Program to find number of distinct coin sums we can make with coins and quantities in Python?

Suppose we have a list of values called coins and another list called quantities of the same length. The value of ith coin is coins[i] and we currently have quantities[i] number of ith coin. We have to find number of distinct coin sum values we can get by using non-empty group of these coins.

So, if the input is like coins = [1, 2, 5] quantities = [1, 2, 1], then the output will be 10, as we can have the following distinct coin sums [1] = 1, [2] = 2, [1,2] = 3, [2,2] = 4, [5] = 5,[1,5] = 6, [2,5] = 7, [1,2,5] = 8, [2,2,5] = 9, [1,2,2,5] = 10.

To solve this, we will follow these steps:

Define a function rec() . This will take i, res

if i is same as size of coins , then
   return
for k in range 0 to quantities[i] + 1, do
   cur := res + k * coins[i]
   insert cur into fres
   rec(i + 1, cur)
From the main method, do the following:
fres := a new set
rec(0, 0)
return size of fres - 1

Example

 Live Demo

class Solution:
   def solve(self, coins, quantities):
      def rec(i, res):
         if i == len(coins):
            return
         for k in range(0, quantities[i] + 1):
            cur = res + k * coins[i]
            fres.add(cur)
            rec(i + 1, cur)

      fres = set()
      rec(0, 0)
      return len(fres) - 1

ob = Solution()
coins = [1, 2, 5]
quantities = [1, 2, 1]
print(ob.solve(coins, quantities))

Input

[1, 2, 5], [1, 2, 1]

Output

10

Arnab Chakraborty

Updated on: 10-Nov-2020

448 Views

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