Mathematical Algorithms Challenge

A method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, where each type of case is checked to see if the proposition in question holds.

Smallest element in the unsorted portion of a list is selected and then swapped with the element at the beginning of the sorted portion of the list

Compares the adjacent pair of elements of the list and swaps them if they are in the wrong order.

(sometimes called a linear search) examines a sequence of data objects one by one until a match is encountered (successful search), or the list is exhausted without finding a match (unsuccessful search).

It is the process of finding the exact copy of pattern/s 𝑷𝑷 with all substrings of a given text 𝑻𝑻. Those comparisons between substring and pattern proceed character by character unless a mismatch is found. Whenever a mismatch is found, the pattern is shifted one (1) position to the right and comparison is repeated until a match is found or until the end of the text is reached.

It is a brute-force approach to a combinatorial problem. It essentially generates a list of all potential solutions to the problem systematically, evaluates potential solutions one by one, disqualifies the infeasible ones, and, for an optimization problem, keeps track of the best one found so far.

Its goal is to find the least expensive or shortest way to visit through a given set of 𝑛𝑛 cities once and return to the original starting point.

A path that begins and ends at the same vertex and passes through all other vertices of the graph exactly one time. It is named after the Irish mathematician Sir William Rowan Hamilton

Requires pairing of 𝑛𝑛 people to execute 𝑛𝑛 jobs in such a way that the total cost/profit of the pairings is minimized or maximized.

It is also known as Flood’s Technique or Matrix Reduction Method. It is used to find minimum matches in which the time of completion or cost of making all activities by the number of persons is minimized. It was first published by Harold W. Kuhn in 1955.

It was based on the earlier work of Hungarian mathematicians Dénes König and Jenö Egerváry.

Each entity is to be assigned to exactly one (1) task. Each task is to be performed by exactly one (1) entity.