Magical Girl Haze 计蒜客-A1958（分层最短路）

题意：

给一张有向图，可以把$k$条边的边权变成$0$，求点$1$到$n$的最短路。

思路：

$dp$+$dijkstra$思想。

$dis[i][k]$表示点$1$到$i$实行了$k$次把边权变为$0$的操作之后的最短距离。转移为：

$dis[v][k]=min(dis[v][k],dis[u][k]+w)$

$dis[v][k+1]=min(dis[v][k+1],dis[u][k])$

代码：

//#include<bits/stdc++.h>
#include <set>
#include <map>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <string>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>

#define ll long long
#define pll pair<ll,ll>
#define pii pair<int,int>
#define bug printf("*********
")
#define FIN freopen("input.txt","r",stdin);
#define FON freopen("output.txt","w+",stdout);
#define IO ios::sync_with_stdio(false),cin.tie(0)
#define ls root<<1
#define rs root<<1|1
#define pb push_back

using namespace std;
const int inf = 2e9 + 7;
const ll Inf = 1e18 + 7;
const int maxn = 2e5 + 5;
const int mod = 1e9 + 7;

struct node
{
    int v, w, next;
}edge[maxn<<1];

struct qnode
{
    int u, k;
    ll dis;
    qnode(int u,int k,ll dis):u(u),k(k),dis(dis){}
    bool operator <(const qnode& a)const {
        return dis > a.dis;
    }
};

int head[maxn], tot = 0;
ll dis[maxn][20];
int n, m, k;

void init()
{
    tot = 0;
    memset(head, -1, sizeof head);
}

void add(int u, int v, int w)
{
    edge[tot].v = v, edge[tot].w = w;
    edge[tot].next = head[u];
    head[u] = tot++;
}

ll dij()
{
    priority_queue<qnode>q;
    
    for (int i = 1; i <= n; ++i)
        for (int j = 0; j <= k; ++j)    dis[i][j] = Inf;

    dis[1][0] = 0;
    q.push(qnode(1, 0, 0));
    while (!q.empty())
    {
        int u = q.top().u, kk = q.top().k;
        if (u == n)    return dis[u][kk];//已经全部更新结束
        q.pop();
        for (int i = head[u]; i != -1; i = edge[i].next)
        {
            int v = edge[i].v, w = edge[i].w;
            if (dis[u][kk] + w < dis[v][kk])//保留这条边
            {
                dis[v][kk] = dis[u][kk] + w;
                q.push(qnode(v, kk, dis[v][kk]));
            }
            if (kk != k)//去除这条边
            {
                if (dis[v][kk + 1] > dis[u][kk])
                {
                    dis[v][kk + 1] = dis[u][kk];
                    q.push(qnode(v, kk + 1, dis[v][kk + 1]));
                }
            }
        }
    }
    return -1;
}

int main()
{
    int T;
    scanf("%d", &T);
    while (T--)
    {
        init();
        scanf("%d %d %d", &n, &m, &k);
        while (m--)
        {
            int u, v, w;
            scanf("%d %d %d", &u, &v, &w);
            add(u, v, w);
        }
        printf("%d
", dij());
    }
}