Recursive Algorithm Time Complexity: Coin Change
By : Jorge Naranhoe
Date : March 29 2020, 07:55 AM
I think the issue was by ths following , The two pieces of code are the same except that the second uses recursion instead of a for loop to iterate over the coins. That makes their runtime complexity the same (although the second piece of code probably has worse memory complexity because of the extra recursive calls, but that may get lost in the wash). For example, here's partial evaluation of the second count in the case where S = [1, 5, 10] and m=3. On each line, I expand the leftmost definition of count. code :
count(S, 3, 100)
= count(S, 2, 100) + count(S, 3, 90)
= count(S, 1, 100) + count(S, 2, 95) + count(S, 3, 90)
= count(S, 0, 100) + count(S, 1, 99) + count(S, 2, 95) + count(S, 3, 90)
= 0 + count(S, 1, 99) + count(S, 2, 95) + count(S, 3, 90)

DP Coin Change Algorithm  Retrieve coin combinations from table
By : AliT
Date : March 29 2020, 07:55 AM
will help you Sure you can. We define a new function get_solution(i,j) which means all solution for your table[i][j]. You can think it returns an array of array, for example, the output of get_solution(4,3) is [[1,1,1,1],[2,1],[2,2],[3,1]]. Then:

What is the time complexity of this coin changing combination algorithm?
By : Arun Singh
Date : March 29 2020, 07:55 AM
wish helps you Assume a case where amount, n, is very large and the values of each coin is very small compared to n and let the size of the coin array be c. In fact, in the worst case, we can assume the value of every coin to be about 1. In the tree representing the call stack that your solution builds, each node would branch c times. Each level of the tree subtracts the value of a coin (in the worst case is about 1) from n so the depth (or height) of the tree would be n. So we're looking at a cbranch tree with height n. The number of vertices, V = c^0 + c^1 + c^2 + c^3 + ... + c^(n1) + c^n. You can see what this series reduces to here. The calculation for number of edges, E, is similar. This algorithm has O(c^n) time complexity.

What is the time complexity of this coin change algorithm?
By : cybermole
Date : March 29 2020, 07:55 AM
I wish this help you As Enrico Borba commented: Your analysis seems correct to me. You have O(amount * number of coins) cells in your table and to compute any cell in the table you run a loop (number of coins) times. The code you wrote has this complexity. It's likely that there is a different algorithm that has O(amount * number of coins) complexity.

Why does the greedy coin change algorithm not work for some coin sets?
By : slenders
Date : March 29 2020, 07:55 AM
seems to work fine A set which forms a matroid ( https://en.wikipedia.org/wiki/Matroid) can be used to solve the coin changing problem by using greedy approach. In brief, a matroid is an ordered pair M = (S,l) satisfying the following conditions: S is a finite nonempty set l is a nonempty family of subsets of S, called the independent subsets,such that if B>l and A is a subset of B, then A > l If A> l, B> l and A < B, then there is some element x> BA such that A U {x} >l

