Find row with maximum and minimum number of zeroes in given Matrix

Last Updated : 22 Jun, 2022

Given a 2D matrix containing only zeroes and ones, where each row is sorted. The task is to find the row with the maximum number of 0s and the row with minimum number of 0s.
Example:

Input: mat[][] = {
{0, 1, 1, 1},
{0, 0, 1, 1},
{1, 1, 1, 1},
{0, 0, 0, 0}}
Output:
Row with min zeroes: 3
Row with max zeroes: 4
Input: mat[][] = {
{0, 1, 1, 1},
{0, 0, 1, 1},
{0, 0, 0, 1},
{0, 0, 0, 0}}
Output:
Row with min zeroes: 1
Row with max zeroes: 4

Simple approach: A simple method is to do a row-wise traversal of the matrix, count the number of 0s in each row, and compare the count with max and min. Finally, return the index of row with maximum 0s and minimum 0s. The time complexity of this method is O(M*N) where M is a number of rows and N is a number of columns in matrix.
Efficient approach: Since each row is sorted, we can use Binary Search to find the count of 0s in each row. The idea is to find the index of first instance of 1 in each row.
The count of 0s in that row will be:

If 1 exists in the row, then count of 0s will be equal to the index of first 1 in the row considering zero-based indexing.
If 1 does not exist in the row, then count of 0s will be N which is the total number of columns in the matrix.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
#define R 4
#define C 4
 
// Function to find the index of first 1
// in the binary array arr[]
int first(bool arr[], int low, int high)
{
    if (high >= low) {
 
        // Get the middle index
        int mid = low + (high - low) / 2;
 
        // Check if the element at middle index is first 1
        if ((mid == 0 || arr[mid - 1] == 0) && arr[mid] == 1)
            return mid;
 
        // If the element is 0, recur for right side
        else if (arr[mid] == 0)
            return first(arr, (mid + 1), high);
 
        // If element is not first 1, recur for left side
        else
            return first(arr, low, (mid - 1));
    }
    return -1;
}
 
// Function to print rows with maximum
// and minimum number of zeroes
void rowWith0s(bool mat[R][C])
{
    // Initialize max values
    int max_row_index = 0, max = INT_MIN;
 
    // Initialize min values
    int min_row_index = 0, min = INT_MAX;
 
    // Traverse for each row and count number of 0s
    // by finding the index of first 1
    int i, index;
 
    for (i = 0; i < R; i++) {
        index = first(mat[i], 0, C - 1);
 
        int cntZeroes = 0;
 
        // If index = -1, that is there is no 1
        // in the row, count of zeroes will be C
        if (index == -1) {
            cntZeroes = C;
        }
 
        // Else, count of zeroes will be index
        // of first 1
        else {
            cntZeroes = index;
        }
 
        // Find max row index
        if (max < cntZeroes) {
            max = cntZeroes;
            max_row_index = i;
        }
 
        // Find min row index
        if (min > cntZeroes) {
            min = cntZeroes;
            min_row_index = i;
        }
    }
 
    cout << "Row with min 0s: " << min_row_index + 1;
    cout << "\nRow with max 0s: " << max_row_index + 1;
}
 
// Driver code
int main()
{
    bool mat[R][C] = { { 0, 0, 0, 1 },
                       { 0, 1, 1, 1 },
                       { 1, 1, 1, 1 },
                       { 0, 0, 0, 0 } };
 
    rowWith0s(mat);
 
    return 0;
}

Java

// Java implementation of the approach
import java.io.*;
 
class GFG 
{
     
static int R = 4;
static int C = 4;
 
// Function to find the index of first 1
// in the binary array arr[]
static int first(int arr[], int low, int high)
{
    if (high >= low) 
    {
 
        // Get the middle index
        int mid = low + (high - low) / 2;
 
        // Check if the element at middle index is first 1
        if ((mid == 0 || arr[mid - 1] == 0) && arr[mid] == 1)
            return mid;
 
        // If the element is 0, recur for right side
        else if (arr[mid] == 0)
            return first(arr, (mid + 1), high);
 
        // If element is not first 1, recur for left side
        else
            return first(arr, low, (mid - 1));
    }
    return -1;
}
 
// Function to print rows with maximum
// and minimum number of zeroes
static void rowWith0s(int mat[][])
{
    // Initialize max values
    int max_row_index = 0, max = Integer.MIN_VALUE;
 
    // Initialize min values
    int min_row_index = 0, min = Integer.MAX_VALUE;
 
    // Traverse for each row and count number of 0s
    // by finding the index of first 1
    int i, index;
 
    for (i = 0; i < R; i++) 
    {
        index = first(mat[i], 0, C - 1);
 
        int cntZeroes = 0;
 
        // If index = -1, that is there is no 1
        // in the row, count of zeroes will be C
        if (index == -1) 
        {
            cntZeroes = C;
        }
 
        // Else, count of zeroes will be index
        // of first 1
        else
        {
            cntZeroes = index;
        }
 
        // Find max row index
        if (max < cntZeroes) 
        {
            max = cntZeroes;
            max_row_index = i;
        }
 
        // Find min row index
        if (min > cntZeroes) 
        {
            min = cntZeroes;
            min_row_index = i;
        }
    }
 
        System.out.println ("Row with min 0s: " + (min_row_index + 1));
        System.out.println ("Row with max 0s: " + (max_row_index + 1));
}
 
// Driver code
public static void main (String[] args)
{
 
    int mat[][] = { { 0, 0, 0, 1 },
                    { 0, 1, 1, 1 },
                    { 1, 1, 1, 1 },
                    { 0, 0, 0, 0 } };
 
    rowWith0s(mat);
 
 
}
}
 
// This code is contributed by ajit.

Python3

# Python3 implementation of the approach
 
import sys
 
R = 4
C = 4
 
# Function to find the index of first 1 
# in the binary array arr[] 
def first(arr, low, high) : 
 
    if (high >= low) :
 
        # Get the middle index 
        mid = low + (high - low) // 2; 
 
        # Check if the element at middle index is first 1 
        if ((mid == 0 or arr[mid - 1] == 0) and arr[mid] == 1) :
            return mid; 
 
        # If the element is 0, recur for right side 
        elif (arr[mid] == 0) :
            return first(arr, (mid + 1), high); 
 
        # If element is not first 1, recur for left side 
        else :
            return first(arr, low, (mid - 1)); 
     
    return -1; 
 
 
# Function to print rows with maximum 
# and minimum number of zeroes 
def rowWith0s(mat) : 
 
    # Initialize max values 
    row_index = 0; max = -(sys.maxsize - 1); 
 
    # Initialize min values 
    min_row_index = 0; min = sys.maxsize; 
 
    # Traverse for each row and count number of 0s 
    # by finding the index of first 1 
     
    for i in range(R) :
         
        index = first(mat[i], 0, C - 1); 
 
        cntZeroes = 0; 
 
        # If index = -1, that is there is no 1 
        # in the row, count of zeroes will be C 
        if (index == -1) :
            cntZeroes = C; 
 
        # Else, count of zeroes will be index 
        # of first 1 
        else :
            cntZeroes = index; 
 
        # Find max row index 
        if (max < cntZeroes) :
            max = cntZeroes; 
            max_row_index = i; 
         
        # Find min row index 
        if (min > cntZeroes) :
            min = cntZeroes; 
            min_row_index = i; 
 
    print("Row with min 0s:",min_row_index + 1); 
    print("Row with max 0s:", max_row_index + 1); 
 
 
# Driver code 
if __name__ == "__main__" : 
 
    mat = [
            [ 0, 0, 0, 1 ], 
            [ 0, 1, 1, 1 ], 
            [ 1, 1, 1, 1 ], 
            [ 0, 0, 0, 0 ]
        ]; 
 
    rowWith0s(mat); 
 
    # This code is contributed by AnkitRai01

C#

// C# implementation of the approach
using System;     
     
class GFG 
{
     
static int R = 4;
static int C = 4;
 
// Function to find the index of first 1
// in the binary array arr[]
static int first(int []arr, int low, int high)
{
    if (high >= low) 
    {
 
        // Get the middle index
        int mid = low + (high - low) / 2;
 
        // Check if the element at middle index is first 1
        if ((mid == 0 || arr[mid - 1] == 0) && arr[mid] == 1)
            return mid;
 
        // If the element is 0, recur for right side
        else if (arr[mid] == 0)
            return first(arr, (mid + 1), high);
 
        // If element is not first 1, recur for left side
        else
            return first(arr, low, (mid - 1));
    }
    return -1;
}
 
// Function to print rows with maximum
// and minimum number of zeroes
static void rowWith0s(int [,]mat)
{
    // Initialize max values
    int max_row_index = 0, max = int.MinValue;
 
    // Initialize min values
    int min_row_index = 0, min = int.MaxValue;
 
    // Traverse for each row and count number of 0s
    // by finding the index of first 1
    int i, index;
 
    for (i = 0; i < R; i++) 
    {
        index = first(GetRow(mat,i), 0, C - 1);
 
        int cntZeroes = 0;
 
        // If index = -1, that is there is no 1
        // in the row, count of zeroes will be C
        if (index == -1) 
        {
            cntZeroes = C;
        }
 
        // Else, count of zeroes will be index
        // of first 1
        else
        {
            cntZeroes = index;
        }
 
        // Find max row index
        if (max < cntZeroes) 
        {
            max = cntZeroes;
            max_row_index = i;
        }
 
        // Find min row index
        if (min > cntZeroes) 
        {
            min = cntZeroes;
            min_row_index = i;
        }
    }
 
        Console.WriteLine ("Row with min 0s: " + (min_row_index + 1));
        Console.WriteLine ("Row with max 0s: " + (max_row_index + 1));
}
 
public static int[] GetRow(int[,] matrix, int row)
{
    var rowLength = matrix.GetLength(1);
    var rowVector = new int[rowLength];
 
    for (var i = 0; i < rowLength; i++)
    rowVector[i] = matrix[row, i];
 
    return rowVector;
} 
 
// Driver code
public static void Main (String[] args)
{
 
    int [,]mat = { { 0, 0, 0, 1 },
                    { 0, 1, 1, 1 },
                    { 1, 1, 1, 1 },
                    { 0, 0, 0, 0 } };
 
    rowWith0s(mat);
 
 
}
}
 
/* This code contributed by PrinciRaj1992 */

Javascript

<script>
 
// JavaScript implementation of the approach
 
     
var R = 4;
var C = 4;
 
// Function to find the index of first 1
// in the binary array arr
function first(arr , low , high)
{
    if (high >= low) 
    {
 
        // Get the middle index
        var mid = low + parseInt((high - low) / 2);
 
        // Check if the element at middle 
        // index is first 1
        if ((mid == 0 || arr[mid - 1] == 0) &&
        arr[mid] == 1)
            return mid;
 
        // If the element is 0, recur for right side
        else if (arr[mid] == 0)
            return first(arr, (mid + 1), high);
 
        // If element is not first 1, 
        // recur for left side
        else
            return first(arr, low, (mid - 1));
    }
    return -1;
}
 
// Function to print rows with maximum
// and minimum number of zeroes
function rowWith0s(mat)
{
    // Initialize max values
    var max_row_index = 0, max = Number.MIN_VALUE;
 
    // Initialize min values
    var min_row_index = 0, min = Number.MAX_VALUE;
 
    // Traverse for each row and count number of 0s
    // by finding the index of first 1
    var i, index;
 
    for (i = 0; i < R; i++) 
    {
        index = first(mat[i], 0, C - 1);
 
        var cntZeroes = 0;
 
        // If index = -1, that is there is no 1
        // in the row, count of zeroes will be C
        if (index == -1) 
        {
            cntZeroes = C;
        }
 
        // Else, count of zeroes will be index
        // of first 1
        else
        {
            cntZeroes = index;
        }
 
        // Find max row index
        if (max < cntZeroes) 
        {
            max = cntZeroes;
            max_row_index = i;
        }
 
        // Find min row index
        if (min > cntZeroes) 
        {
            min = cntZeroes;
            min_row_index = i;
        }
    }
 
        document.write("Row with min 0s: " +
        (min_row_index + 1)+"<br/>");
        document.write("Row with max 0s: " + 
        (max_row_index + 1));
}
 
// Driver code
 
    var mat = [ [ 0, 0, 0, 1 ],
                [ 0, 1, 1, 1 ],
                [ 1, 1, 1, 1 ],
                [ 0, 0, 0, 0 ] ];
 
    rowWith0s(mat);
     
// This code contributed by Rajput-Ji
 
</script>

Output:

Row with min 0s: 3
Row with max 0s: 4

Time Complexity: O(R*logC), as we are using a loop to traverse R times and in each traversal we are calling the function first which will cost O(logC) time as we are using binary search.

Auxiliary Space: O(1), as we are not using any extra space.

Maximum number of ones in a N*N matrix with given constraints

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Find row with maximum and minimum number of zeroes in given Matrix

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