P - The Shortest Path in Nya Graph HDU - 4725

最短路
不是每两个点之间按层数设置边权 + 额外边权 TLE
是相邻两层之间设置边权 + 额外边权

需注意 add 添加得是点的关系而不是层得关系

以下加边得方法 TLE 了，应该是因为太多重复加边，如 2 1-2 2-1 ； 1 1-2

     map<int, int> mp;scanf("%d%d%d", &N, &M, &C);for(int i = 1; i <= N; i++) scanf("%d", &num[i]), mp[num[i]] = i;for(int i = 1; i <= N; i++) {if(num[i] == 1) add(i, mp[2], C), add(mp[2], i, C);else if(num[i] == N) add(i, mp[N-1], C), add(mp[N-1], i, C);else add(i, mp[num[i]+1], C), add(mp[num[i]+1], i, C), add(mp[num[i]-1], i, C), add(i, mp[num[i]-1], C);}for(int i = 1; i <= M; i++) {scanf("%d%d%d", &u, &v, &w);add(u, v, w); add(v, u, w);}

由于点的个数太多，如果对每个相邻层之间的每个点都建边，当只有两层时，DJ最坏复杂度为 O(n^2)
所以不能对层与层之间的所有点之间建边，可以在每一层找一个出点，一个入点，层内每个点都与出入点建边，边权为0，通过出入点与外界联系

建边如下

     for(int i = 1; i <= N; i++) {scanf("%d", &x);lay[x] = 1; // x 层中有点add(i, N + 2*x, 0); // num[i] 层的出点 add(N + 2*x - 1, i, 0);  // num[i] 层的入点 }for(int i = 1; i <= N; i++) {if(lay[i] && lay[i+1]) {add(N+i*2, N+(i+1)*2-1, C); add(N+(i+1)*2, N+i*2-1, C); // 相邻层之间由出入点相连 }}for(int i = 1; i <= M; i++) {scanf("%d%d%d", &u, &v, &w);add(u, v, w); add(v, u, w);}

AC代码

#include<iostream>
#include<cstdio>
#include<queue>
#include<algorithm>
#include<cstring>
#include<map>
using namespace std;
const int maxn = 3e5+10;
const int inf = 1e9+7;
int N, M, C;
int lay[maxn];
int head[maxn], cnt, dis[maxn];
bool vis[maxn];
struct edge {int to, next, w;
}e[maxn*2];void add(int u, int v, int w) {e[++cnt].next = head[u];e[cnt].to = v;e[cnt].w = w;head[u] = cnt;
}typedef struct node {int u, dist;
} cam;bool operator < (const node &a, const  node &b) {return a.dist > b.dist;
}void dijkstra() {for(int i = 0; i <= N*3; i++) dis[i] = inf; // 因为点的个数有 3*N = N + 2*N cam s; s.dist = 0; s.u = 1;dis[1] = 0;priority_queue<cam> heap;heap.push(s);while(heap.size()) {cam now = heap.top(); heap.pop();if(vis[now.u]) continue;vis[now.u] = 1;for(int i = head[now.u]; i; i = e[i].next) {int to = e[i].to;if(dis[to] > now.dist + e[i].w) {dis[to] = now.dist + e[i].w;cam tmp; tmp.dist = dis[to]; tmp.u = to;heap.push(tmp);}}}
}void init() {memset(head, 0, sizeof(head));cnt = 0;memset(vis, 0, sizeof(vis));memset(lay, 0, sizeof(lay));
}int main() {//  freopen("test.in", "r", stdin);int T; scanf("%d", &T);int kase = 0;while(T--) {init();int u, v, w, x;scanf("%d%d%d", &N, &M, &C);for(int i = 1; i <= N; i++) {scanf("%d", &x);lay[x] = 1; // x 层中有点add(i, N + 2*x, 0); // num[i] 层的出点 add(N + 2*x - 1, i, 0);  // num[i] 层的入点 }for(int i = 1; i <= N; i++) {if(lay[i] && lay[i+1]) {add(N+i*2, N+(i+1)*2-1, C); add(N+(i+1)*2, N+i*2-1, C); // 相邻层之间由出入点相连 }}for(int i = 1; i <= M; i++) {scanf("%d%d%d", &u, &v, &w);add(u, v, w); add(v, u, w);}dijkstra();
//      for(int i = 1; i <= N; i++) cout << dis[i] << endl;if(dis[N] == inf) printf("Case #%d: -1\n", ++kase);else printf("Case #%d: %d\n", ++kase, dis[N]);}return 0;
}

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P - The Shortest Path in Nya Graph HDU - 4725

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