分层图最短路

Posted 2022-09-13 accpted

分层图最短路

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll inf = 0x3f3f3f3f3f3f3f3f;
const int maxn=100005;
struct node1 
    int u, v;
    ll w;

    bool operator<(const node1 &b) const 
        if (u == b.u && v == b.v) return w < b.w;
        if (u == b.u) return v < b.v;
        return u < b.u;
    
a[maxn*2];
struct node2
    int v,next;
    ll w;
e[maxn*2];

struct node3 
    int x, y;
    ll dis;

    node3() ;

    node3(int _x, int _y, int _dis) : x(_x), y(_y), dis(_dis) ;

    bool operator<(const node3 &b) const 
        return dis > b.dis;
    
;
int t,head[maxn],n,m,k;

void init()
    t=0;
    memset(head,0, sizeof(head));


void add(int u,int v,ll w)
    t++;
    e[t].v=v;
    e[t].w=w;
    e[t].next=head[u];
    head[u]=t;

ll d[maxn][15];
bool vis[maxn][15];

void dijkstra() 
    memset(vis, 0, sizeof(vis));
    memset(d, 0x3f, sizeof(d));
    d[1][0] = 0;
    priority_queue<node3> q;
    q.push(node3(1, 0, 0));
    while (!q.empty()) 
        node3 tmp = q.top();
        q.pop();
        int x = tmp.x;
        int y = tmp.y;
        if (vis[x][y]) continue;
        vis[x][y] = 1;
        for (int i = head[x]; i; i = e[i].next) 
            int v = e[i].v;
            if (d[x][y] + e[i].w < d[v][y]) 
                d[v][y] = d[x][y] + e[i].w;
                q.push(node3(v, y, d[v][y]));
            
            if (y + 1 <= k && d[x][y] < d[v][y + 1]) 
                d[v][y + 1] = d[x][y];
                q.push(node3(v, y + 1, d[v][y + 1]));
            
        
    

int main() 
    int _;
    scanf("%d", &_);
    while (_--) 
        init();
        scanf("%d%d%d", &n, &m, &k);
        for (int i = 1; i <= m; i++) 
            scanf("%d%d%lld", &a[i].u, &a[i].v, &a[i].w);
        
        sort(a + 1, a + m + 1);
        int preu = -1, prev = -1;
        for (int i = 1; i <= m; i++) 
            if (a[i].u != preu || a[i].v != prev) 
                add(a[i].u,a[i].v,a[i].w);
                preu = a[i].u;
                prev = a[i].v;
            
        
        dijkstra();
        ll ans = inf;
        for (int i = 0; i <= k; i++) ans = min(ans, d[n][i]);
        printf("%lld\n", ans);
    
    return 0;