Given an array arr[] consisting of N non-negative integers, the task is to find the number of operations required to make all array elements equal. In each operation, any array element can be changed to its nearest smaller array element.
Examples:
Input: arr[] = {2, 5, 4, 3, 5, 4}
Output: 11
Explanation:
Step 1: Replace all 5s with 4s. Therefore, arr[] = {2, 4, 4, 3, 4, 4}. Count of operations = 2
Step 2: Replace all 4s with 3s. Therefore, arr[] = {2, 3, 3, 3, 3, 3}. Count of operations = 4
Steps 3: Replace all 3s with 2s. Therefore, arr[] = {2, 2, 2, 2, 2, 2}. Count of operations = 5
Therefore, total number of operations = 11Input : arr[] = {2, 2, 2}
Output : 0
Approach: The idea is to use a sorting algorithm and a Map data structure. Follow the steps below to solve the problem:
- Initialize a Map to store the frequency of each array element except for the minimum element where keys (K) are the set of unique elements and values (V) are their frequencies.
- Sort the Map in decreasing order based on the keys.
- Initialize two variables ans and prev_val with 0 to store the current answer and the prefix sum respectively.
- Now iterate the Map and add the corresponding frequencies of each element along with prev_val to ans as ans = ans + (freq) + prev_val
- While iterating the Map, increment prev_val every time by the frequency of the current element.
- After traversing the Map completely, print ans as the minimum number of operations.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to print the minimum number of // decrements to make all elements equals int MinimumNoOfOperations( int arr[], int n)
{ // Find minimum element
int min_ele = INT_MAX;
for ( int i = 0; i < n; ++i) {
min_ele = min(min_ele, arr[i]);
}
// Stores frequencies of array elements
map< int , int , greater< int > > mp;
// Update frequencies in the Map
for ( int i = 0; i < n; ++i) {
if (arr[i] == min_ele)
continue ;
else
mp[arr[i]]++;
}
// Iterate the map
map< int , int >::iterator it;
// Stores the count of
// decrements at each iteration
int prev_val = 0;
// Stores the total
// count of decrements
int ans = 0;
// Calculate the number of decrements
for (it = mp.begin(); it != mp.end();
++it) {
ans += (it->second + prev_val);
prev_val += it->second;
}
// Return minimum operations
return ans;
} // Driver Code int main()
{ // Given array
int arr[] = { 2, 5, 4, 3, 5, 4 };
// Given size
int size = sizeof (arr)
/ sizeof (arr[0]);
// Function call
cout << MinimumNoOfOperations(
arr, size);
return 0;
} |
// Java program for the // above approach import java.util.*;
class solution{
// Function to print the minimum // number of decrements to make // all elements equals static int MinimumNoOfOperations( int arr[],
int n)
{ // Find minimum element
int min_ele = Integer.MAX_VALUE;
for ( int i = 0 ; i < n; ++i)
{
min_ele = Math.min(min_ele,
arr[i]);
}
// Stores frequencies of array
// elements
TreeMap<Integer,
Integer> mp =
new TreeMap<Integer,
Integer>(
Collections.reverseOrder());
// Update frequencies in
// the Map
for ( int i = 0 ; i < n; ++i)
{
if (arr[i] == min_ele)
continue ;
else
mp.put(arr[i],
mp.getOrDefault(arr[i], 0 ) + 1 );
}
// Stores the count of
// decrements at each
// iteration
int prev_val = 0 ;
// Stores the total
// count of decrements
int ans = 0 ;
// Calculate the number of
// decrements
for (Map.Entry<Integer,
Integer> it : mp.entrySet())
{
ans += (it.getValue() + prev_val);
prev_val += it.getValue();
}
// Return minimum operations
return ans;
} // Driver Code public static void main(String args[])
{ // Given array
int arr[] = { 2 , 5 , 4 , 3 , 5 , 4 };
// Given size
int size = arr.length;
// Function call
System.out.println(
MinimumNoOfOperations(arr, size));
} } // This code is contributed by bgangwar59 |
# Python3 program for the above approach import sys
# Function to print the minimum number of # decrements to make all elements equals def MinimumNoOfOperations(arr, n):
# Find minimum element
min_ele = sys.maxsize
for i in range (n):
min_ele = min (min_ele, arr[i])
# Stores frequencies of array elements
mp = {}
# Update frequencies in the Map
for i in range (n):
if (arr[i] = = min_ele):
continue
else :
mp[arr[i]] = mp.get(arr[i], 0 ) + 1
# Stores the count of
# decrements at each iteration
prev_val = 0
# Stores the total
# count of decrements
ans = 0
# Calculate the number of decrements
for it in mp:
ans + = (mp[it] + prev_val)
prev_val + = mp[it]
# Return minimum operations
return ans
# Driver Code if __name__ = = '__main__' :
# Given array
arr = [ 2 , 5 , 4 , 3 , 5 , 4 ]
# Given size
size = len (arr)
# Function call
print (MinimumNoOfOperations(arr, size))
# This code is contributed by mohit kumar 29 |
// C# program for the // above approach using System.Collections.Generic;
using System;
using System.Linq;
class GFG{
// Function to print the minimum // number of decrements to make // all elements equals static int MinimumNoOfOperations( int []arr,
int n)
{ // Find minimum element
int min_ele = 1000000000;
for ( int i = 0; i < n; ++i)
{
min_ele = Math.Min(min_ele, arr[i]);
}
// Stores frequencies of array
// elements
Dictionary< int ,
int > mp = new Dictionary< int ,
int >();
// Update frequencies in
// the Map
for ( int i = 0; i < n; ++i)
{
if (arr[i] == min_ele)
continue ;
else
{
if (mp.ContainsKey(arr[i]) == true )
mp[arr[i]] += 1;
else
mp[arr[i]] = 1;
}
}
// Stores the count of
// decrements at each
// iteration
int prev_val = 0;
// Stores the total
// count of decrements
int ans = 0;
// Calculate the number of
// decrements
var val = mp.Keys.ToList();
foreach ( var key in val)
{
ans += (mp[key] + prev_val);
prev_val += mp[key];
}
// Return minimum operations
return ans;
} // Driver Code public static void Main(String[] args)
{ // Given array
int []arr = { 2, 5, 4, 3, 5, 4 };
// Given size
int size = arr.Length;
// Function call
Console.WriteLine(MinimumNoOfOperations(
arr, size));
} } // This code is contributed by Stream_Cipher |
<script> // Javascript program for the above approach // Function to print the minimum number of // decrements to make all elements equals function MinimumNoOfOperations(arr, n)
{ // Find minimum element
var min_ele = 1000000000;
for ( var i = 0; i < n; ++i) {
min_ele = Math.min(min_ele, arr[i]);
}
// Stores frequencies of array elements
var mp = new Map();
// Update frequencies in the Map
for ( var i = 0; i < n; ++i) {
if (arr[i] == min_ele)
continue ;
else
{
if (mp.has(arr[i]))
{
mp.set(arr[i], mp.get(arr[i])+1);
}
else
{
mp.set(arr[i], 1);
}
}
}
// Stores the count of
// decrements at each iteration
var prev_val = 0;
// Stores the total
// count of decrements
var ans = 0;
var keys = [];
mp.forEach((value, key) => {
keys.push(key);
});
keys.sort((a,b)=>b-a);
// Calculate the number of decrements
keys.forEach(value => {
ans += (mp.get(value) + prev_val);
prev_val += mp.get(value);
});
// Return minimum operations
return ans;
} // Driver Code // Given array var arr = [2, 5, 4, 3, 5, 4];
// Given size var size = arr.length
// Function call document.write( MinimumNoOfOperations( arr, size));
</script> |
11
Time Complexity: O(N) where N is the size of the array.
Auxiliary Space: O(N)