【題解】LuoGu4822：[BJWC2012]凍結

原題傳送門
分層圖最短路套路
可以去看這道題目
Code：

#include <bits/stdc++.h>
#define maxn 100010
using namespace std;
struct node{
	int val, dis;
	bool operator < (const node &x) const{ return x.dis < dis; }
};
priority_queue <node> q;
struct Edge{
	int to, next, len;
}edge[maxn << 1];
int num, head[maxn], dis[maxn], vis[maxn], n, m, k;

inline int read(){
	int s = 0, w = 1;
	char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') w = -1;
	for (; isdigit(c); c = getchar()) s = (s << 1) + (s << 3) + (c ^ 48);
	return s * w;
}

void addedge(int x, int y, int z){ edge[++num] = (Edge){y, head[x], z}, head[x] = num; }

int main(){
	n = read(), m = read(), k = read();
	for (int i = 1; i <= m; ++i){
		int x = read(), y = read(), z = read();
		for (int j = 0; j <= k; ++j){
			addedge(j * n + x, j * n + y, z), addedge(j * n + y, j * n + x, z);
			addedge(j * n + x, (j + 1) * n + y, z >> 1), addedge(j * n + y, (j + 1) * n + x, z >> 1);
		}
	}
	for (int i = 0; i <= k; ++i) addedge((i + 1) * n, (i + 2) * n, 0);
	for (int i = 2; i <= n * (k + 1); ++i) dis[i] = 1e9;
	q.push((node){1, 0});
	while (!q.empty()){
		node tmp = q.top(); q.pop();
		int u = tmp.val;
		if (vis[u]) continue;
		vis[u] = 1;
		for (int i = head[u]; i; i = edge[i].next){
			int v = edge[i].to;
			if (dis[v] > dis[u] + edge[i].len){
				dis[v] = dis[u] + edge[i].len;
				if (!vis[v]) q.push((node){v, dis[v]});
			}
		}
	}
	printf("%d\n", dis[n * (k + 1)]);
	return 0;
}