Python | Find the equivalent discount in successive discounts in percentages

You are given n successive discounts in percentages. Your task is to find the equivalent discount in percentage. Input will contain a list in which each element of the list will be discount in percentage that will be negative in sign. Examples:

Input :  a = [-10, -35, -60, -75]
Output :  -94.14

Input :  a = [-5, -20, -10.-23]
Output :  -49.08

SUCCESSIVE CHANGES = A + B + (A*B) / 100 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 successive 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 the above formula and store the result in result variable and so on.

Code: Python program for finding the equivalent discount in successive discounts in percentages.

Python3

# Function to find the equivalent discount in
# successive discounts in percentages
def equivalentdis(a):
    if(len(a)== 1):
        return(a[0])
    else:
        # successive change from two = a[0] + a[1]+ (a[0]*a[1])/100
        change =(a[0] + a[1]+ (a[0]*a[1])/100)
        for i in range(2, len(a)):
            # iterating a[0] + a[1]+ (a[0]*a[1])/100
            # len(a)-2 times
            change = (change + a[i]+(change * a[i]) / 100)
        return change;
# Driver code
print(equivalentdis([-10, -20, -30, -40]))

Output :

-69.75999999999999

Time Complexity: O(n), where n is the size of a 
Auxiliary Space: O(1), as no extra space is required