文章目錄

• 測試資料
• 結果
• 實現
• 完整程式碼

測試資料

結果

實現

void PrintPath(int u, int v, int path[][maxSize]) {
	int mid;
	if (path[u][v]==-1) {
		//直接輸出，沒有中間點
		printf("<%c,%c> ", vertexs[u], vertexs[v]);
	} else { //有中間點
		mid = path[u][v];
		PrintPath(u, mid, path);
		PrintPath(mid, v, path);
	}
}
void Floyd(int n, int MGraph[
 
][maxSize], int path[][maxSize]) {
	int i,j,v;
	int A[maxSize][maxSize]; //最短路徑

	//初始化：A-1沒有考慮中間節點
	for (i=0; i<n; ++i) {
		for (j=0; j<n; j++) {
			A[i][j] = MGraph[i][j];
			path[i][j] = -1;
		}
	}
	//迴圈考慮中間節點
	for (v=0; v<n; ++v) {
		for (i=0; i<n; ++i) {
			for (j=0; j<n; ++j) {
				if (A[i]
 
[j]>A[i][v]+A[v][j]) {
					A[i][j] = A[i][v] + A[v][j];
					path[i][j] = v;
				}
			}
		}
	}
}

舉例：每一步執行

【工作原理】

完整程式碼

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

#define maxSize 10
#define INF 100

int MGraph[maxSize][maxSize]; //鄰接矩陣
char vertexs[maxSize]; //結點資訊

void PrintPath(int u, int v,
 
 int path[][maxSize]) {
	int mid;
	if (path[u][v]==-1) {
		//直接輸出，沒有中間點
		printf("<%c,%c> ", vertexs[u], vertexs[v]);
	} else { //有中間點
		mid = path[u][v];
		PrintPath(u, mid, path);
		PrintPath(mid, v, path);
	}
}
void Floyd(int n, int MGraph[][maxSize], int path[][maxSize]) {
	int i,j,v;
	int A[maxSize][maxSize]; //最短路徑

	//初始化：A-1沒有考慮中間節點
	for (i=0; i<n; ++i) {
		for (j=0; j<n; j++) {
			A[i][j] = MGraph[i][j];
			path[i][j] = -1;
		}
	}
	//迴圈考慮中間節點
	for (v=0; v<n; ++v) {
		for (i=0; i<n; ++i) {
			for (j=0; j<n; ++j) {
				if (A[i][j]>A[i][v]+A[v][j]) {
					A[i][j] = A[i][v] + A[v][j];
					path[i][j] = v;
				}
			}
		}
	}
}

int main() {
/*
7
ABCDEFG
10000 18 10000 10000 10000 19 18
18 10000 8 10000 10000 10000 20
10000 8 10000 20 10000 10000 10000
10000 10000 20 10000 9 16 15
10000 10000 10000 9 10000 3 10000
19 10000 10000 16 3 10000 15
18 20 10000 15 10000 15 10000
0 2
0 3
0 4
1 6
4 6
3 6
*/
	int n;
	int i,j;
	char tmp[maxSize+5];
	int path[maxSize][maxSize];
	int start,end;

	scanf("%d", &n); //結點數
	scanf("%s", tmp); //結點資訊
	for (i=0; i<n; i++)
		vertexs[i] = tmp[i];
	for (i=0; i<n; i++) { //矩陣
		for (j=0; j<n; j++) {
			scanf("%d", &MGraph[i][j]);
		}
	}

	Floyd(n, MGraph, path);

	//列印path陣列
	printf("- path陣列\n");
	printf("結點");
	for (i=0; i<n; i++) {
		printf("\t%c", vertexs[i]);
	}
	printf("\n");
	for (i=0; i<n; i++) {
		printf("%c\t", vertexs[i]);
		for (j=0; j<n; j++) {
			printf("%d\t", path[i][j]);
		}
		printf("\n");
	}
	//輸出最短路徑
	while (1) {
		printf("\n\n>>> 輸入起始點的下標（空格間隔）：");
		scanf("%d %d" , &start, &end); //輸入兩個測試的頂點，求v->w的最短路徑
		printf("%c->%c最短路徑：", vertexs[start], vertexs[end]);
		PrintPath(start, end, path);
	}
	

	return 0;
}