HDU1595 find the longest of the shortest

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题目来源:http://acm.hdu.edu.cn/showproblem.php?pid=1595


find the longest of the shortest

Time Limit: 1000/5000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3310    Accepted Submission(s): 1225


Problem Description
Marica is very angry with Mirko because he found a new girlfriend and she seeks revenge.Since she doesn't live in the same city, she started preparing for the long journey.We know for every road how many minutes it takes to come from one city to another.
Mirko overheard in the car that one of the roads is under repairs, and that it is blocked, but didn't konw exactly which road. It is possible to come from Marica's city to Mirko's no matter which road is closed.
Marica will travel only by non-blocked roads, and she will travel by shortest route. Mirko wants to know how long will it take for her to get to his city in the worst case, so that he could make sure that his girlfriend is out of town for long enough.Write a program that helps Mirko in finding out what is the longest time in minutes it could take for Marica to come by shortest route by non-blocked roads to his city.
 

Input
Each case there are two numbers in the first row, N and M, separated by a single space, the number of towns,and the number of roads between the towns. 1 ≤ N ≤ 1000, 1 ≤ M ≤ N*(N-1)/2. The cities are markedwith numbers from 1 to N, Mirko is located in city 1, and Marica in city N.
In the next M lines are three numbers A, B and V, separated by commas. 1 ≤ A,B ≤ N, 1 ≤ V ≤ 1000.Those numbers mean that there is a two-way road between cities A and B, and that it is crossable in V minutes.
 

Output
In the first line of the output file write the maximum time in minutes, it could take Marica to come to Mirko.
 

Sample Input
5 61 2 41 3 32 3 12 4 42 5 74 5 16 71 2 12 3 43 4 44 6 41 5 52 5 25 6 55 71 2 81 4 102 3 92 4 102 5 13 4 73 5 10
 

Sample Output
111327

O(N²)的Dijkstra算法。在第一次用Dijkstra算法时记录到达每个节点的最短路上的前一个节点,这样就可以找出最短路径。

枚举每一条边,依次删除后跑Dijkstra,这样就可求出最长最短路。


代码:

#include <cstdio>#include <cstdlib>#include <algorithm>#include <iostream>#include <cstring>using namespace std;const int inf=1e9;int g[1001][1010];int dis[1001];bool vis[1001];int p[1001];int n,m;void dijkstra(){for(int i=2;i<=n;i++)dis[i]=inf;dis[1]=0;memset(vis,0,sizeof(vis));for(int i=1;i<=n;i++){int mark=-1,tot=inf;for(int j=1;j<=n;j++){if(vis[j]==0){if(tot>dis[j]){tot=dis[j];mark=j;}}}vis[mark]=1;for(int j=1;j<=n;j++){dis[j]=min(dis[j],dis[mark]+g[mark][j]);}}}int main(){ios::sync_with_stdio(false);while(cin>>n>>m){for(int i=1;i<=n;i++){for(int j=1;j<=n;j++){g[i][j]=i==j?0:inf;}}for(int i=1;i<=m;i++){int a,b,v;cin>>a>>b>>v;g[a][b]=g[b][a]=min(g[a][b],v);}for(int i=2;i<=n;i++)dis[i]=inf;dis[1]=0;memset(vis,0,sizeof(vis));for(int i=1;i<=n;i++){int mark=-1,tot=inf;for(int j=1;j<=n;j++){if(vis[j]==0){if(tot>dis[j]){tot=dis[j];mark=j;}}}vis[mark]=1;for(int j=1;j<=n;j++){if(dis[j]>dis[mark]+g[mark][j]){p[j]=mark;dis[j]=dis[mark]+g[mark][j];}}}int tot=0;for(int i=n;i!=1;i=p[i]){int t=g[i][p[i]];g[i][p[i]]=g[p[i]][i]=inf;dijkstra();g[i][p[i]]=g[p[i]][i]=t;if(dis[n]!=inf)tot=max(tot,dis[n]);}cout<<tot<<endl;}return 0;}