Change-Making Problem (Change-Making Problem)
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Description
Given an unlimited amount of coins of denominations $c_1, \ldots, c_n$, and a desired sum $S$, find the minimum number of coins necessary to make $S$.
Parameters
n: number of coin denominations
S: sum to be made
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Brute Force | 1940 | $O(S^n)$ | $O(n)$ | Exact | Deterministic | |
| Dynamic Programming | 1953 | $O(Sn)$ | $O(Sn)$ | Exact | Deterministic | Time |
| Probabilistic Convolution Tree | 2014 | $O(n log n)$ | $O(n log n)$ | Deterministic | Time & Space |
Time Complexity graph
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Space Complexity graph
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Pareto Decades graph
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