;
pv[i] = &V[i];
}

while(ne--){
scanf("%d %d %d", &v1, &v2, &w);

//Making Edge v1 to v2.
list* ptr = (list*)malloc(sizeof(list));
ptr->v = v2;
ptr->w = w;

}
else{
ptr->next = tmp;
}

}
scanf("%d %d", &v1, &v2);

//Remove multiline comment below to print the graph.

// printf("\nPrinting G:\n");
// for(int i = 0; i < nv; i++){
//     printf("%d: ", i);
//     }
//     printf("\n");
// }

// printf("V1: %d, v2: %d", v1, v2);
//CALL BFS
BFS(V, pv, v1, v2, nv);
printf("%d", V[v2].d - V[v1].d);
// int child = v2;
// int parent = V[v2].parent;
// printf("\n");
// while(parent != v1){
// 	printf("(w = %d)", V[child].d - V[parent].d);
// 	child = parent;
// 	parent = V[parent].parent;
// }
// printf("(w = %d)", V[child].d - V[parent].d);
}
return 0;
}```