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Minimum swaps to group all 0s together in Binary Circular Array

  • Last Updated : 28 Jan, 2022

Given a binary circular array arr[] of size N, the task is to find the minimum swaps to group all 0s together in the array.

Examples:

Input: arr[] = {1, 0, 1, 0, 0, 1, 1}
Output: 1
Explanation: Here are a few of the ways to group all the 0’s together:

  1. {1, 1, 0, 0, 0, 1, 1} using 1 swap.
  2. {1, 0, 0, 0, 1, 1, 1} using 1 swap.
  3. {0, 0, 1, 1, 1, 1, 0} using 2 swaps (using the circular property of the array).

There is no way to group all 0’s together with 0 swaps. Thus, the minimum number of swaps required is 1.

Input: arr[] = {0, 0, 1, 1, 0}
Output: 0
Explanation: All the 0’s are already grouped together due to the circular property of the array. 
Thus, the minimum number of swaps required is 0.

 

Approach: The task can be solved using the sliding window technique. Follow the below steps to solve the problem:

  • Count the total number of 0s. Let m be that number
  • Find the contiguous region of length m that has the most 0s in it
  • The number of 1s in this region is the minimum required swaps. Each swap will move one 0 into the region and one 1 out of the region.
  • Finally, use modulo operation for handling the case of the circular arrays.

Below is the implementation of the above approach.

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to count min swap
// to get all zeros together
int minSwaps(int nums[], int N)
{
    int count_1 = 0;
 
    if (N == 1)
        return 0;
 
    for (int i = 0; i < N; i++) {
        if (nums[i] == 0)
            count_1++;
    }
 
    // Window size for counting
    // maximum  no. of 1s
    int windowsize = count_1;
    count_1 = 0;
 
    for (int i = 0; i < windowsize; i++) {
        if (nums[i] == 0)
            count_1++;
    }
 
    // For storing maximum count of 1s in
    // a window
    int mx = count_1;
    for (int i = windowsize; i < N + windowsize; i++) {
        if (nums[i % N] == 0)
            count_1++;
        if (nums[(i - windowsize) % N] == 0)
            count_1--;
        mx = max(count_1, mx);
    }
    return windowsize - mx;
}
 
// Driver code
int main()
{
    int nums[] = { 1, 0, 1, 0, 0, 1, 1 };
    int N = sizeof(nums) / sizeof(nums[0]);
    cout << minSwaps(nums, N);
    return 0;
}

Java




// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;
 
class GFG {
 
  // Function to count min swap
  // to get all zeros together
  static int minSwaps(int nums[], int N)
  {
    int count_1 = 0;
 
    if (N == 1)
      return 0;
 
    for (int i = 0; i < N; i++) {
      if (nums[i] == 0)
        count_1++;
    }
 
    // Window size for counting
    // maximum  no. of 1s
    int windowsize = count_1;
    count_1 = 0;
 
    for (int i = 0; i < windowsize; i++) {
      if (nums[i] == 0)
        count_1++;
    }
 
    // For storing maximum count of 1s in
    // a window
    int mx = count_1;
    for (int i = windowsize; i < N + windowsize; i++) {
      if (nums[i % N] == 0)
        count_1++;
      if (nums[(i - windowsize) % N] == 0)
        count_1--;
      mx = Math.max(count_1, mx);
    }
    return windowsize - mx;
  }
 
  // Driver code
  public static void main (String[] args) {
    int nums[] = { 1, 0, 1, 0, 0, 1, 1 };
    int N = nums.length;
    System.out.println( minSwaps(nums, N));
  }
}
 
// This code is contributed by hrithikgarg03188.

Python3




# python3 program for the above approach
 
# Function to count min swap
# to get all zeros together
def minSwaps(nums, N):
 
    count_1 = 0
 
    if (N == 1):
        return 0
 
    for i in range(0, N):
        if (nums[i] == 0):
            count_1 += 1
 
    # Window size for counting
    # maximum no. of 1s
    windowsize = count_1
    count_1 = 0
 
    for i in range(0, windowsize):
        if (nums[i] == 0):
            count_1 += 1
 
    # For storing maximum count of 1s in
    # a window
    mx = count_1
    for i in range(windowsize, N + windowsize):
        if (nums[i % N] == 0):
            count_1 += 1
        if (nums[(i - windowsize) % N] == 0):
            count_1 -= 1
        mx = max(count_1, mx)
 
    return windowsize - mx
 
# Driver code
if __name__ == "__main__":
 
    nums = [1, 0, 1, 0, 0, 1, 1]
    N = len(nums)
    print(minSwaps(nums, N))
 
    # This code is contributed by rakeshsahni

C#




// C# program for the above approach
using System;
class GFG
{
 
  // Function to count min swap
  // to get all zeros together
  static int minSwaps(int []nums, int N)
  {
    int count_1 = 0;
 
    if (N == 1)
      return 0;
 
    for (int i = 0; i < N; i++) {
      if (nums[i] == 0)
        count_1++;
    }
 
    // Window size for counting
    // maximum  no. of 1s
    int windowsize = count_1;
    count_1 = 0;
 
    for (int i = 0; i < windowsize; i++) {
      if (nums[i] == 0)
        count_1++;
    }
 
    // For storing maximum count of 1s in
    // a window
    int mx = count_1;
    for (int i = windowsize; i < N + windowsize; i++) {
      if (nums[i % N] == 0)
        count_1++;
      if (nums[(i - windowsize) % N] == 0)
        count_1--;
      mx = Math.Max(count_1, mx);
    }
    return windowsize - mx;
  }
 
  // Driver code
  public static void Main()
  {
    int []nums = { 1, 0, 1, 0, 0, 1, 1 };
    int N = nums.Length;
    Console.Write(minSwaps(nums, N));
  }
}
 
// This code is contributed by Samim Hossain Mondal.

Javascript




<script>
      // JavaScript code for the above approach
 
      // Function to count min swap
      // to get all zeros together
      function minSwaps(nums, N) {
          let count_1 = 0;
 
          if (N == 1)
              return 0;
 
          for (let i = 0; i < N; i++) {
              if (nums[i] == 0)
                  count_1++;
          }
 
          // Window size for counting
          // maximum  no. of 1s
          let windowsize = count_1;
          count_1 = 0;
 
          for (let i = 0; i < windowsize; i++) {
              if (nums[i] == 0)
                  count_1++;
          }
 
          // For storing maximum count of 1s in
          // a window
          let mx = count_1;
          for (let i = windowsize; i < N + windowsize; i++) {
              if (nums[i % N] == 0)
                  count_1++;
              if (nums[(i - windowsize) % N] == 0)
                  count_1--;
              mx = Math.max(count_1, mx);
          }
          return windowsize - mx;
      }
 
      // Driver code
      let nums = [1, 0, 1, 0, 0, 1, 1];
      let N = nums.length;
      document.write(minSwaps(nums, N));
 
       // This code is contributed by Potta Lokesh
  </script>

 
 

Output
1

 

Time Complexity: O(N)
Auxiliary Space: O(1)

 


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