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Maximum size rectangle binary sub-matrix with all 1s in C++
In this tutorial, we will be discussing a program to find maximum size rectangle binary sub-matrix with all 1s.
For this we will be provided with 2D matrix containing zeroes and ones. Our task is to find the largest 2D matrix subset containing only ones.
Example
#include <bits/stdc++.h>
using namespace std;
#define R 4
#define C 4
//finding the maximum area
int maxHist(int row[]) {
stack<int> result;
int top_val;
int max_area = 0;
int area = 0;
int i = 0;
while (i < C) {
if (result.empty() || row[result.top()] <= row[i])
result.push(i++);
else {
top_val = row[result.top()];
result.pop();
area = top_val * i;
if (!result.empty())
area = top_val * (i - result.top() - 1);
max_area = max(area, max_area);
}
}
while (!result.empty()) {
top_val = row[result.top()];
result.pop();
area = top_val * i;
if (!result.empty())
area = top_val * (i - result.top() - 1);
max_area = max(area, max_area);
}
return max_area;
}
//returning area of largest required subset
int maxRectangle(int A[][C]) {
int result = maxHist(A[0]);
for (int i = 1; i < R; i++) {
for (int j = 0; j < C; j++)
if (A[i][j])
A[i][j] += A[i - 1][j];
result = max(result, maxHist(A[i]));
}
return result;
}
int main() {
int A[][C] = {
{ 0, 1, 1, 0 },{ 1, 1, 1, 1 },{ 1, 1, 1, 1 },{ 1, 1, 0, 0 },
};
cout << "Area of maximum rectangle is " <<
maxRectangle(A);
return 0;
}Output
Area of maximum rectangle is 8
Updated on: 03-Jul-2020
101 Views
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