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Minimum number of steps to make all elements of array equal

  • Difficulty Level : Medium
  • Last Updated : 17 Aug, 2021
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Given two arrays A[] and B[] of the same length, the task is to find the minimum number of steps required to make all the elements of the array equal by replacing the element with the difference of the corresponding element from array B. 
Note: If this is not possible print -1.
Examples: 

Input: A[] = {5, 7, 10, 5, 15} B[] = {2, 2, 1, 3, 5} 
Output:
Explanation: 
Steps to convert Array elements equal – 
Index 0: 5 is not changed, Steps Taken = 0 
Index 1: 7 – (2 * 1) = 5, Steps Taken = 1 
Index 2: 10 – (1 * 5) = 5, Steps Taken = 5 
Index 3: 5 is not changed, Steps Taken = 0 
Index 4: 15 – (5 * 2) = 5, Steps Taken = 2 
Therefore, total steps required = 0 + 1 + 5 + 0 + 2 = 8

Input: A[] = {5, 6}, B[] = {4, 3} 
Output: -1 
Explanation: 
It’s not possible to make all elements of array equal. 

Approach: The idea is to find the value at which the array elements can be converged, this value will definitely lie in between 0 to the minimum value of the array. Below is the illustration of the approach: 

  • Initially, mark the flag as False, to check that the array is convertible or not.
  • Run a while loop until the minimum of the array is greater than -1. 
    • Iterate over the indices of the array, that is from 0 to length – 1
    • For each index, check that if the element at that index in array A is greater than the minimum of the array, If yes then update the array element A[i] as A[i] – B[i].
    • Increment the number of steps by 1.
    • Check that all the array elements are equal if yes then mark the flag as True and break the while loop
    • Otherwise, repeat the steps above to compute the total number of steps required.
  • Finally, check if the flag is True, If yes then the array is convertible.

Explanation with Example: 
Given arrays be – A[] = {5, 7, 10, 5, 15}, B[] = {2, 2, 1, 3, 5} 



Array ACurrent IndexMinimum of Array AStepsComments
{5, 7, 10, 5, 15}050No operation !
{5, 5, 10, 5, 15}151Array element is subtracted once. 7 – 2 = 5
{5, 5, 9, 5, 15}252Array element is subtracted once. 10 – 1 = 9
{5, 5, 8, 5, 15}253Array element is subtracted once. 9 – 1 = 8
{5, 5, 7, 5, 15}254Array element is subtracted once. 8 – 1 = 7
{5, 5, 6, 5, 15}255Array element is subtracted once. 7 – 1 = 6
{5, 5, 5, 5, 15}256Array element is subtracted once. 6 – 1 = 5
{5, 5, 5, 5, 10}457Array element is subtracted once. 15 – 5 = 10
{5, 5, 5, 5, 5}458Array element is subtracted once. 10 – 5 = 5

Below is the implementation of the above approach: 

C++




// C++ implementation to find the
// minimum number of steps to convert
// array by subtracting the corresponding
// element from array B
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the minimum steps
void minimumSteps(int ar1[], int ar2[], int n)
{
     
    // Counter to store the steps
    int ans = 0;
      
    // Flag to check that
    // array is converted
    bool flag = true;
      
    // Loop until the minimum of the
    // array is greater than -1
    while (*min_element(ar1, ar1 + n) > -1)
    {
        int a = *min_element(ar1, ar1 + n);
         
        // Loop to convert the array
        // elements by substraction
        for(int i = 0; i < n; i++)
        {
            if (ar1[i] != a)
            {
                ar1[i] -= ar2[i];
                ans += 1;
            }
        }
         
        set<int> s1(ar1, ar1 + n);
         
        // If the array is converted
        if (s1.size() == 1)
        {
            flag = false;
            cout << ans << endl;
            break;
        }
    }
     
    if (flag)
    {
        cout << -1 << endl;
    }
}
         
// Driver Code
int main()
{
    int n = 5;
    int ar1[] = { 5, 7, 10, 5, 15 };
    int ar2[] = { 1, 2, 1, 5, 5 };
      
    // Function call
    minimumSteps(ar1, ar2, n);
  
    return 0;
}
 
// This code is contributed by rutvik_56

Java




// Java implementation to find the
// minimum number of steps to convert
// array by subtracting the corresponding
// element from array B
import java.util.*;
class GFG{
  
// Function to find the
// minimum steps
static void minimumSteps(int ar1[],
                         int ar2[],
                         int n)
{
  // Counter to store the steps
  int ans = 0;
 
  // Flag to check that
  // array is converted
  boolean flag = true;
 
  // Loop until the minimum of the
  // array is greater than -1
  while (Arrays.stream(ar1).min().getAsInt() > -1)
  {
    int a = Arrays.stream(ar1).min().getAsInt();
 
    // Loop to convert the array
    // elements by substraction
    for(int i = 0; i < n; i++)
    {
      if (ar1[i] != a)
      {
        ar1[i] -= ar2[i];
        ans += 1;
      }
    }
 
    HashSet<Integer> s1 = new HashSet<>();
    for(int i = 0; i < n; i++)
    {
      s1.add(ar1[i]);
    }
 
    // If the array is converted
    if (s1.size() == 1)
    {
      flag = false;
      System.out.print(ans + "\n");
      break;
    }
  }
 
  if (flag)
  {
    System.out.print(-1 + "\n");
  }
}
         
// Driver Code
public static void main(String[] args)
{
  int n = 5;
  int ar1[] = {5, 7, 10, 5, 15};
  int ar2[] = {1, 2, 1, 5, 5};
 
  // Function call
  minimumSteps(ar1, ar2, n);
}
}
 
// This code is contributed by Princi Singh

Python3




# Python3 implementation to find the
# minimum number of steps to convert
# array by subtracting the corresponding
# element from array B
 
# Function to find the minimum steps
def minimumSteps(ar1, ar2, n):
     
    # Counter to store the steps
    ans = 0
     
    # Flag to check that
    # array is converted
    flag = True
     
    # Loop until the minimum of the
    # array is greater than -1
    while min(ar1)>-1:
        a = min(ar1)
         
        # Loop to convert the array
        # elements by substraction
        for i in range(n):
            if ar1[i]!= a:
                ar1[i]-= ar2[i]
                ans+= 1
                 
        # If the array is converted
        if len(set(ar1))== 1:
            flag = False
            print(ans)
            break
    if flag:
        print(-1)
 
# Driver Code
if __name__ == "__main__":
    n = 5
    ar1 = [5, 7, 10, 5, 15]
    ar2 = [1, 2, 1, 5, 5]
     
    # Function Call
    minimumSteps(ar1, ar2, n)

C#




// C# implementation to
// find the minimum number
// of steps to convert array
// by subtracting the
// corresponding element from
// array B
using System;
using System.Linq;
using System.Collections.Generic;
class GFG{
  
// Function to find the
// minimum steps
static void minimumSteps(int []ar1,
                         int []ar2,
                         int n)
{
  // Counter to store the steps
  int ans = 0;
 
  // Flag to check that
  // array is converted
  bool flag = true;
 
  // Loop until the minimum of the
  // array is greater than -1
  while (ar1.Min() > -1)
  {
    int a = ar1.Min();
 
    // Loop to convert the array
    // elements by substraction
    for(int i = 0; i < n; i++)
    {
      if (ar1[i] != a)
      {
        ar1[i] -= ar2[i];
        ans += 1;
      }
    }
 
    HashSet<int> s1 = new HashSet<int>();
     
    for(int i = 0; i < n; i++)
    {
      s1.Add(ar1[i]);
    }
 
    // If the array is converted
    if (s1.Count == 1)
    {
      flag = false;
      Console.Write(ans + "\n");
      break;
    }
  }
 
  if (flag)
  {
    Console.Write(-1 + "\n");
  }
}
         
// Driver Code
public static void Main(String[] args)
{
  int n = 5;
  int []ar1 = {5, 7, 10, 5, 15};
  int []ar2 = {1, 2, 1, 5, 5};
 
  // Function call
  minimumSteps(ar1, ar2, n);
}
}
 
// This code is contributed by 29AjayKumar
Output: 
8

 

Performance Analysis: 

  • Time Complexity: O(N2 logN) As in the above approach, there are two loops to convert the array. The outer loop takes O(N) and the inner loop takes O(NlogN) as we are using set in the inner loop.
  • Auxiliary Space: O(N). We are using a set that takes O(N) extra space. 

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