Coin Change Problem in Python

Problem

Given a target amount n and a list (array) of distinct coin values, what’s the fewest coins needed to make the change amount.

For example:

If n = 10 and coins = [1,5,10]. Then there are 4 possible ways to make change:

1+1+1+1+1+1+1+1+1+1
5 + 1+1+1+1+1
5+5
10

With 1 coin being the minimum amount.

Solution

Implement your solution below:

def rec_coin(target,coins):
    min_coins = target
    
    if target in coins:
        return 1
    else:
        for value in [ c for c in coins if c<= target]:
            num_coins = rec_coin(target-value, coins) + 1
            min_coins = min(num_coins, min_coins)
    return min_coins
    pass

rec_coin(10,[1,5])

rec_coin(63,[1,5,10,25])

Test Your Solution

"""
RUN THIS CELL TO TEST YOUR FUNCTION.
NOTE: NON-DYNAMIC FUNCTIONS WILL TAKE A LONG TIME TO TEST. 
"""

from nose.tools import assert_equal

class TestCoins(object):
    
    def check(self,solution):
        coins = [1,5,10,25]
        assert_equal(solution(45,coins),3)
        assert_equal(solution(23,coins),5)
        assert_equal(solution(74,coins),8)
        print ('Passed all tests.')
# Run Test

test = TestCoins()
test.check(rec_coin)

Recommended: Introduction to Recursion