【图论补完计划】poj 3613(Floyd 快速幂)
Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 7463 | Accepted: 2922 |
Description
For their physical fitness program, N (2 ≤ N ≤ 1,000,000) cows have decided to run a relay race using the T (2 ≤ T ≤ 100) cow trails throughout the pasture.
Each trail connects two different intersections (1 ≤ I1i ≤ 1,000; 1 ≤ I2i ≤ 1,000), each of which is the termination for at least two trails. The cows know the lengthi of each trail (1 ≤ lengthi ≤ 1,000), the two intersections the trail connects, and they know that no two intersections are directly connected by two different trails. The trails form a structure known mathematically as a graph.
To run the relay, the N cows position themselves at various intersections (some intersections might have more than one cow). They must position themselves properly so that they can hand off the baton cow-by-cow and end up at the proper finishing place.
Write a program to help position the cows. Find the shortest path that connects the starting intersection (S) and the ending intersection (E) and traverses exactly N cow trails.
Input
* Line 1: Four space-separated integers: N, T, S, and E
* Lines 2..T+1: Line i+1 describes trail i with three space-separated integers: lengthi , I1i , and I2i
Output
* Line 1: A single integer that is the shortest distance from intersection S to intersection E that traverses exactly N cow trails.
Sample Input
2 6 6 4 11 4 6 4 4 8 8 4 9 6 6 8 2 6 9 3 8 9
Sample Output
10
#include <iostream> #include <cstdio> #include <cstring> #include <vector> #include <set> using namespace std; const int maxn=1005; const int inf=1e9; int mp[maxn][maxn]; int tmp[maxn][maxn]; int mmp[maxn][maxn]; int res[maxn][maxn]; int cord[maxn]; bool used[maxn]; int n,m,st,ed; int num; void init(){ for(int i=0;i<maxn;i++){ for(int j=0;j<maxn;j++){ mp[i][j]=inf; tmp[i][j]=inf; mmp[i][j]=inf; res[i][j]=inf; } res[i][i]=0; } } void floyd(int a[][maxn],int b[][maxn],int c[][maxn]){ for(int k=0;k<num;k++) for(int i=0;i<num;i++) for(int j=0;j<num;j++) if(a[cord[i]][cord[j]]>b[cord[i]][cord[k]]+c[cord[k]][cord[j]]) a[cord[i]][cord[j]]=b[cord[i]][cord[k]]+c[cord[k]][cord[j]]; } void trans(int a[][maxn],int b[][maxn]){ for(int i=0;i<num;i++){ for(int j=0;j<num;j++){ a[cord[i]][cord[j]]=b[cord[i]][cord[j]]; b[cord[i]][cord[j]]=inf; } } } void quick_mod(){ while(n){ if(n&1){ floyd(mmp,res,mp); trans(res,mmp); } floyd(tmp,mp,mp); trans(mp,tmp); n>>=1; } } int main(){ scanf("%d %d %d %d",&n,&m,&st,&ed); init(); for(int i=0;i<m;i++){ int u,v,w; scanf("%d %d %d",&w,&u,&v); if(!used[u]){ used[u]=1; cord[num++]=u; } if(!used[v]){ used[v]=1; cord[num++]=v; } mp[u][v]=mp[v][u]=min(mp[u][v],w); } quick_mod(); printf("%d\n",res[st][ed]); return 0; }