NOIAC#71. 作畫鬼才

題目傳送門

分析

二維差分的板子。
首先一副畫的差異度 $d_i$是原圖差異度 $D$

程式碼

#include<bits/stdc++.h>
const int N = 1e3 + 10, M = 3e5 + 10;
int ri() {
	char c = getchar(); int x = 0, f = 1; for(;c < '0' || c > '9'; c = getchar()) if(c == '-') f = -1;
	for(;c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) - '0' + c; return x * f;
}
char rc() {
	char c = getchar(); for(;c < 'a' || c > 'z'; c = getchar()) ;
	return c;
}
int ch[N][N], cnt[N][N];
int x[M], y[M], _x[M], _y[M], col[M], n, m, k, s; 
long long sum, mp[30][N][N], val[N][N];
void Add(int x, int y, int _x, int _y, int c) {
	++mp[c][x][y]; ++mp[c][_x + 1][_y + 1];
	--mp[c][x][_y + 1]; --mp[c][_x + 1][y];
}
long long Query(int x, int y, int _x, int _y, int c) {
	long long ret = sum;
	for(int i = 0;i < s; ++i) 
		ret += abs(c - i) * (mp[i][_x][_y] - mp[i][x - 1][_y] - mp[i][_x][y - 1] + mp[i][x - 1][y - 1]);
	ret -= val[_x][_y] - val[x - 1][_y] - val[_x][y - 1] + val[x - 1][y - 1];
	return ret;
}
int main() {
	n = ri(); m = ri(); k = ri(); s = ri();
	for(int i = 1;i <= n; ++i) 
		for(int j = 1;j <= m; ++j)
			ch[i][j] = rc() - 'a';
	for(int i = 1;i <= k; ++i) {
		x[i] = ri(); y[i] = ri(); _x[i] = ri(); _y[i] = ri(); col[i] = rc() - 'a';
		Add(x[i], y[i], _x[i], _y[i], col[i]);
	}
	for(int i = 1;i <= n; ++i)
		for(int j = 1;j <= m; ++j)
			for(int c = 0;c < s; ++c)
				mp[c][i][j] += mp[c][i - 1][j] + mp[c][i][j - 1] - mp[c][i - 1][j - 1],
				cnt[i][j] += mp[c][i][j];
	for(int i = 1;i <= n; ++i)
		for(int j = 1;j <= m; ++j)
			mp[ch[i][j]][i][j] += k - cnt[i][j];
	for(int i = 1;i <= n; ++i)
		for(int j = 1;j <= m; ++j) {
			for(int c = 0;c < s; ++c)
				val[i][j] += abs(c - ch[i][j]) * mp[c][i][j];
			sum += val[i][j];
		}
	for(int i = 1;i <= n; ++i)
		for(int j = 1;j <= m; ++j) {
			for(int c = 0;c < s; ++c)
				mp[c][i][j] += mp[c][i - 1][j] + mp[c][i][j - 1] - mp[c][i - 1][j - 1];
			val[i][j] += val[i - 1][j] + val[i][j - 1] - val[i - 1][j - 1];
		}
	long long ans = 1e18; int id;
	for(int i = 1;i <= k; ++i) {
		long long t = Query(x[i], y[i], _x[i], _y[i], col[i]);
		if(ans > t) 
			ans = t, id = i;
	}
	printf("%lld %d\n", ans, id);
	return 0;
}