What is Python Program for Coin Change using Recursion?

In this article, we will learn Python Program for Coin Change using Recursion,This free Python tutorial for complete beginners will help you learn Python from scratch.

Python Program for Coin Change using Recursion

Python Program for Coin Change using Dynamic Programming (Memoization) :

Recurrence Relation:

count(coins,n,sum) = count(coins,n,sum-count[n-1]) + count(coins,n-1,sum)

For each coin, there are 2 options.

Include the current coin: Subtract the current coin’s denomination from the target sum and call the count function recursively with the updated sum and the same set of coins i.e., count(coins, n, sum – coins[n-1] )
Exclude the current coin: Call the count function recursively with the same sum and the remaining coins. i.e., count(coins, n-1,sum ).

The final result will be the sum of both cases.

Base case:

If the target sum (sum) is 0, there is only one way to make the sum, which is by not selecting any coin. So, count(0, coins, n) = 1.
If the target sum (sum) is negative or no coins are left to consider (n == 0), then there are no ways to make the sum, so count(sum, coins, 0) = 0.
Coin Change | DP-7

Below is the Implementation of the above approach:

Python3

# Recursive Python3 program for
# coin change problem.
 
# Returns the count of ways we can sum
# coins[0...n-1] coins to get sum "sum"
 
 
def count(coins, n, sum):
 
    # If sum is 0 then there is 1
    # solution (do not include any coin)
    if (sum == 0):
        return 1
 
    # If sum is less than 0 then no
    # solution exists
    if (sum < 0):
        return 0
 
    # If there are no coins and sum
    # is greater than 0, then no
    # solution exist
    if (n <= 0):
        return 0
 
    # count is sum of solutions (i)
    # including coins[n-1] (ii) excluding coins[n-1]
    return count(coins, n - 1, sum) + count(coins, n, sum-coins[n-1])
 
 
# Driver program to test above function
coins = [1, 2, 3]
n = len(coins)
print(count(coins, n, 5))
 
# This code is contributed by Smitha Dinesh Semwal

Output

Time Complexity: O(2^sum)
Auxiliary Space: O(sum)

Python Program for Coin Change | DP-7

Write a Python program for a given integer array of coins[ ] of size N representing different types of denominations and an integer sum, the task is to find the number of ways to make a sum by using different denominations.

Examples:

Input: sum = 4, coins[] = {1,2,3},
Output: 4
Explanation: there are four solutions: {1, 1, 1, 1}, {1, 1, 2}, {2, 2}, {1, 3}.

Input: sum = 10, coins[] = {2, 5, 3, 6}
Output: 5
Explanation: There are five solutions: {2,2,2,2,2}, {2,2,3,3}, {2,2,6}, {2,3,5} and {5,5}.