Minimum increments of Non-Decreasing Subarrays required to make Array Non-Decreasing

Given an array arr[] consisting of N integers, the task is to find the minimum number of operations required to make the array non-decreasing, where, each operation involves incrementing all elements of a non-decreasing subarray from the given array by 1.

Examples:

Input: arr[] = {1, 3, 1, 2, 4} 
Output: 2 
Explanation:
Operation 1: Incrementing arr[2] modifies array to {1, 3, 2, 2, 4} 
Operation 2: Incrementing subarray {arr[2], arr[3]} modifies array to {1, 3, 3, 3, 4} 
Therefore, the final array is non-decreasing.
Input: arr[] = {1, 3, 5, 10} 
Output: 0 
Explanation: The array is already non-decreasing.

Approach: Follow the steps below to solve the problem:

• If the array is already a non-decreasing array, then no changes required.
• Otherwise, for any index i where 0 ≤ i < N, if arr[i] > arr[i+1], add the difference to ans.
• Finally, print ans as answer.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to return to the minimum
// number of operations required to
// make the array non-decreasing
int getMinOps(int arr[], int n)
{

    // Stores the count of operations
    int ans = 0;
    for(int i = 0; i < n - 1; i++)
    {

        // If arr[i] > arr[i + 1], add
        // arr[i] - arr[i + 1] to the answer
        // Otherwise, add 0
        ans += max(arr[i] - arr[i + 1], 0);
    }
    return ans;
}

// Driver Code
int main()
{
    int arr[] = { 1, 3, 1, 2, 4 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << (getMinOps(arr, n));
}

// This code is contributed by PrinciRaj1992

Java

// Java Program to implement the
// above approach
import java.io.*;
import java.util.*;

class GFG {

    // Function to return to the minimum
    // number of operations required to
    // make the array non-decreasing
    public static int getMinOps(int[] arr)
    {
        // Stores the count of operations
        int ans = 0;
        for (int i = 0; i < arr.length - 1; i++) {

            // If arr[i] > arr[i + 1], add
            // arr[i] - arr[i + 1] to the answer
            // Otherwise, add 0
            ans += Math.max(arr[i] - arr[i + 1], 0);
        }

        return ans;
    }

    // Driver Code
    public static void main(String[] args)
    {
        int[] arr = { 1, 3, 1, 2, 4 };

        System.out.println(getMinOps(arr));
    }
}

Python3

# Python3 program to implement
# the above approach

# Function to return to the minimum
# number of operations required to
# make the array non-decreasing
def getMinOps(arr):

    # Stores the count of operations
    ans = 0

    for i in range(len(arr) - 1):

        # If arr[i] > arr[i + 1], add
        # arr[i] - arr[i + 1] to the answer
        # Otherwise, add 0
        ans += max(arr[i] - arr[i + 1], 0)

    return ans

# Driver Code

# Given array arr[]
arr = [ 1, 3, 1, 2, 4 ]

# Function call
print(getMinOps(arr))

# This code is contributed by Shivam Singh

C#

// C# Program to implement the
// above approach
using System;
class GFG
{

  // Function to return to the minimum
  // number of operations required to
  // make the array non-decreasing
  public static int getMinOps(int[] arr)
  {
    // Stores the count of operations
    int ans = 0;
    for (int i = 0; i < arr.Length - 1; i++)
    {

      // If arr[i] > arr[i + 1], add
      // arr[i] - arr[i + 1] to the answer
      // Otherwise, add 0
      ans += Math.Max(arr[i] - arr[i + 1], 0);
    }
    return ans;
  }

  // Driver Code
  public static void Main(String[] args)
  {
    int[] arr = { 1, 3, 1, 2, 4 };

    Console.WriteLine(getMinOps(arr));
  }
}

// This code is contributed by Amit Katiyar

Javascript

<script>
// Java Script  Program to implement the
// above approach

    // Function to return to the minimum
    // number of operations required to
    // make the array non-decreasing
    function getMinOps( arr)
    {
        // Stores the count of operations
        let ans = 0;
        for (let i = 0; i < arr.length - 1; i++) {

            // If arr[i] > arr[i + 1], add
            // arr[i] - arr[i + 1] to the answer
            // Otherwise, add 0
            ans += Math.max(arr[i] - arr[i + 1], 0);
        }

        return ans;
    }

    // Driver Code

        let arr = [ 1, 3, 1, 2, 4 ];

        document.write(getMinOps(arr));

//contributed by bobby

</script>

Output:

2

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