Change-Making Problem: Difference between revisions
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== Parameters == | == Parameters == | ||
n: number of coin denominations | $n$: number of coin denominations | ||
S: sum to be made | $S$: sum to be made | ||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Dynamic Programming (Change-Making Problem Change-Making Problem)|Dynamic Programming]] || 1953 || $O(Sn)$ || $O(Sn)$ || Exact || Deterministic || [https://dl-acm-org.ezproxy.canberra.edu.au/doi/10.1145/321864.321874 Time] | | [[Dynamic Programming (Change-Making Problem Change-Making Problem)|Dynamic Programming]] || 1953 || $O(Sn)$ || $O(Sn)$ || Exact || Deterministic || [https://dl-acm-org.ezproxy.canberra.edu.au/doi/10.1145/321864.321874 Time] | ||
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| [[Probabilistic Convolution Tree (Change-Making Problem Change-Making Problem)|Probabilistic Convolution Tree]] || 2014 || $O(n log n)$ || $O(n log n)$ || || Deterministic || [https://www-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/pubmed/24626234 Time] & [https://pubmed-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/24626234/ Space] | | [[Probabilistic Convolution Tree (Change-Making Problem Change-Making Problem)|Probabilistic Convolution Tree]] || 2014 || $O(n \log n)$ || $O(n log n)$ || || Deterministic || [https://www-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/pubmed/24626234 Time] & [https://pubmed-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/24626234/ Space] | ||
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[[File:Change-Making Problem - Time.png|1000px]] | [[File:Change-Making Problem - Time.png|1000px]] | ||
Latest revision as of 09:12, 28 April 2023
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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