Convert to Strictly increasing array with minimum changes

Given an array of n integers. Write a program to find minimum number of changes in array so that array is strictly increasing. In strictly increasing array A[i] < A[i+1] for 0 <= i < n

Examples:

Input : arr[] = { 1, 2, 6, 5, 4}
Output : 2
We can a[2] to any value between 2 and 5 
and a[4] to any value greater then 5. 

Input : arr[] = { 1, 2, 3, 5, 7, 11 }
Output : 0
Array is already strictly increasing.

The problem is variation of Longest Increasing Subsequence. The numbers which are already a part of LIS need not to be changed. So minimum elements to change is difference of size of array and number of elements in LIS.

C++

// CPP program to find min elements to
// change so array is strictly increasing
#include <bits/stdc++.h>
using namespace std;

// To find min elements to remove from array
// to make it strictly increasing
int minRemove(int arr[], int n)
{
    int LCS[n], len = 0;

    // Mark all elements of LCS as 1
    for (int i = 0; i < n; i++)
        LCS[i] = 1;

    // Find LCS of array
    for (int i = 1; i < n; i++) {
        for (int j = 0; j < i; j++) {
            if (arr[i] > arr[j])
                LCS[i] = max(LCS[i], LCS[j] + 1);
        }
        len = max(len, LCS[i]);
    }

    // Return min changes for array
    // to strictly increasing
    return n - len;
}

// Driver program to test minRemove()
int main()
{
    int arr[] = { 1, 2, 6, 5, 4 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << minRemove(arr, n);

    return 0;
}

Java

// Java program to find min elements to
// change so array is strictly increasing
public class Main {

    // To find min elements to remove from array
    // to make it strictly increasing
    static int minRemove(int arr[], int n)
    {
        int LCS[] = new int[n];
        int len = 0;

        // Mark all elements of LCS as 1
        for (int i = 0; i < n; i++)
            LCS[i] = 1;

        // Find LCS of array
        for (int i = 1; i < n; i++) {
            for (int j = 0; j < i; j++) {
                if (arr[i] > arr[j])
                    LCS[i] = Math.max(LCS[i], 
                                 LCS[j] + 1);
            }
            len = Math.max(len, LCS[i]);
        }

        // Return min changes for array
        // to strictly increasing
        return n - len;
    }

    // Driver program to test minRemove()
    public static void main(String[] args)
    {
        int arr[] = { 1, 2, 6, 5, 4 };
        int n = arr.length;

        System.out.println(minRemove(arr, n));
    }
}


Output:

2

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