P4568 [JLOI2011]飞行路线（分层图最短路）

题目链接：https://www.luogu.org/problemnew/show/P4568

思路：分层图模板题。分层图讲解，点我。

第一种方法：

#include 
#include 
#include 
#include 
#include 
#include 
#define ll long long
#define inf 0x3f3f3f3f
#define pii pair
const int mod = 1e9+7;
const int maxn = 6e6+7;
using namespace std;
struct node {int to,w,next;} edge[maxn];
int head[maxn], cnt;
int dis[maxn], vis[maxn];
int n, m, s, t, k;
struct Dijkstra
{
    void init()
    {
        memset(head,-1,sizeof(head));
        memset(dis,0x3f,sizeof(dis));
        memset(vis,0,sizeof(vis));
        cnt = 0;
    }
 
    void add(int u,int v,int w)
    {
        edge[cnt].to = v;
        edge[cnt].w = w;
        edge[cnt].next = head[u];
        head[u] = cnt ++;
    }
 
    void dijkstra()
    {
        priority_queue,greater > q;
        dis[s] = 0; q.push({dis[s],s});
        while(!q.empty())
        {
            int now = q.top().second;
            q.pop();
            if(vis[now]) continue;
            vis[now] = 1;
            for(int i = head[now]; i != -1; i = edge[i].next)
            {
                int v = edge[i].to;
                if(!vis[v] && dis[v] > dis[now] + edge[i].w)
                {
                    dis[v] = dis[now] + edge[i].w;
                    q.push({dis[v],v});
                }
            }
        }
    }
}dj;
 
int main()
{
    while(~scanf("%d%d%d", &n, &m, &k))
    {
        dj.init(); scanf("%d%d",&s,&t);
        while(m--)
        {
            int u, v, w;
            scanf("%d%d%d",&u, &v, &w);
            for(int i = 0; i <= k; i++)
            {
                dj.add(u + i * n, v + i * n, w);
                dj.add(v + i * n, u + i * n, w);
                if(i != k)
                {
                    dj.add(u + i * n, v + (i + 1) * n, 0);
                    dj.add(v + i * n, u + (i + 1) * n, 0);
                }
            }
        }
        dj.dijkstra(); int ans = inf;
        for(int i = 0; i <= k; i++)
            ans = min(ans, dis[t + i * n]);
 
        printf("%d\n",ans);
    }
}

第二种方法： 

#include 
#include 
#include 
#include 
#include 
#include 
#define ll long long
#define inf 0x3f3f3f3f
#define pii pair
const int mod = 1e9+7;
const int maxn = 1e5+7;
using namespace std;
struct node{int to, w, next, cost; } edge[maxn];
int head[maxn], cnt;
int dis[maxn][15], vis[maxn][15];
int n, m, s, t, k;
struct Dijkstra
{
    void init()
    {
        memset(head,-1,sizeof(head));
        memset(dis,127,sizeof(dis));
        memset(vis,0,sizeof(vis));
        cnt = 0;
    }
 
    void add(int u,int v,int w)
    {
        edge[cnt].to = v;
        edge[cnt].w = w;
        edge[cnt].next = head[u];
        head[u] = cnt ++;
    }
 
    void dijkstra()
    {
        priority_queue , greater > q;
        dis[s][0] = 0;
        q.push({0, s});
        while(!q.empty())
        {
            int now = q.top().second; q.pop();
            int c = now / n; now %= n;
            if(vis[now][c]) continue;
            vis[now][c] = 1;
            for(int i = head[now]; i != -1; i = edge[i].next)
            {
                int v = edge[i].to;
                if(!vis[v][c] && dis[v][c] > dis[now][c] + edge[i].w)
                {
                    dis[v][c] = dis[now][c] + edge[i].w;
                    q.push({dis[v][c], v + c * n});
                }
            }
            if(c < k)
            {
                for(int i = head[now]; i != -1; i = edge[i].next)
                {
                    int v = edge[i].to;
                    if(!vis[v][c+1] && dis[v][c+1] > dis[now][c])
                    {
                        dis[v][c+1] = dis[now][c];
                        q.push({dis[v][c+1], v + (c + 1) * n});
                    }
                }
            }
        }
    }
}dj;
 
int main()
{
    while(~scanf("%d%d%d", &n, &m, &k))
    {
        dj.init(); scanf("%d%d",&s,&t);
        while(m--)
        {
            int u, v, w;
            scanf("%d%d%d",&u, &v, &w);
            dj.add(u, v, w);
            dj.add(v, u, w);
        }
        dj.dijkstra();
        int ans = inf;
        for(int i = 0; i <= k; i++)
            ans = min(ans, dis[t][i]);
        printf("%d\n", ans);
    }
}
/*
5 6 1
0 4
0 1 5
1 2 5
2 3 5
3 4 5
2 3 3
0 2 100
*/