# D1 Maths Definitions

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- Created by: Lizzy Day
- Created on: 08-03-15 18:26

Algorithm

a precise set of instructions so clear that it will allow anyone/anything to use it to achieve a particular goal in a specified number of steps.

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Flow Chart

a visual representation of an algorithm in which boxes and lines are used to indicate different steps in a process

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Bubble sort

an algorithm to sort a list into alphabetical or numerical order

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Adjacent

next to eachother.

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Pass

one run through a set of steps in an algorithm which may be repeated

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Quick sort

an algorithm to sort a list into alphabetical or numerical order

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Pivot

the item selected in the quick sort which are either less than or more than a particular pivot value. Each sub-list remains in the order of the items before comparison with the pivot.

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Binary Search

an algorithm to check whether a particular value appears in an ordered numerical or alphabetical list

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Ordered List

a list that has been sorted, perhaps by the quick sort or bubble sort algorithm

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Bin-packing algorithm

a class of problems in which it is desirable to fit items of varying small sizes into containers of a larger size, called bins. The sizes may typically refer to lengths or times.

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Optimal Solution

the best possible answer to a problem. A sub-optimal solution is one which is not optimal.

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First-fit algorithm

a quick, but often sub-optimal, bin-packing algorithm in which unsorted items are placed in the first bin possible

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First-fit decreasing algorithm

an easy, two-step bin-packing algorithm hat gives fairly good, but possibly sub-optimal solutions by solving the items first, then applying the first-fit algorithm

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Full-Bin packing

a bin-packing routine which relies on intelligence. The user spots combinations of items that will fit together and then fits remaining items by using the first-fit algorithm. It is slow but often results in an optimal solution

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Graph

an object consisting of points which are connected by lines

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Vertex

a point on a graph

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Node

another name for a vertex or a point on a graph

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Edge

a line connecting a pair of points on a graph. These 'points' may be a single point

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Arc

another name for an edge.

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Weight

a number associated with an edge (arc) that represents length, cost, time or some other variable associated with this line

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Weighted Graph

a graph in which all edges have a weight

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Network

a shorter name for a weighted graph

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Vertex set

the set of all nodes or vertices of a graph

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Edge set

the set of all arcs or edges of a graph

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Subgraph

starting from an original graph G, select some or all of the vertices and some of the edges. A subgraph is part of the original graph

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Degree (of a vertex)

is the number of edges incident to it. The degree of a node is the number of arcs coming from it

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Valency (of a vertex)

another name for the degree of a vertex

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Order (of a vertex)

yet another name for the degree of a vertex

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Handshaking lemma

the sum of the degrees of all vertices in a graph must be even since we count each edge twice- once from each end of the 'handshake' between it's vertices.

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Even Degree

a vertex which has a degree which is an even number

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Odd degree

a vertex which has a degree which is an odd number

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Walk

a finite sequence of edges, such that the end vertex of one edge is the start of the next edge

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Path

a finite sequence of edges, such that the end vertex of one edge is the start of the next edge and in which no vertex appears more than once.

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Cycle

a path which is then 'closed' by the addition of an extra edge which joins the path's ending vertex back to the paths starting vetex

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Circuit

another name for a cycle

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Connected (vertex)

two vertices are connected if there is a path between them.

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Connected (graph)

a graph is connected if all possible pairs of vertices in it are connected

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Loop

an edge that starts and finished at the same vertex

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Simple graph

a graph in which there are no loops and no pair of vertices has more than one edge joining them directly

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Directed edge

an edge in which the direction of connection matters and is shown by an arrow

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Directed graph

a graph that contains directed edges

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Digraph

a directed graph

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Tree

a connected graph that contains no cycles

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Spanning tree

a subgraph which includes all the vertices but only sufficient of the edges to be a tree

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Bipartite graph

a graph which contains two sets of vertices, X and Y in which all the edges join a vertex in set X to a vertex in set Y

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Eulerian graph

all even nodes

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Semi Eulerian graph

exactly 2 odd nodes

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Non Eulerian graph

all odd nodes

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## Other cards in this set

### Card 2

#### Front

a visual representation of an algorithm in which boxes and lines are used to indicate different steps in a process

#### Back

Flow Chart

### Card 3

#### Front

an algorithm to sort a list into alphabetical or numerical order

#### Back

### Card 4

#### Front

next to eachother.

#### Back

### Card 5

#### Front

one run through a set of steps in an algorithm which may be repeated

#### Back

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