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 %

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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:-

Simply, Apply sucessive change formula between arr[0] and arr[1] and store the result in result variable
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 %

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python 3

C#

PHP

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