Overall percentage change from successive changes

Given an array Arr which represent the percentage change. The task is to determine the Percentage increase after these percentage change.

Examples:

Input:  arr[] = {10, 20, 30, 10}
Output: Percentage change is = 88.76 %

Input:  arr[] = {20, 15, 9, 7}
Output: Percentage change is = 60.94 %

Solution without successive change:-

let us take a number N = 120.
and percentage changes are given as, arr[] = {10, 20, 30, 10}
Now, if we first increase 120 by 10% i.e 120 * 1.1 We get N = 132
again if we increase it by 20% i.e 132 * 1.2 We get N = 158.4
again if we increase it by 30% i.e 158.4 * 1.3 We get N = 205.92
and lastly if we further increase it by 10% i.e 205.92 * 1.1 We get N = 226.51

Now, Percentage change = (226.51 – 120) / 120 = 0.8876
percentage change = 0.8876 * 100 = 88.76 %

How does this formula work?
Let x be the initial value. After A% change, value of x becomes (x + x*A/100)
After successive B% change, value of x becomes (x + x*A/100) + (x + x*A/100)*B/100. So increment in x’s value is x*(A + B + A*B/100)/100. In terms of percentage, we can say that the value is incremented by (A + B + A*B/100)%

Approach:-

1. Simply, Apply successive change formula between arr[0] and arr[1] and store the result in result variable
2. Now, calculate successive change between result and arr[2] using above formula and store the result in result variable and so on..

Below is the implementation of the above approach:


C++
// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;

float successiveChange(int arr[], int N)
{
    float var1, var2, result = 0;

    var1 = arr[0];
    var2 = arr[1];

    // Calculate successive change of 1st 2 change
    result = var1 + var2 + (float(var1 * var2) / 100);

    // Calculate successive change
    // for rest of the value
    for (int i = 2; i < N; i++)
        result = result + arr[i] + (float(result * arr[i]) / 100);

    return result;
}

// Driver code
int main()
{
    int arr[] = {10, 20, 30, 10};
    int N = sizeof(arr) / sizeof(arr[0]);

    // Calling function
    float result = successiveChange(arr, N);

    cout << "Percentage change is = " << result << " %";
    return 0;
}
Java
  // Java implementation of above approach

import java.io.*;

class GFG {


static float successiveChange(int arr[], int N)
{
    float var1, var2, result = 0;

    var1 = arr[0];
    var2 = arr[1];

    // Calculate successive change of 1st 2 change
    result = var1 + var2 + ((var1 * var2) / 100);

    // Calculate successive change
    // for rest of the value
    for (int i = 2; i < N; i++)
        result = result + arr[i] + ((result * arr[i]) / 100);

    return result;
}

// Driver code
    public static void main (String[] args) {
        int []arr = {10, 20, 30, 10};
    int N = arr.length;

    // Calling function
    float result = successiveChange(arr, N);

    System.out.println("Percentage change is = " + result + " %");
    }
}
// This code is contributed by shs..
Python 3
# Python implementation of above approach
def successiveChange(arr, N):

    result = 0;

    var1 = arr[0];
    var2 = arr[1];

    # Calculate successive change of 1st 2 change
    result = float(var1 + var2 +
            (float(var1 * var2) / 100));


    # Calculate successive change
    # for rest of the value
    for i in range(2, N):
        result = (result + arr[i] +
                 (float(result * arr[i]) / 100));

    return result;

# Driver code
arr = [10, 20, 30, 10];
N = len(arr) ;

# Calling function
result = successiveChange(arr, N);
print ("Percentage change is = %.2f" %
                       (result), "%");

# This code is contributed
# by Shivi_Aggarwal
C#
// C# implementation of above approach
using System;

class GFG {


static float successiveChange(int []arr, int N)
{
    float var1, var2, result = 0;

    var1 = arr[0];
    var2 = arr[1];

    // Calculate successive change of 1st 2 change
    result = var1 + var2 + ((var1 * var2) / 100);

    // Calculate successive change
    // for rest of the value
    for (int i = 2; i < N; i++)
        result = result + arr[i] + ((result * arr[i]) / 100);

    return result;
}

// Driver code
    public static void Main () {
        int []arr = {10, 20, 30, 10};
    int N = arr.Length;

    // Calling function
    float result = successiveChange(arr, N);

    Console.WriteLine("Percentage change is = " + result + " %");
    }
}
// This code is contributed by shs..
PHP
<?php
// PHP implementation of above approach

function successiveChange($arr, $N)
{
    $result = 0;

    $var1 = $arr[0];
    $var2 = $arr[1];

    // Calculate successive change
    // of 1st 2 change
    $result = $var1 + $var2 +
            (($var1 * $var2) / 100);

    // Calculate successive change
    // for rest of the value
    for ($i = 2; $i <$N; $i++)
        $result = $result + $arr[$i] +
                (($result * $arr[$i]) / 100);

    return $result;
}

// Driver code
$arr = array(10, 20, 30, 10);
$N = count($arr);

// Calling function
$result = successiveChange($arr, $N);

echo "Percentage change is = " ,
                 $result , " %";

// This code is contributed by shs..
?>
Output:

Percentage change is = 88.76 %