Contents
How do you find the minimum number of denominations?
Algorithm:
- Sort the array of coins in decreasing order.
- Initialize result as empty.
- Find the largest denomination that is smaller than current amount.
- Add found denomination to result. Subtract value of found denomination from amount.
- If amount becomes 0, then print result.
- Else repeat steps 3 and 4 for new value of V.
How can you model a coin change problem using recursion?
We can recursively define the problem as: count(S, n, total) = count(S, n, total-S[n]) + count(S, n-1, total); That is, for each coin. Include current coin S[n] in solution and recur with remaining change total-S[n] with the same number of coins.
What is the time complexity of coin change problem?
Every coin has 2 options, to be selected or not selected. So, Time Complexity = O(A^m), where m is the number of coins given (Think!) Space Complexity: O(A) for the recursion call stack.
How to get distinct ways for each coin?
For example, for set {1, 2, 3}, it returns 7 as some ways are permutations of each other, as shown below: How can we get distinct ways? The idea is somewhat similar to the Knapsack problem. We can recursively define the problem as: That is, for each coin.
How to find number of coins needed to make changes with given?
When that amount of money cannot be accommodated by any combination of the coins, return -1. So if the input is [1,2,5], and the amount is 64, the output is 14. This is formed using 12*5 + 2 + 2 = 64. Let us see the following implementation to get better understanding −
How to calculate minimum number of coins for a value v?
The minimum number of coins for a value V can be computed using below recursive formula. If V == 0, then 0 coins required. If V > 0 minCoins (coins [0..m-1], V) = min {1 + minCoins (V-coin [i])} where i varies from 0 to m-1 and coin [i] <= V
Which is the most common variation of the coin change problem?
Change-making problem. It is also the most common variation of the coin change problem, a general case of partition in which, given the available denominations of an infinite set of coins, the objective is to find out the number of possible ways of making a change for a specific amount of money, without considering the order of the coins.