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P2216 [HAOI2007] 理想的正方形

https://www.luogu.com.cn/record/166784303
This commit is contained in:
Baoshuo Ren 2024-07-18 09:07:10 +08:00
parent 5037bd1813
commit 780296a1bf
Signed by: baoshuo
GPG Key ID: 00CB9680AB29F51A

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S2OJ/P2216/P2216.cpp Normal file
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#include <iostream>
#include <deque>
#include <limits>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 1005;
int a, b, n, g[N][N],
ans = std::numeric_limits<int>::max();
// row_min[i][j] 表示第 i 行的第 j 个元素到第 j + n - 1 个元素的最小值(长度 n
int row_min[N][N], row_max[N][N];
int col_min[N][N], col_max[N][N];
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> a >> b >> n;
for (int i = 1; i <= a; i++)
for (int j = 1; j <= b; j++)
cin >> g[i][j];
// 先处理每行的最大、最小值
for (int i = 1; i <= a; i++) {
std::deque<int> q_min, q_max;
for (int j = 1; j <= b; j++) {
while (!q_min.empty() && g[i][q_min.back()] >= g[i][j]) q_min.pop_back();
q_min.push_back(j);
if (q_min.front() <= j - n) q_min.pop_front();
while (!q_max.empty() && g[i][q_max.back()] <= g[i][j]) q_max.pop_back();
q_max.push_back(j);
if (q_max.front() <= j - n) q_max.pop_front();
if (j >= n) {
row_min[i][j - n + 1] = g[i][q_min.front()];
row_max[i][j - n + 1] = g[i][q_max.front()];
}
}
}
// 再基于上面的结果处理每列的最大、最小值
for (int j = 1; j <= b; j++) {
std::deque<int> q_min, q_max;
for (int i = 1; i <= a; i++) {
while (!q_min.empty() && row_min[q_min.back()][j] >= row_min[i][j]) q_min.pop_back();
q_min.push_back(i);
if (q_min.front() <= i - n) q_min.pop_front();
while (!q_max.empty() && row_max[q_max.back()][j] <= row_max[i][j]) q_max.pop_back();
q_max.push_back(i);
if (q_max.front() <= i - n) q_max.pop_front();
if (i >= n) {
col_min[i - n + 1][j] = row_min[q_min.front()][j];
col_max[i - n + 1][j] = row_max[q_max.front()][j];
}
}
}
for (int i = 1; i <= a - n + 1; i++) {
for (int j = 1; j <= b - n + 1; j++) {
ans = std::min(ans, col_max[i][j] - col_min[i][j]);
}
}
cout << ans << endl;
return 0;
}