LuoguP3831 [SHOI2012]回家的路 分层图+最短路

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妥妥的分层图

分横竖来建图，同一列的点（+起点终点）相邻之间连长度为距离*2的边，中转站分成两个点，互相连长度为1的边。
注意起点和终点是可以既从横点开始也从竖点开始的，所以横竖点互相连长度为0的边就行了。

#include
#include
#include
#include
using namespace std;
const int MAXN = 500001;
const int MAXM = 1000001;

struct Sta{
    int x, y, num;
}c[MAXM];

struct Node{
    int u, dis;
    inline bool operator < (const Node &a) const{
        return dis > a.dis;
    }
};

int fir[MAXN], nxt[MAXM], to[MAXM], len[MAXM], cnt;
int dis[MAXN], vis[MAXN];

inline int read(){
    int k = 0, f = 1; char ch = getchar();
    while(ch < '0' || ch > '9'){if(ch == '-') f = -1; ch = getchar();}
    while(ch >= '0' && ch <= '9'){k = k*10 + ch - '0'; ch = getchar();}
    return k * f;
}

inline void add_edge(int a, int b, int l){
    len[cnt] = l;
    to[cnt] = b;
    nxt[cnt] = fir[a];
    fir[a] = cnt++;
}

inline bool cmp1(Sta a, Sta b){
    if(a.x == b.x) return a.y < b.y;
    return a.x < b.x;
}

inline bool cmp2(Sta a, Sta b){
    if(a.y == b.y) return a.x < b.x;
    return a.y < b.y;
}

void Dijkstra(int u){
    int D;
    priority_queue <Node> q; q.push((Node){u, 0});
    memset(dis, 0x3f, sizeof(dis)); dis[u] = 0;
    Node Tmp;
    while(!q.empty()){
        Tmp = q.top(); q.pop();
        u = Tmp.u, D = Tmp.dis;
        if(D > dis[u] || vis[u]) continue;
        vis[u] = true;
//		printf("u = %d, D = %d\n", u, D);
        for(int i = fir[u]; i != -1; i = nxt[i]){
            int v = to[i];
            if(dis[v] > dis[u] + len[i]){
                dis[v] = dis[u] + len[i];
                q.push((Node){v, dis[v]});
            }
        }
    }
}

int main(){
//	freopen("in.txt", "r", stdin);
    memset(fir, -1, sizeof(fir));
    int n = read(), m = read() + 2;
    for(int i = 1; i <= m; i++){
        c[i].x = read(), c[i].y = read(), c[i].num = i;
//		add_edge(i, i + m + 2, 1);
//		add_edge(i + m + 2, i, 1);
    }
    for(int i = 1; i <= m - 2; i++){
        add_edge(i, i + m, 1);
        add_edge(i + m, i, 1);
    }
    for(int i = m - 1; i <= m; i++){
        add_edge(i, i + m, 0);
        add_edge(i + m, i, 0);
    }
     
//	printf("n = %d, m = %d\n", n, m);
    
    sort(c + 1, c + m + 1, cmp1);
    for(int i = 2; i <= m; i++){
        if(c[i].x == c[i - 1].x){
            int D = (c[i].y - c[i - 1].y) * 2;
            add_edge(c[i].num, c[i - 1].num, D);
            add_edge(c[i - 1].num, c[i].num, D);
        }
    }
    
    sort(c + 1, c + m + 1, cmp2);
    for(int i = 2; i <= m; i++){
        if(c[i].y == c[i - 1].y){
//			printf("%d %d\n", c[i].num, c[i - 1].num);
            int D = (c[i].x - c[i - 1].x) * 2;
            add_edge(c[i].num + m, c[i - 1].num + m, D);
            add_edge(c[i - 1].num + m, c[i].num + m, D);
        }
    }
    
    Dijkstra(m - 1);
    if(dis[m] == 0x3f3f3f3f) dis[m] = -1;
    printf("%d", dis[m]);
    return 0;
}