Change-Making Problem: Difference between revisions

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(Created page with "{{DISPLAYTITLE:Change-Making Problem (Change-Making Problem)}} == 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 == <pre>n: number of coin denominations S: sum to be made</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-align:center;" width="100%" ! Name !! Year !! Time !! Space !! Approximation Factor !!...")
 
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== Parameters ==  
== Parameters ==  


<pre>n: number of coin denominations
n: number of coin denominations
S: sum to be made</pre>
 
S: sum to be made


== Table of Algorithms ==  
== Table of Algorithms ==  

Revision as of 12:03, 15 February 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

Change-Making Problem - Time.png

Space Complexity graph

Change-Making Problem - Space.png

Pareto Decades graph

Change-Making Problem - Pareto Frontier.png