/*
Program: all-pairs-shortest-path-v2.c (Report comments/bugs to chikh@yuntech.edu.tw)
Function: 修改all-pairs-shortest-path-v1.c使得A與Y矩陣能依圖內的頂點總數作配置，避免
		預先配置過大的100x100陣列空間而形成浪費 
*/

#include <stdio.h>
#include <stdlib.h>	/* for exit() */

#define Inf 		1073741823	/* 此為2^30-1的大數字，為本程式假設的無限大值；可改用limits.h定義的INT_MAX */

void init(int ***A, int ***Y)	/* 讀取輸入資料檔、設定相鄰矩陣，把相關資料結構作初始化 */ 
{
    FILE *fptr;
    int  i, j;
    int  weight, N;

    if ((fptr=fopen("shortestPath.dat","r")) == NULL) {	/* 開啟資料檔 */
        perror("shortestPath.dat");
        exit(1);
    }

    fscanf(fptr,"%d",&N);		/* 讀取圖形節點數 */
    
    *A = (int **)malloc((N+1)*sizeof(int *));
    *Y = (int **)malloc((N+1)*sizeof(int *));
    for (i = 0; i <= N; i++) {
        (*A)[i] = (int *)malloc((N+1)*sizeof(int));
        (*Y)[i] = (int *)malloc((N+1)*sizeof(int));
    }
	
    (*A)[0][0] = N;
    for (i = 1; i <= N; i++ )
        for (j = 1; j <= N; j++) {
			(*A)[i][j] = (i==j)? 0: Inf;	/* 初始化A[1..N][1..N]相鄰矩陣，所有元素均先預設為∞ */
            (*Y)[i][j] = (i==j)? i: -1; 
        } 
 
    while (fscanf(fptr,"%d %d %d",&i,&j,&weight) != EOF) { 
    	(*A)[i][j] = weight;       /* 讀取連接頂點i與j的邊的權重值 */
    	(*Y)[i][j] = i;
    }
	 
	fclose(fptr);
}

void floydWarshall(int ***A, int ***Y) 
{
	int i, j, k;
	int N = (*A)[0][0]; //無法使用sizeof(A[0])/sizeof(A[0][0])判讀維度，因以malloc()配置所得記憶體空間不具結構 

	for (k = 1; k <= N; k++) 
    	for (i = 1; i <= N; i++) 
      		for (j = 1; j <= N; j++) 
        		if ((*A)[i][k] + (*A)[k][j] < (*A)[i][j]) {
					(*A)[i][j] = (*A)[i][k] + (*A)[k][j];
					(*Y)[i][j] = (*Y)[k][j];
				} 
		//上面二層for迴圈用於檢視/修正每二頂點(i,j)之間有否經由k(中繼頂點)能得更小距離值 	
}

void printMatrix(int **A) 
{
	int i, j;
	int N = A[0][0]; 
	
  	for (i = 1; i <= N; i++) {
    	for (j = 1; j <= N; j++) {
      		if (A[i][j] == Inf)
        		printf("%5s","∞");
      		else
        		printf("%4d",A[i][j]);
    	}
    	printf("\n");
  	}
}

void backtrack(int **Y, int source, int dest) 
{
	int k = Y[source][dest];
	
	if (source == dest) {
		printf("頂點%d →",source);
		return;
	}
	if (Y[source][dest] == -1) {
        printf("頂點%d與%d之間沒有路徑存在  ",source,dest);
        return;
    }
    backtrack(Y,source,k);
    printf(" %d →",dest);
}

void traverseMatrix(int **Y) 
{
	int i, j, k, source, sink; 
	
	printf("\n源點 => ");
    scanf("%d",&source);
    printf("終點 => ");
    scanf("%d",&sink);
	
	printf("最短路徑：");
	backtrack(Y,source,sink);
	printf("\b\b  ");
}

void freeMemory(int **A, int **Y) 
{
	int i, N = A[0][0];
	
	for (i = 0; i <= N; i++) { 
		free(A[i]); 
		free(Y[i]); 
	} 
	free(A); 
	free(Y);
}

int main() {
	int **A, **Y;
            
	init(&A,&Y);			/* 讀取輸入資料檔、設定相鄰矩陣，並把相關資料結構作初始化 */
	floydWarshall(&A,&Y);
  	printMatrix(A);
  	traverseMatrix(Y);
  	freeMemory(A,Y);
  	
  	return 0;
}