hdu - 2870 - Largest Submatrix（dp / 单调栈）

题意：一个由 a, b, c, w, x, y, z 组成的 m 行 n 列(1 ≤ m, n ≤ 1000)的字母矩阵，w 可以转成 a, b，x 可以转成 b, c，y 可以转成 a, c，z 可以转成 a, b, c。问由相同字母组成的最大子矩阵的面积。

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=2870

——>>依次求a, b, c的最大子矩阵。。

求一个矩阵的最大子矩阵：http://blog.csdn.net/scnu_jiechao/article/details/40677547

#include <cstdio>
#include <cstring>
#include <algorithm>using std::max;const int MAXN = 1000 + 10;int m, n;
int ret;
int h[MAXN];
int L[MAXN], R[MAXN];
char G[MAXN][MAXN];void Read()
{for (int i = 1; i <= m; ++i){getchar();for (int j = 1; j <= n; ++j){G[i][j] = getchar();}}
}void Init()
{ret = 0;
}void Dp()
{for (int i = 1; i <= n; ++i){L[i] = i;while (L[i] - 1 >= 1 && h[L[i] - 1] >= h[i]){L[i] = L[L[i] - 1];}}for (int i = n; i >= 1; --i){R[i] = i;while (R[i] + 1 <= n && h[R[i] + 1] >= h[i]){R[i] = R[R[i] + 1];}}for (int i = 1; i <= n; ++i){ret = max(ret, (R[i] - L[i] + 1) * h[i]);}
}void GetTargetMax(char target, char c1, char c2, char c3)
{memset(h, 0, sizeof(h));for (int i = 1; i <= m; ++i){for (int j = 1; j <= n; ++j){char& x = G[i][j];if (x == target || x == c1 || x == c2 || x == c3){++h[j];}else{h[j] = 0;}}Dp();}
}void Output()
{printf("%d\n", ret);
}int main()
{while (scanf("%d%d", &m, &n) == 2){Read();Init();GetTargetMax('a', 'w', 'y', 'z');GetTargetMax('b', 'w', 'x', 'z');GetTargetMax('c', 'x', 'y', 'z');Output();}return 0;
}

单调栈实现：

#include <cstdio>
#include <cstring>
#include <algorithm>using std::max;const int MAXN = 1000 + 10;int m, n;
int ret;
int h[MAXN];
int L[MAXN], R[MAXN];
char G[MAXN][MAXN];struct MS
{int st[MAXN];int top;MS(): top(0) {}void Init(){top = 0;}void PushMin(const int* A, const int& i){while (top != 0 && A[i] <= A[st[top - 1]]){--top;}st[top++] = i;}int Size(){return top;}int Second(){return st[top - 2];}
};void Read()
{for (int i = 1; i <= m; ++i){getchar();for (int j = 1; j <= n; ++j){G[i][j] = getchar();}}
}void Init()
{ret = 0;
}void Update()
{MS ms;for (int i = 1; i <= n; ++i){ms.PushMin(h, i);if (ms.Size() == 1){L[i] = 1;}else{L[i] = ms.Second() + 1;}}ms.Init();for (int i = n; i >= 1; --i){ms.PushMin(h, i);if (ms.Size() == 1){R[i] = n;}else{R[i] = ms.Second() - 1;}}for (int i = 1; i <= n; ++i){ret = max(ret, (R[i] - L[i] + 1) * h[i]);}
}void GetTargetMax(char target, char c1, char c2, char c3)
{memset(h, 0, sizeof(h));for (int i = 1; i <= m; ++i){for (int j = 1; j <= n; ++j){char& x = G[i][j];if (x == target || x == c1 || x == c2 || x == c3){++h[j];}else{h[j] = 0;}}Update();}
}void Output()
{printf("%d\n", ret);
}int main()
{while (scanf("%d%d", &m, &n) == 2){Read();Init();GetTargetMax('a', 'w', 'y', 'z');GetTargetMax('b', 'w', 'x', 'z');GetTargetMax('c', 'x', 'y', 'z');Output();}return 0;
}