Given a 2D binary matrix filled with 0‘s and 1‘s, find the largest square containing only 1‘s and return its area.
Example:
Input: 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 Output: 4
Approach #1: DP. [C++]
class Solution {
public:
int maximalSquare(vector<vector<char>>& matrix) {
if (matrix.empty()) return 0;
int m = matrix.size();
int n = matrix[0].size();
vector<vector<int>> dp(m+1, vector<int>(n+1, 0));
for (int i = 1; i <= m; ++i) {
for (int j = 1; j <= n; ++j) {
dp[i][j] = matrix[i-1][j-1] - ‘0‘
+ dp[i-1][j]
+ dp[i][j-1]
- dp[i-1][j-1];
}
}
int ans = 0;
for (int i = 1; i <= m; ++i) {
for (int j = 1; j <= n; ++j) {
for (int k = min(m-i+1, n-j+1); k > 0; --k) {
int sum = dp[i+k-1][j+k-1]
- dp[i+k-1][j-1]
- dp[i-1][j+k-1]
+ dp[i-1][j-1];
if (sum == k * k) {
ans = max(ans, sum);
break;
}
}
}
}
return ans;
}
};
Analysis:
http://zxi.mytechroad.com/blog/dynamic-programming/leetcode-221-maximal-square/
原文：https://www.cnblogs.com/ruruozhenhao/p/10386129.html