Given two positive integers n and r where n > r >1. The task is to find the value of f(n)/(f(r)*f(n-r)). F(n) is deined as follows:
1-1 *2-2 *3-3 *….. n-n
Input: n = 5, r = 3 Output: 1/200000 Input: n = 3, r = 2 Output: 1/27
A naive approach to solve this question is to calculate f(n), f(r) and f(n-r) separately and then calculating the result as per given formula but that will cost a bit high of time complexity.
A better approach to solve this question is to find the greater value among r and n-r and then after using the property f(n) = f(n-1)* n-n = f(n-1)/nn of given function, eliminate the greater among f(r) and f(n-r) from numerator and denominator. After that calculate the rest of value by using simple loop and power function.
find max(r, n-r).
iterate from max(r, n-r) to n
result = ((result * i-i / (i-max(r, n-r)) -(i-max(r, n-r)) )
Below is the implementation of the above approach:
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