Check if array can be converted into strictly decreasing sequence

Given an array arr[], the task is to check whether given array can be converted into a strictly decreasing sequence with the help of the below operation: 

• Decrease any element(if it is greater than 1) by 1 in one operation

Examples:

Input: arr[] = {11, 11, 11, 11} 
Output : Yes 
Explanation:
The given sequence can be converted into 
arr[] = {11, 10, 9, 8}
Input: arr[] = {1, 1} 
Output: No 
Explanation:
The given sequence cannot be converted into strictly decreasing sequence 

Approach: The idea is to check whether every element of the array is greater than or equal to (N – index of element), because if it is greater than or equal to (N – index of element) that means array can be converted into [N, N-1, N-2, ….1]
Below is the implementation of the above approach: 

C++

// C++ implementation to check that
// array can be converted into a
// strictly decreasing sequence
#include <bits/stdc++.h>
using namespace std;

// Function to check that array
// can be converted into a
// strictly decreasing sequence
bool check(int* arr, int n)
{
    bool flag = true;

    // Loop to check that each element is
    // greater than the (N - index)
    for (int i = 0; i < n; i++) {

        // If element is less than (N - index)
        if (arr[i] < n - i) {
            flag = false;
        }
    }

    // If array can be converted
    if (flag) {
        return true;
    }
    else {
        return false;
    }
}

// Driver Code
int main()
{
    int arr1[] = { 11, 11, 11, 11 };
    int n1 = sizeof(arr1) / sizeof(arr1[0]);

    // Function calling
    if (check(arr1, n1)) {
        cout << "Yes" << endl;
    }
    else {
        cout << "No" << endl;
    }
}

Java

// Java implementation to check that
// array can be converted into a
// strictly decreasing sequence
class GFG{

// Function to check that array
// can be converted into a
// strictly decreasing sequence
static boolean check(int []arr, int n)
{
    boolean flag = true;

    // Loop to check that each element is
    // greater than the (N - index)
    for (int i = 0; i < n; i++)
    {

        // If element is less than (N - index)
        if (arr[i] < n - i)
        {
            flag = false;
        }
    }

    // If array can be converted
    if (flag)
    {
        return true;
    }
    else
    {
        return false;
    }
}

// Driver Code
public static void main(String[] args)
{
    int arr1[] = { 11, 11, 11, 11 };
    int n1 = arr1.length;

    // Function calling
    if (check(arr1, n1))
    {
        System.out.print("Yes" + "\n");
    }
    else
    {
        System.out.print("No" + "\n");
    }
}
}

// This code is contributed by amal kumar choubey

Python3

# Python3 implementation to check that
# array can be converted into a
# strictly decreasing sequence

# Function to check that array
# can be converted into a
# strictly decreasing sequence
def check(arr, n):

    flag = True;

    # Loop to check that each element
    # is greater than the (N - index)
    for i in range(n):

        # If element is less than (N - index)
        if (arr[i] < n - i):
            flag = False;

    # If array can be converted
    if (flag):
        return True;
    else:
        return False;

# Driver Code
if __name__ == '__main__':

    arr1 = [ 11, 11, 11, 11 ];
    n1 = len(arr1);

    # Function calling
    if (check(arr1, n1)):
        print("Yes");
    else:
        print("No");

# This code is contributed by sapnasingh4991

C#

// C# implementation to check that
// array can be converted into a
// strictly decreasing sequence
using System;

class GFG{

// Function to check that array
// can be converted into a
// strictly decreasing sequence
static bool check(int []arr, int n)
{
    bool flag = true;

    // Loop to check that each element is
    // greater than the (N - index)
    for(int i = 0; i < n; i++)
    {

       // If element is less than (N - index)
       if (arr[i] < n - i)
       {
           flag = false;
       }
    }

    // If array can be converted
    if (flag)
    {
        return true;
    }
    else
    {
        return false;
    }
}

// Driver Code
static public void Main(String[] args)
{
    int []arr1 = { 11, 11, 11, 11 };
    int n1 = arr1.Length;

    // Function calling
    if (check(arr1, n1))
    {
        Console.Write("Yes" + "\n");
    }
    else
    {
        Console.Write("No" + "\n");
    }
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// javascript implementation to check that
// array can be converted into a
// strictly decreasing sequence

// Function to check that array
// can be converted into a
// strictly decreasing sequence
function check(arr,n)
{
    var flag = true;

    // Loop to check that each element is
    // greater than the (N - index)
    for (let i = 0; i < n; i++) {

        // If element is less than (N - index)
        if (arr[i] < n - i) {
            flag = false;
        }
    }

    // If array can be converted
    if (flag) {
        return true;
    }
    else {
        return false;
    }
}


    let arr1= [ 11, 11, 11, 11 ];
    let n1 = arr1.length;

    // Function calling
    if (check(arr1, n1)) {
     document.write("Yes");
     }
    else {
        document.write("No");
     }

     // This code is contributed by vaibhavrabadiya117.
</script>

Output:

Yes

Time Complexity: O(n)

Auxiliary Space: O(1)