Maximize boxes required to keep at least one black and one white shirt

Given three numbers W, B, and O representing the quantities of white, black, and other colors shirts respectively, the task is to find the maximum number of boxes required such that each box contains three shirts consisting of at least one white and black shirt using the given quantity of shirts.

Examples:

Input: W = 3, B = 3, O = 1
Output: 2
Explanation:
Below are the distribution of shirts in the boxes:
Box 1: 1 white shirt, 1 black shirt and 1 shirt of other color.
Box 2: 2 white shirts and 1 black shirt.
Box 3: 1 black shirt
Since, only 2 boxes satisfy the given condition which is the maximum possible number of boxes with the given quantity of shirts. Therefore, print 2.

Input: W = 4, B = 6, O = 0
Output: 3

Approach: The given problem can be solved by using the Binary Search. The idea is to search for the maximum number of boxes in the search space formed by the lower and upper bound. It can be observed that the lower bound and the upper bound of the count of the box is 0 and minimum of W and B respectively. Follow the steps below to solve the problem:

• Initialize a variable, say ans as 0 to store the required result.
• Initialize two variables, say low as 0 and high as the minimum of (W, B).
• Loop until the value of low is less than high and perform the following steps:
  • Find the middle value of low and high in a variable, say mid.
  • Check if the maximum number of boxes can be equal to mid, then update the value of ans to mid and update the search space in the right half by updating the value of low.
  • Otherwise, update the search space to the left half by updating the value of high.
• Print the value of ans as the result.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the maximum number
// of boxes such that each box contains
// three shirts comprising of at least
// one white and black shirt
void numberofBoxes(int W, int B, int O)
{
    // Stores the low and high pointers
    // for binary search
    int low = 0, high = min(W, B);

    // Store the required answer
    int ans = 0;

    // Loop while low <= high
    while (low <= high) {

        // Store the mid value
        int mid = low + (high - low) / 2;

        // Check if the mid number of
        // boxes can be used
        if (((W >= mid) and (B >= mid))
            and ((W - mid) + (B - mid) + O)
                    >= mid) {

            // Update answer and recur
            // for the right half
            ans = mid;
            low = mid + 1;
        }

        // Else, recur for the left half
        else
            high = mid - 1;
    }

    // Print the result
    cout << ans;
}

// Driver Code
int main()
{
    int W = 3, B = 3, O = 1;
    numberofBoxes(W, B, O);
    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to find the maximum number
// of boxes such that each box contains
// three shirts comprising of at least
// one white and black shirt
static void numberofBoxes(int W, int B, int O)
{

    // Stores the low and high pointers
    // for binary search
    int low = 0, high = Math.min(W, B);

    // Store the required answer
    int ans = 0;

    // Loop while low <= high
    while (low <= high)
    {

        // Store the mid value
        int mid = low + (high - low) / 2;

        // Check if the mid number of
        // boxes can be used
        if (((W >= mid) && (B >= mid)) &&
            ((W - mid) + (B - mid) + O) >= mid)
        {

            // Update answer and recur
            // for the right half
            ans = mid;
            low = mid + 1;
        }

        // Else, recur for the left half
        else
            high = mid - 1;
    }

    // Print the result
    System.out.println(ans);
}

// Driver Code
public static void main(String args[])
{
    int W = 3, B = 3, O = 1;

    numberofBoxes(W, B, O);
}
}

// This code is contributed by avijitmondal1998

Python3

# Python3 program for the above approach

# Function to find the maximum number
# of boxes such that each box contains
# three shirts comprising of at least
# one white and black shirt
def numberofBoxes(W, B, O):

    # Stores the low and high pointers
    # for binary search
    low = 0
    high = min(W, B)

    # Store the required answer
    ans = 0

    # Loop while low <= high
    while (low <= high):

        # Store the mid value
        mid = low + (high - low) // 2

        # Check if the mid number of
        # boxes can be used
        if (((W >= mid) and (B >= mid)) and ((W - mid) + (B - mid) + O) >= mid):
            # Update answer and recur
            # for the right half
            ans = mid
            low = mid + 1

        # Else, recur for the left half
        else:
            high = mid - 1

    # Print result
    print (ans)

# Driver Code
if __name__ == '__main__':
    W = 3
    B = 3
    O = 1
    numberofBoxes(W, B, O)

# This code is contributed by mohit kumar 29.

C#

// C# program for the above approach

using System;
class GFG {

    // Function to find the maximum number
    // of boxes such that each box contains
    // three shirts comprising of at least
    // one white and black shirt
    static void numberofBoxes(int W, int B, int O)
    {
        // Stores the low and high pointers
        // for binary search
        int low = 0, high = Math.Min(W, B);

        // Store the required answer
        int ans = 0;

        // Loop while low <= high
        while (low <= high) {

            // Store the mid value
            int mid = low + (high - low) / 2;

            // Check if the mid number of
            // boxes can be used
            if (((W >= mid) &&(B >= mid))
                    &&((W - mid) + (B - mid) + O)
                >= mid) {

                // Update answer and recur
                // for the right half
                ans = mid;
                low = mid + 1;
            }

            // Else, recur for the left half
            else
                high = mid - 1;
        }

        // Print the result
        Console.Write(ans);
    }

    // Driver Code
    public static void Main()
    {
        int W = 3, B = 3, O = 1;
        numberofBoxes(W, B, O);
    }
}

// This code is contributed by ukasp.

Javascript

<script>

// Javascript program for the above approach

// Function to find the maximum number
// of boxes such that each box contains
// three shirts comprising of at least
// one white and black shirt
function numberofBoxes(W, B, O)
{

    // Stores the low and high pointers
    // for binary search
    let low = 0, high = Math.min(W, B);

    // Store the required answer
    let ans = 0;

    // Loop while low <= high
    while (low <= high)
    {

        // Store the mid value
        let mid = low + Math.floor((high - low) / 2);

        // Check if the mid number of
        // boxes can be used
        if (((W >= mid) && (B >= mid)) &&
            ((W - mid) + (B - mid) + O) >= mid)
        {

            // Update answer and recur
            // for the right half
            ans = mid;
            low = mid + 1;
        }

        // Else, recur for the left half
        else
            high = mid - 1;
    }

    // Print the result
    document.write(ans);
}

// Driver Code
let W = 3, B = 3, O = 1;
numberofBoxes(W, B, O);

// This code is contributed by gfgking

</script>

Output:

2

Time Complexity: O(log(min(W, B)))
Auxiliary Space: O(1)