uva10099+uvauva10048-优快云博客

本文介绍了一种使用Floyd算法解决图论中寻找路径问题的方法，包括两个实例：一是求解最小的最大值问题，二是求解最大的最小值问题。通过两道UVa在线评测系统的题目进行演示，展示了如何用Floyd算法更新路径矩阵。

题意：一个求最小的最大值，一个求最大的最小值，思路一样

思路：floyd

代码：

uva10048:

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
int c, s, q;
const int inf = 0x3f3f3f3f;
int mmap[105][105];
void floyd() {
	for(int i=1; i<=c; i++)
		for(int j=1; j<=c; j++)
			for(int z=1; z<=c; z++) {
				mmap[j][z] = min(mmap[j][z], max(mmap[j][i], mmap[i][z]));
			}

}
int main() {
	int a,b,d;
	int cas = 1;
	while(scanf("%d%d%d", &c, &s, &q) && (c+q+s)) {
		memset(mmap, inf, sizeof(mmap));
		for(int i=0; i<s; i++) {
			scanf("%d%d%d", &a, &b, &d);
			
			mmap[a][b] = mmap[b][a] = d;
		}
		floyd();
		if(cas != 1)
		printf("\n");
	
		printf("Case #%d\n", cas++);
		for(int i=0; i<q; i++) {
			scanf("%d%d", &a, &b);
			if(mmap[a][b] != inf)
			printf("%d\n", mmap[a][b]);
			else printf("no path\n");
		}

	}
	return 0;

uva10099:

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int maxn = 105;
int f,s;
int q,d,t;
int mmap[maxn][maxn];
void floyd() {
	for(int k=1; k<=f; k++)
		for(int i=1; i<=f; i++)
			for(int j=1; j<=f; j++) {
				mmap[i][j] = max(mmap[i][j], min(mmap[i][k], mmap[k][j]));
			}
}

int main() {
	int a, b, c;
	int cas = 1;
	while(scanf("%d%d", &f, &s) && (f+s)) {
		memset(mmap, 0, sizeof(mmap));
		for(int i=0; i<s; i++) {
			scanf("%d%d%d", &a, &b, &c);
			mmap[a][b] = mmap[b][a] = c;
		}
		scanf("%d%d%d", &q, &d, &t);
		floyd();
		a = 0;
		if(t%mmap[q][d]) a = 1;
		int ans = t/(mmap[q][d]-1)+a;
		printf("Scenario #%d\n", cas++);
		printf("Minimum Number of Trips = %d\n", ans);
		printf("\n");

	}
		
			

	return 0;
}