LuoguP3831 [SHOI2012]回家的路 分層圖+最短路
阿新 • • 發佈:2018-12-20
妥妥的分層圖
分橫豎來建圖,同一列的點(+起點終點)相鄰之間連長度為距離*2的邊,中轉站分成兩個點,互相連長度為1的邊。 注意起點和終點是可以既從橫點開始也從豎點開始的,所以橫豎點互相連長度為0的邊就行了。
#include<queue>
#include<cstdio>
#include<cstring>
#include<algorithm>
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;
}