Luogu P1462 通往奥格瑞玛的道路

Posted 2020-12-02 Mystical-W

思路

使得最大值最下，这不是典型的二分答案吗

二分最大的费用

后面用SPFA实现，只需要在进行松弛操作的时候进行一下调整

使得所有沿途的点的话费都小于这个二分出来的花费

 

代码

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <cstring>
#define MAXN 10007
#define MAXm 100007
#define INF 2147483647
#define int long long

using namespace std;

int n, m, b, f[MAXN], first[MAXN], dis[MAXN], s = 1;
int u[MAXm], v[MAXm], w[MAXm], next[MAXm], maxn, Ans;
bool vis[MAXN];
deque<int> Q;

bool SPFA(int s, int p) {
        if(f[1] >= p) return false;
        memset(vis, false, sizeof(vis));
        for(int i=1; i<=n; i++) {dis[i] = INF;} dis[s] = 0;
        while(!Q.empty()) {Q.pop_front();}
        Q.push_front(s); vis[s] = 1;
        while(!Q.empty()) {
                int x = Q.front();
                int k = first[Q.front()];
                Q.pop_front();
                while(k != -1) {
                        if(dis[v[k]] > dis[u[k]]+w[k]&&f[v[k]] <= p) {
                                dis[v[k]] = dis[u[k]]+w[k];
                                if(!vis[v[k]]) {
                                        vis[v[k]] = 1;
                                        if(dis[v[k]] > dis[x]) Q.push_back(v[k]);
                                        else Q.push_front(v[k]);
                                }
                        }
                        k = next[k];
                }
                vis[x] = 0;
        }
        if(dis[n] < b) return true;
        else return false;
}

main() {
        scanf("%lld%lld%lld", &n, &m, &b);
        for(int i=1; i<=n; i++) {scanf("%lld", &f[i]); maxn = max(maxn, f[i]);}
        memset(first, -1, sizeof(first));
        for(int i=1; i<=n; i++) {dis[i] = INF;} dis[s] = 0;
        for(int i=1; i<=2*m; i++) {
                scanf("%lld%lld%lld", &u[i], &v[i], &w[i]);
                next[i] = first[u[i]];
                first[u[i]] = i;
                i++;
                u[i] = v[i-1], v[i] = u[i-1], w[i] = w[i-1];
                next[i] = first[u[i]];
                first[u[i]] = i;
        }
        int l = 1, r = maxn;
        bool mark = false;
        while(l <= r) {
                int mid = (l+r)/2;
                if(SPFA(1, mid)) {
                        r = mid-1;
                        mark = true;
                }
                else l = mid+1;
        }
        if(mark == false) printf("AFK");
        else printf("%lld\n", l);
        return 0;
}