Luogu P4009 汽车加油行驶问题

题目链接 \(Click\) \(Here\)

分层图。。好长时间没写差点要忘了\(hhhhh\)，其实思路还是很明了的。

注意需要强制消费。

#include <bits/stdc++.h>
using namespace std;

const int N = 110010;
const int M = 550010;
#define int long long

int n, k, A, B, C, have, val[110][110];

int node (int x, int y, int f) {
	return (f - 1) * n * n + (x - 1) * n + y;
}

bool in_map (int x, int y) {
	return 1 <= x && x <= n && 1 <= y && y <= n;
}

int cnt, head[N];

struct edge {
	int nxt, to, w;

	edge (int _nxt = 0, int _to = 0, int _w = 0) {
		nxt = _nxt, to = _to, w = _w;
	}
}e[M];

void add_edge (int u, int v, int w) {
	e[++cnt] = edge (head[u], v, w); head[u] = cnt;
}

int dis[N];

struct Node {
	int pos, dis;
	bool operator < (Node rhs) const {return dis > rhs.dis;}
	Node (int _pos = 0, int _dis = 0) {pos = _pos, dis = _dis;}
};

priority_queue <Node> q;

int dijkstra (int s, int t) {
	memset (dis, 0x3f, sizeof (dis));
	dis[s] = 0; q.push (Node (s, 0));
	while (!q.empty ()) {
		Node u = q.top (); q.pop ();
		if (dis[u.pos] < u.dis) continue;
		for (int i = head[u.pos]; i; i = e[i].nxt) {
			int v = e[i].to;
			if (dis[v] > dis[u.pos] + e[i].w) {
				dis[v] = dis[u.pos] + e[i].w;
				q.push (Node (v, dis[v]));
			}
		}
	}
	return dis[t];
}

signed main () {
	cin >> n >> k >> A >> B >> C;
	for (int i = 1; i <= n; ++i) {
		for (int j = 1; j <= n; ++j) {
			cin >> have;
			val[i][j] = have ? A : A + C;
		}
	}
	int s = node (n, n, k + 1) + 1;
	int t = node (n, n, k + 1) + 2;
	add_edge (s, node (1, 1, 1), 0);
	for (int i = 1; i <= k + 1; ++i) {
		for (int x = 1; x <= n; ++x) {
			for (int y = 1; y <= n; ++y) {
				if (i <= k) {
					if (i == 1 || val[x][y] != A) {
						if (in_map (x + 1, y + 0)) add_edge (node (x, y, i), node (x + 1, y + 0, i + 1), 0);
						if (in_map (x + 0, y + 1)) add_edge (node (x, y, i), node (x + 0, y + 1, i + 1), 0);
						if (in_map (x - 1, y - 0)) add_edge (node (x, y, i), node (x - 1, y - 0, i + 1), B);
						if (in_map (x - 0, y - 1)) add_edge (node (x, y, i), node (x - 0, y - 1, i + 1), B);
					}
				}
				add_edge (node (x, y, i), node (x, y, 1), val[x][y]);
			}
		}
		add_edge (node (n, n, i), t, 0);
	}
	cout << dijkstra (s, t) << endl;
}