The minimum number of coins the sum of which is S

Question

Given a list of N coins, their values (V1, V2, ... , VN), and the total sum S. Find the minimum number of coins the sum of which is S (we can use as many coins of one type a

Answer 1

As already pointed out, Dynamic Programming suits best for this problem. I have written a Python program for this:-

def sumtototal(total, coins_list):
    s = [0]
    for i in range(1, total+1):
        s.append(-1)
        for coin_val in coins_list:
            if i-coin_val >=0 and s[i-coin_val] != -1 and (s[i] > s[i-coin_val] or s[i] == -1):
                s[i] = 1 + s[i-coin_val]

    print s
    return s[total]

total = input()
coins_list = map(int, raw_input().split(' '))
print sumtototal(total, coins_list)

For input:

12 2 3 5

The output would be:

[0, -1, 1, 1, 2, 1, 2, 2, 2, 3, 2, 3, 3] 3 The list_index is the total needed and the value at list_index is the no. of coins needed to get that total. The answer for above input(getting a value 12) is 3 ( coins of values 5, 5, 2).