Question

how to make greedy coin change algorithm optimal with backtracking ?

is it possible if int requiredCoins (the minimum number of coin) is given as parameter?

Answer 1

INF = 100000 #infinity

# k is number of denominations of the coin or length of d
# d is denomination vector of coin,
# n is the value for which change has to be made

def coin_change(d, n, k):
M = [0]*(n+1)
S = [0]*(n+1) # we are also assigning the value of i to the variable 'coin' because this coin 'i' is giving us the minimum value and thus, it will be the coin to be stored in the array

for j in range(1, n+1):
minimum = INF
coin = 0

for i in range(1, k+1):
if(j >= d[i]):
minimum = min(minimum, 1+M[j-d[i]])
coin = i
M[j] = minimum
S[j] = coin

l = n
while(l>0):
print(d[S[l]])
l = l-d[S[l]]
return M[n]

if __name__ == '__main__':
d = [0, 1, 2, 3]
coin_change(d, 6, 3)