Merge pull request #117 from matthewsamuel95/edit

maximal rectangle solved

Author: matthewsamuel95

Math/max_sub_rectangle/maxSubRectangle.cpp

@@ -0,0 +1,92 @@
+//Problem : Given a 2D binary matrix filled with 0's and 1's, find the largest rectangle containing only 1's and return its area.
+
+
+#include <string>
+#include <iostream>
+#include <vector>
+#include <cmath>
+#include <climits>
+#include <stack>
+
+using namespace std;
+
+// credit to http://www.geeksforgeeks.org/largest-rectangle-under-histogram/
+int getMaxArea(vector<int> hist, int n)
+{
+	// Create an empty stack. The stack holds indexes of hist[] array
+	// The bars stored in stack are always in increasing order of their
+	// heights.
+	stack<int> s;
+
+	int max_area = 0; // Initalize max area
+	int tp; // To store top of stack
+	int area_with_top; // To store area with top bar as the smallest bar
+
+	// Run through all bars of given histogram
+	int i = 0;
+	while (i < n)
+	{
+		// If this bar is higher than the bar on top stack, push it to stack
+		if (s.empty() || hist[s.top()] <= hist[i])
+			s.push(i++);
+
+		// If this bar is lower than top of stack, then calculate area of rectangle 
+		// with stack top as the smallest (or minimum height) bar. 'i' is 
+		// 'right index' for the top and element before top in stack is 'left index'
+		else
+		{
+			tp = s.top(); // store the top index
+			s.pop(); // pop the top
+
+			// Calculate the area with hist[tp] stack as smallest bar
+			area_with_top = hist[tp] * (s.empty() ? i : i - s.top() - 1);
+
+			// update max area, if needed
+			if (max_area < area_with_top)
+				max_area = area_with_top;
+		}
+	}
+
+	// Now pop the remaining bars from stack and calculate area with every
+	// popped bar as the smallest bar
+	while (s.empty() == false)
+	{
+		tp = s.top();
+		s.pop();
+		area_with_top = hist[tp] * (s.empty() ? i : i - s.top() - 1);
+
+		if (max_area < area_with_top)
+			max_area = area_with_top;
+	}
+
+	return max_area;
+}
+
+int main(){
+	int row,col;
+	cin>>row>>col;
+	int check;
+	vector< vector<int> > matrix(row, vector<int>(col, 0));
+	vector<int> table(col);
+	for(int r=0;r<row;r++){
+		for(int c=0;c<col;c++){
+			cin>>matrix[r][c];
+			if(r==0)
+				table[c]=matrix[r][c];
+		}
+	}
+	int max=0;
+	for(int r=0;r<row;r++){
+		for(int c=0;c<col;c++)
+		{
+			if(matrix[r][c]==0)
+				table[c]=0;
+			else
+				table[c]+=1;
+		}
+		check=getMaxArea(table,table.size());
+		if(max<check)
+			max=check;
+	}
+	cout<<max<<endl;
+}