Minimum number of Merge Operations to make an Array Palindrome


Difficulty Level Easy
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Array Math

Problem Statement

In the “Minimum number of Merge Operations to make an Array Palindrome” problem we have given an array “a[]”. Find the minimum number of merge_operations are required to make an array palindrome. Note, A palindrome is a word, phrase, or sequence that reads the same backward as forwards.

Input Format

The first line containing an integer n.

Second-line containing n integer separated by space(” “).

Output Format

The first and only one line containing an integer value which denotes the minimum number of merge_operations to make an array palindrome.

Constraints

  • 1<=n<=10^5
  • 1<=a[i]<=10^6

Example

5
23 45 65 45 23
0

Explanation: Given array is already a palindrome, So the number of operations took is 0.

4
1 7 9 1
1

Explanation: Number of mergeĀ  operations are 1. mereging 7, 9 makes the array palindrome.

5
1 3 8 6 1
2

Here the minimum number of merge operations took is 2 to make it a palindrome.

Algorithm

1. Create two variables i,j. i will point to the start of the array and j to the end.
Till iĀ  less then or equal to j

  • If arr[i] = arr[j], then there is no need to merge the elements. Increment i and decrement j
  • If arr[i] > arr[j], then do merge operation at index j ie, arr[j-1] = arr[j-1] + arr[j], decrement j and increment the no of merge operations count by 1
  • If arr[i] < arr[j], then do merge operation at index i ie, arr[i+1] = arr[i+1] + arr[i], increment i and increment the no of merge operations count by 1.

Implementation

C++ Program for Minimum number of Merge Operations to make an Array Palindrome

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

int main()
{
  int n;
  cin>>n;
  int a[n];
  for(int i=0;i<n;i++)
  {
      cin>>a[i];
  }
  int ans = 0;
  for (int i=0,j=n-1; i<=j;)
  {
    if(a[i]==a[j])
    {
      i++;
      j--;
    }
    else if(a[i]>a[j])
    {
      j--;
      a[j]+=a[j+1] ;
      ans++;
    }
    else
    {
      i++;
      a[i]+=a[i-1];
      ans++;
    }
  }
  cout<<ans<<endl;
  return 0;
}

Java Program for Minimum number of Merge Operations to make an Array Palindrome

import java.util.Scanner;
class sum
{
    public static void main(String[] args)
    {
        Scanner sr = new Scanner(System.in);
        int n=sr.nextInt();
        int a[]= new int[n];
        for(int i=0;i<n;i++)
        {
            a[i]=sr.nextInt();
        }
        int ans = 0;
  for (int i=0,j=n-1; i<=j;)
  {
    if(a[i]==a[j])
    {
      i++;
      j--;
    }
    else if(a[i]>a[j])
    {
      j--;
      a[j]+=a[j+1] ;
      ans++;
    }
    else
    {
      i++;
      a[i]+.
=a[i-1];
      ans++;
    }
  }
  System.out.println(ans);
    }
}
7
1 2 3 5 3 2 4
4

Complexity Analysis

Time Complexity

O(n) where n is the size of the given array. Here we visit the array once and find the desired answer.

Space Complexity

O(1) because we don’t declare any auxiliary space here.

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