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Educational Codeforces Round 123 - D(思维题)

发布时间 2023-09-21 20:26:17作者: Qiansui

目录

D. Cross Coloring

题意
$n \times m $ 的方格纸上进行 q 次操作，每次操作选择某整行 x 和某整列 y，使得行 x 和列 y 均涂上 k 种颜色中的一种。问你最终的方案数

思路

代码

//>>>Qiansui
#include<bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define mem(x,y) memset(x, y, sizeof(x))
#define debug(x) cout << #x << " = " << x << '\n'
#define debug2(x,y) cout << #x << " = " << x << " " << #y << " = "<< y << '\n'
//#define int long long

using namespace std;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pull;
typedef pair<double, double> pdd;
/*

*/
const int maxm = 2e5 + 5, inf = 0x3f3f3f3f, mod = 998244353;
const ll INF = 0x3f3f3f3f3f3f3f3f;

void solve(){
	int n, m, k, q;
	cin >> n >> m >> k >> q;
	vector<pii> a;
	for(int i = 0; i < q; ++ i){
		int x, y;
		cin >> x >> y;
		a.push_back({x, y});
	}
	vector<bool> r(n + 1, false), c(m + 1, false);
	ll ans = 1, sr = n, sc = m;
	for(int i = a.size() - 1; i >= 0; -- i){
		int u = a[i].first, v = a[i].second;
		if(!r[u] || !c[v]){
			bool f = false;
			if(!r[u] && sc) f = true;
			if(!c[v] && sr) f = true;
			if(f) ans = ans * k % mod;
			if(!r[u]) -- sr;
			if(!c[v]) -- sc;
			r[u] = c[v] = true;
		}
	}
	cout << ans << '\n';
	return ;
}

signed main(){
	ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
	int _ = 1;
	cin >> _;
	while(_ --){
		solve();
	}
	return 0;
}