Maximum sub-matrix area having count of 1's one more than count of 0's

// C# implementation to find
// the maximum area sub-matrix
// having count of 1's
// one more than count of 0's
using System;
using System.Collections.Generic;
using System.Collections;

class GFG{

// Function to find the length of longest
// subarray having count of 1's one more
// than count of 0's
static int lenOfLongSubarr(int []arr, int n,
                       ref int start, ref int finish)
{
    
    // unordered_map 'um' implemented as
    // hash table
    Dictionary<int,
               int> um = new Dictionary<int, 
                                        int>();
    
    int sum = 0, maxLen = 0;
 
    // Traverse the given array
    for(int i = 0; i < n; i++) 
    {
        
        // Accumulating sum
        sum += arr[i];
 
        // When subarray starts form index '0'
        if (sum == 1) 
        {
            start = 0;
            finish = i;
            maxLen = i + 1;
        }
 
        // Make an entry for 'sum' if it is
        // not present in 'um'
        else if (!um.ContainsKey(sum))
            um[sum] = i;
 
        // Check if 'sum-1' is present in 'um'
        // or not
        if (um.ContainsKey(sum - 1))
        {
            
            // Update 'start', 'finish'
            // and maxLength
            if (maxLen < (i - um[sum - 1]))
                start = um[sum - 1] + 1;
                
            finish = i;
            maxLen = i - um[sum - 1];
        }
    }
    
    // Required maximum length
    return maxLen;
}
 
// Function to find the maximum
// area sub-matrix having
// count of 1's one more than count of 0's
static void largestSubmatrix(int [,]mat, int n)
{
    
    // Variables to store final
    // and intermediate results
    int finalLeft = 0, finalRight = 0,
         finalTop = 0, finalBottom = 0;
    int maxArea = 0, len, start = 0, finish = 0;
    
    int []temp = new int[n];
    
    // Set the left column
    for(int left = 0; left < n; left++)
    {
        
        // Initialize all elements of temp as 0
        Array.Fill(temp, 0);
 
        // Set the right column for the
        // left column set by outer loop
        for(int right = left; right < n; right++)
        {
            
            // Calculate sum between current left 
            // and right for every row 'i', 
            // consider '0' as '-1'
            for(int i = 0; i < n; ++i)
                temp[i] += mat[i, right] == 0 ? -1 : 1;
 
            // Function to set the 'start' and 'finish'
            // variables having index values of
            // temp[] which contains the longest
            // subarray of temp[] having count of 1's
            // one more than count of 0's
            len = lenOfLongSubarr(temp, n, ref start, 
                                           ref finish);
 
            // Compare with maximum area
            // so far and accordingly update the
            // final variables
            if ((len != 0) &&
                (maxArea < (finish - start + 1) * 
                             (right - left + 1)))
            {
                finalLeft = left;
                finalRight = right;
                finalTop = start;
                finalBottom = finish;
                maxArea = (finish - start + 1) *
                            (right - left + 1);
            }
        }
    }
 
    // Print final values
    Console.Write("(Top, Left): (" + finalTop +
                  ", " + finalLeft + ")\n");
    
    Console.Write("(Bottom, Right): (" + finalBottom + 
                     ", " + finalRight + ")\n");
    
    Console.Write("Maximum area: " + maxArea);
 
}

// Driver code
public static void Main(string[] args) 
{
    int [,]mat = new int[,]{ { 1, 0, 0, 1 },
                             { 0, 1, 1, 1 },
                             { 1, 0, 0, 0 },
                             { 0, 1, 0, 1 } };
    int n = 4;
    
    largestSubmatrix(mat, n);
}
}

// This code is contributed by rutvik_56