Magical Girl Haze 南京网络赛2018

Posted 2021-01-03 wtsruvf

题意：

　　就是使不大于k条路的权值变为零后求最短路

解析：

　　d[i][j]表示使j条路变为权值后从起点到点i的最短路径

这题不能用spfa做  tle

#include <iostream>
#include <cstdio>
#include <sstream>
#include <cstring>
#include <map>
#include <cctype>
#include <set>
#include <vector>
#include <stack>
#include <queue>
#include <algorithm>
#include <cmath>
#include <bitset>
#define rap(i, a, n) for(int i=a; i<=n; i++)
#define rep(i, a, n) for(int i=a; i<n; i++)
#define lap(i, a, n) for(int i=n; i>=a; i--)
#define lep(i, a, n) for(int i=n; i>a; i--)
#define rd(a) scanf("%d", &a)
#define rlld(a) scanf("%lld", &a)
#define rc(a) scanf("%c", &a)
#define rs(a) scanf("%s", a)
#define MOD 2018
#define LL long long
#define ULL unsigned long long
#define Pair pair<int, int>
#define mem(a, b) memset(a, b, sizeof(a))
#define _  ios_base::sync_with_stdio(0),cin.tie(0)
//freopen("1.txt", "r", stdin);
using namespace std;
const int maxn = 100100, INF = 0x3f3f3f3f;
int n, m, k;
int vis[maxn][15];
int d[maxn][15];
map<int, map<int, int> > t;
struct edge{
    int u,v, d;
    edge(int u,int v,int d)
    {
        this->u = u;
        this->v = v;
        this->d = d;
    }

};
vector<edge> Edge;
vector<int> G[maxn<<1];
struct node{
    int u, d, y;
    node(int d,int u, int y)
    {
        this->d = d;
        this->u = u;
        this->y = y;
    }
    bool operator < (const node& a) const {
        return d > a.d;
    }
};
void add(int u,int v,int d)
{
    Edge.push_back(edge(u,v,d));
    G[u].push_back(Edge.size()-1);
}
void dijkstra(int s)
{
    priority_queue<node> Q;
    mem(d, INF);
    d[s][0] = 0;
    mem(vis,0);
    Q.push(node(0, s, 0));
    while(!Q.empty())
    {
        node x = Q.top();Q.pop();
        int u = x.u;
        int y = x.y;
        if(vis[u][y]) continue;
        vis[u][y] = 1;
        for(int i=0;i<G[u].size();i++)
        {
            edge e = Edge[G[u][i]];
            if(d[e.v][y] > d[u][y] + e.d)
            {
                d[e.v][y] = d[u][y] + e.d;
                Q.push(node(d[e.v][y],e.v, y));
            }
            if(y + 1 <= k && d[e.v][y+1] > d[u][y])
            {
                d[e.v][y+1] = d[u][y];
                Q.push(node(d[e.v][y+1], e.v, y+1));
            }
        }
    }
}

int main()
{
    int T;
    rd(T);
    while(T--)
    {
        t.clear();
        Edge.clear();
        for(int i=0; i<maxn; i++) G[i].clear();
        rd(n), rd(m), rd(k);
        int u, v, w;
        for(int i=0; i<m; i++)
        {
            rd(u), rd(v), rd(w);
            if(!t[u][v] || t[u][v] > w)
                t[u][v] = w;
        }
        for(int i=1; i<=n; i++)
            for(map<int, int>::iterator it = t[i].begin(); it!=t[i].end(); it++)
                add(i, it->first, it->second);
        dijkstra(1);
        int mind = INF;
        for(int i=0; i<=k; i++)
            mind = min(mind, d[n][i]);
        cout<< mind <<endl;
    }

    return 0;
}