In this article, we will learn about the solution to the problem statement given below.
Problem statement − We are given N coins and we want to make a change of those coins such that, there is an infinite supply of each value in S. we need to display that in how many ways we can make the change irrespective of order.
We will use the concept of dynamic programming to solve the problem statement to reduce the time complexity.
Now let’s observe the solution in the implementation below −
# dynamic approach def count(S, m, n): # base case table = [[0 for x in range(m)] for x in range(n+1)] # for n=0 for i in range(m): table[i] = 1 # rest values are filled in bottom up manner for i in range(1, n+1): for j in range(m): # solutions including S[j] x = table[i - S[j]][j] if i-S[j] >= 0 else 0 # solutions excluding S[j] y = table[i][j-1] if j >= 1 else 0 # total table[i][j] = x + y return table[n][m-1] # main arr = [1, 3, 2, 4] m = len(arr) n = 5 print(“Number of coins:”,end=””) print(count(arr, m, n))
Number of coins:6
All the variables are declared in the local scope and their references are seen in the figure above.
In this article, we have learned about how we can make a Python Program for Coin Change