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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 k in range 0 to n + 1 - j *denom[i], do
- for j in range 0 to n, do
- A[j] := B[j]
- B[j] := 0
- for j in range 0 to count[i], do
- 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
Updated on: 23-Oct-2021
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