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Minimum value of X to make all array elements equal by either decreasing or increasing by X
  • Last Updated : 10 Oct, 2019
    Given an array of N elements and you can perform two operations on it:
    • Increase any of the array element by X once.
    • Decrease any of the array element by X once.

    The task is to find the minimum most value of X such that all array elements are equal by either applying operation 1, 2 or not applying any operation. If all the array elements cannot be made equal, then print -1.

    Examples:

    Input: a[] = {1, 4, 4, 7, 4, 1}
    Output: 3
    Increase the first and last element by 3.
    Decrease the fourth element by 3.

    Input: {1, 5, 7, 9, 1}
    Output: -1



    Approach: Since both the operations can only be applied once on an array element, the common point of observation is that if there are more than 3 unique elements than the answer is -1. There can arise three cases which are solved in the following ways:

    • If there are 3 unique elements, if abs(el2-el1) == abs(el3-el2), then the answer is abs(el2-el1). If they are not equal then the answer is -1.
    • If there are 2 unique elements, the answer is (el2 – el1) / 2, if el2 – el1 is even, else the answer is (el2 – el1)
    • If there is a single unique element, then the answer is 0

    Below is the implementation of the above approach:

    C++




    // C++ program to implement
    // the above approach
      
    #include <bits/stdc++.h>
    using namespace std;
      
    // Function that returns the
    // minimum value of X
    int findMinimumX(int a[], int n)
    {
      
        // Declare a set
        set<int> st;
      
        // Iterate in the array element
        // and insert them into the set
        for (int i = 0; i < n; i++)
            st.insert(a[i]);
      
        // If unique elements is 1
        if (st.size() == 1)
            return 0;
      
        // Unique elements is 2
        if (st.size() == 2) {
            // Get both el2 and el1
            int el1 = *st.begin();
            int el2 = *st.rbegin();
      
            // Check if they are even
            if ((el2 - el1) % 2 == 0)
                return (el2 - el1) / 2;
            else
                return (el2 - el1);
        }
      
        // If there are 3 unique elements
        if (st.size() == 3) {
            // Get three unique elements
            auto it = st.begin();
            int el1 = *it;
            it++;
            int el2 = *it;
            it++;
            int el3 = *it;
      
            // Check if their difference is same
            if ((el2 - el1) == (el3 - el2))
                return el2 - el1;
            else
                return -1;
        }
      
        // More than 3 unique elements
        return -1;
    }
      
    // Driver code
    int main()
    {
        int a[] = { 1, 4, 4, 7, 4, 1 };
        int n = sizeof(a) / sizeof(a[0]);
        cout << findMinimumX(a, n);
      
        return 0;
    }

    Java




    // Java implementation of the approach
    import java.util.HashSet;
    import java.util.Iterator;
    import java.util.Set;
      
    class GFG 
    {
          
        // Function that returns the
        // minimum value of X
        static int findMinimumX(int a[], int n)
        {
      
            // Declare a set
            Set<Integer> st = new HashSet<>();
      
            // Iterate in the array element
            // and insert them into the set
            for (int i = 0; i < n; i++)
                st.add(a[i]);
      
            // If unique elements is 1
            if (st.size() == 1)
                return 0;
      
            // Unique elements is 2
            if (st.size() == 2
            {
                // Get both el2 and el1
                Iterator<Integer> it = st.iterator();
                int el1 = it.next();
                int el2 = it.next();
      
                // Check if they are even
                if ((el2 - el1) % 2 == 0)
                    return (el2 - el1) / 2;
                else
                    return (el2 - el1);
            }
      
            // If there are 3 unique elements
            if (st.size() == 3
            {
                // Get three unique elements
                Iterator<Integer> it = st.iterator();
                int el1 = it.next();
                int el2 = it.next();
                int el3 = it.next();
      
                // Check if their difference is same
                if ((el2 - el1) == (el3 - el2))
                    return el2 - el1;
                else
                    return -1;
            }
      
            // More than 3 unique elements
            return -1;
        }
      
        // Driver code
        public static void main(String[] args) 
        {
            int a[] = {1, 4, 4, 7, 4, 1};
            int n = a.length;
            System.out.println(findMinimumX(a, n));
        }
    }
      
    // This code is contributed by
    // Rajnis09

    Python3




    # Python 3 program to implement
    # the above approach
      
    # Function that returns the
    # minimum value of X
    def findMinimumX(a, n):
          
        # Declare a set
        st = set()
      
        # Iterate in the array element
        # and insert them into the set
        for i in range(n):
            st.add(a[i])
      
        # If unique elements is 1
        if (len(st) == 1):
            return 0
      
        # Unique elements is 2
        if (len(st) == 2):
              
            # Get both el2 and el1
            st = list(st)
            el1 = st[0]
            el2 = st[1]
      
            # Check if they are even
            if ((el2 - el1) % 2 == 0):
                return int((el2 - el1) / 2)
            else:
                return (el2 - el1)
      
        # If there are 3 unique elements
        if (len(st) == 3):
            st = list(st)
              
            # Get three unique elements
            el1 = st[0]
            el2 = st[1]
            el3 = st[2]
      
            # Check if their difference is same
            if ((el2 - el1) == (el3 - el2)):
                return el2 - el1
            else:
                return -1
      
        # More than 3 unique elements
        return -1
      
    # Driver code
    if __name__ == '__main__':
        a = [1, 4, 4, 7, 4, 1]
        n = len(a)
        print(findMinimumX(a, n))
      
    # This code is contributed by
    # Surendra_Gangwar

    C#




    // C# implementation of the approach
    using System;
    using System.Collections.Generic; 
      
    class GFG 
    {
          
        // Function that returns the
        // minimum value of X
        static int findMinimumX(int []a, int n)
        {
      
            // Declare a set
            List<int> st = new List<int>();
      
            // Iterate in the array element
            // and insert them into the set
            for (int i = 0; i < n; i++)
                if(!st.Contains(a[i]))
                    st.Add(a[i]);
      
            // If unique elements is 1
            if (st.Count == 1)
                return 0;
      
            // Unique elements is 2
            if (st.Count == 2) 
            {
                // Get both el2 and el1
                int el1 = st[0];
                int el2 = st[1];
      
                // Check if they are even
                if ((el2 - el1) % 2 == 0)
                    return (el2 - el1) / 2;
                else
                    return (el2 - el1);
            }
      
            // If there are 3 unique elements
            if (st.Count == 3) 
            {
                // Get three unique elements
                int el1 = st[0];
                int el2 = st[1];
                int el3 = st[2];
      
                // Check if their difference is same
                if ((el2 - el1) == (el3 - el2))
                    return el2 - el1;
                else
                    return -1;
            }
      
            // More than 3 unique elements
            return -1;
        }
      
        // Driver code
        public static void Main(String[] args) 
        {
            int []a = {1, 4, 4, 7, 4, 1};
            int n = a.Length;
            Console.WriteLine(findMinimumX(a, n));
        }
          
    // This code is contributed by Princi Singh
    Output:
    3
    

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