1. 程式人生 > >1416 Warfare And Logistics ( 最短路樹)

1416 Warfare And Logistics ( 最短路樹)

c比較容易求,cc如果一條邊一條邊列舉的話,每刪除一條邊,就要再求一遍任意兩點的最短路,無論是跑一遍floyd或n-1遍dij時間複雜度都很大,我們可以用最短路樹來優化一下,只有刪除最短路樹上的邊,我們再重新求最短路,刪除不是最短路樹上的邊,任意兩點的最短路是不變的,這樣時間複雜度就降了下來,因為每一個源點的最短路樹只有n-1條,求最短路樹只需要記錄一下路徑就可以了

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MAXN = 205;
const int MAXM = 2005;
const int INF = 0x3f3f3f3f;
struct Edge
{
    int to,Next,w;
}edge[MAXM];
int tot,head[MAXN];
int dis[MAXN][MAXN],pre[MAXN][MAXN];
int a[MAXN];
bool vis[MAXN];
void init()
{
    tot = 0;
    memset(head,-1,sizeof(head));
    memset(pre,0,sizeof(pre));
    memset(a,0,sizeof(a));
}
void addedge(int u,int v,int w)
{
    edge[tot].to = v;
    edge[tot].w = w;
    edge[tot].Next = head[u];
    head[u] = tot++;
}
struct node
{
    int u;
    int dis;
    node(){}
    node(int _u,int _dis)
    {
        u = _u;
        dis = _dis;
    }
    bool operator < (const struct node& a) const
    {
        return dis > a.dis;
    }
};
int n,l;
void Dijkstra(int s)
{
    struct node t;
    for(int i = 1; i <= n; i++) {
        vis[i] = false;
        dis[s][i] = INF;
    }
    dis[s][s] = 0;
    priority_queue<node> pq;
    pq.push(node(s,0));
    while(!pq.empty()) {
        t = pq.top();
        pq.pop();
        int u = t.u;
        if(vis[u]) continue;
        vis[u] = true;
        for(int i = head[u]; i != -1; i = edge[i].Next) {
            int v = edge[i].to;
            if(dis[s][v] > dis[s][u] + edge[i].w) {
                pre[s][v] = u;
                dis[s][v] = dis[s][u] + edge[i].w;
                pq.push(node(v,dis[s][v]));
            }
        }
    }
    for(int i = 1; i <= n; i++) {
        if(dis[s][i] >= INF) {
            dis[s][i] = l;
        }
    }
}
int main(void)
{
    int m,u,v,w;
    int ans1,ans2;
    while(scanf("%d %d %d",&n,&m,&l) != EOF) {
        ans1 = ans2 = 0;
        init();
        while(m--) {
            scanf("%d %d %d",&u,&v,&w);
            addedge(u,v,w);
            addedge(v,u,w);
        }
        for(int i = 1; i <= n; i++) {
            Dijkstra(i);
        }
        for(int i = 1; i <= n; i++) {
            for(int j = 1; j <= n; j++) {
                a[i] += dis[i][j];
                ans1 += dis[i][j];
            }
        }
        printf("%d ",ans1);
        for(int i = 0; i < tot; i++) {
            for(int j = head[i]; j != -1; j = edge[j].Next) {
                int res = 0;
                u = i,v = edge[j].to;
                for(int k = 1; k <= n; k++) {
                    if(pre[k][v] != u && pre[k][u] != v) {
                        res += a[k];
                        continue;
                    }
                    int w = edge[j].w;
                    edge[j].w = INF;
                    edge[j ^ 1].w = INF;
                    Dijkstra(k);
                    for(int p = 1; p <= n; p++) {
                        res += dis[k][p];
                    }
                    edge[j].w = w;
                    edge[j ^ 1].w = w;
                    Dijkstra(k);
                }
                ans2 = max(ans2,res);
            }
        }
        printf("%d\n",ans2);
    }
    return 0;
}
/*
*/