POJ 3613 Cow Relays 倍增Floyd

求[S,T]间长度为k的最短路长度。
考虑Floyd算法。发现Floyd每枚举一个中间点，最短路长度就可能翻倍。
利用这个性质，使用类似矩阵乘法的方式计算即可。

#include 
#include 
using namespace std;
#define FOR(i,j,k) for(i=j;i<=k;i++)

int num[1005],size=0;
int get(int i) {
    return num[i]?num[i]:num[i]=++size;
}

struct Matrix {
    int a[105][105];
    Matrix(){int i,j;FOR(i,0,104)FOR(j,0,104)a[i][j]=0x7ffffff;}
} root;

Matrix floyd(Matrix a, Matrix b) {
    Matrix c; int i, j, k;
    FOR(i,1,size) FOR(j,1,size) FOR(k,1,size)
        c.a[i][j]=min(c.a[i][j],a.a[i][k]+b.a[k][j]);
    return c;
}

Matrix quick(Matrix a, int b) {
    Matrix ans; int c=0;
    for(;b;b/=2,a=floyd(a,a)) if(b&1)
        if(!c) { ans=a;c=1; }
        else ans=floyd(ans,a);
    return ans;
}

int main() {
    int n, t, s, e, i, z, x, y;
    scanf("%d%d%d%d", &n, &t, &s, &e);
    memset(num,0,sizeof num);
    s=get(s),e=get(e);
    FOR(i,1,t) {
        scanf("%d%d%d", &z, &x, &y);
        x=get(x),y=get(y);
        root.a[x][y]=root.a[y][x]=z;
    }
    Matrix a=quick(root,n);
    printf("%d",a.a[s][e]);

    return 0;
}

Cow Relays

Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 6499 Accepted: 2536

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