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Overall percentage change from successive changes

  • Last Updated : 18 Dec, 2018

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 sucessive 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 %
    

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