Program to find number of quadruples for which product of first and last pairs are same in Python

Suppose we have a list of numbers called nums, with unique positive numbers nums. We have to find the number of quadruples like (a, b, c, d) from nums such that a*b = c*d, a, b, c and d all are distinct elements of nums.

So, if the input is like nums = [3, 6, 4, 8], then the output will be 8, because the quadruples are [[3,8,6,4], [3,8,4,6], [8,3,6,4], [8,3,4,6], [6,4,3,8], [4,6,3,8], [6,4,8,3], [4,6,8,3]].

To solve this, we will follow these steps −

• c := a new map
• n := size of nums
• for i in range 0 to n - 1, do
  • for j in range i + 1 to n - 1, do
    • x := nums[i] * nums[j]
    • c[x] := 1 + (c[x] if available, otherwise 0)
• ret := 0
• for each x in list of all values in c, do
  • ret := ret + x *(x - 1)
• return ret * 4

Example

Let us see the following implementation to get better understanding −

def solve(nums):
   c = {}
   n = len(nums)
   for i in range(n):
      for j in range(i + 1, n):
         x = nums[i] * nums[j]
         c[x] = c.get(x, 0) + 1
   ret = 0
   for x in c.values():
      ret += x * (x - 1)
   return ret * 4

nums = [3, 6, 4, 8]
print(solve(nums))

Input

[3, 6, 4, 8]

Output

8