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;
}