Program to find number of ways we can get n R.s using Indian denominations in Python

Suppose we have limited coins of denominations (₹1, ₹2, ₹5 and ₹10). We have to find in how many ways can you sum them up to a total of ₹n? We have an array count of size 4, where count[0] indicates coins of ₹1, count[1] indicates coins of ₹2 and so on.

So, if the input is like n = 25 count = [7,3,2,2], then the output will be 9.

To solve this, we will follow these steps −

• denom := [1,2,5,10]
• A := an array of size (n + 1) and fill with 0
• B := a new list from A
• for i in range 0 to (minimum of count[0] and n), do
  • A[i] := 1
• for i in range 1 to 3, do
  • for j in range 0 to count[i], do
    • for k in range 0 to n + 1 - j *denom[i], do
      • B[k + j * denom[i]] := B[k + j * denom[i]] + A[k]
  • for j in range 0 to n, do
    • A[j] := B[j]
    • B[j] := 0
• return A[n]

Example

Let us see the following implementation to get better understanding −

denom = [1,2,5,10]
def solve(n, count):
   A = [0] * (n + 1)
   B = list(A)
   for i in range(min(count[0], n) + 1):
      A[i] = 1
   for i in range(1, 4):
      for j in range(0, count[i] + 1):
         for k in range(n + 1 - j *denom[i]):
            B[k + j * denom[i]] += A[k]
      for j in range(0, n + 1):
         A[j] = B[j]
         B[j] = 0
   return A[n]

n = 25
count = [7,3,2,2]
print(solve(n, count))

Input

25, [7,3,2,2]

Output

9