levo

Searching and Shortest-Path Algorithms

Tracing a shortest-path algorithm by hand

  • 3 things to know
  • Component 1

Overview

One weighted graph carried through the whole algorithm, with the tentative distances after each step and the order in which the nodes settle.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

How is the tentative distance to a node updated during a trace?

Key term

Describe the layout of a table used to trace Dijkstra's algorithm by hand.

Key term

How do you read the route itself out of a completed trace table?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    In the graph P–Q 3, P–R 7, Q–R 2, Q–S 6, R–S 1, R–T 9, S–T 4, what are the tentative distances once the start node P has been processed?

    Model answer

    Node Q has a tentative distance of 3 and node R has 7. Nodes S and T are still at infinity.

  2. 2

    In the graph P–Q 3, P–R 7, Q–R 2, Q–S 6, R–S 1, R–T 9, S–T 4, which node does Dijkstra's algorithm settle second when starting at P?

    Model answer

    Node Q is settled second with a distance of 3. Node Q has the smallest tentative distance of the unvisited nodes.

  3. 3

    In the graph P–Q 3, P–R 7, Q–R 2, Q–S 6, R–S 1, R–T 9, S–T 4, what is the shortest distance from P to R?

    Model answer

    The shortest distance from P to R is 5, along P to Q to R. The direct edge P–R costs 7 and is discarded.

  4. 4

    In the graph P–Q 3, P–R 7, Q–R 2, Q–S 6, R–S 1, R–T 9, S–T 4, what is the shortest distance from P to S?

    Model answer

    The shortest distance from P to S is 6, along P to Q to R to S. The route using the edge Q–S would cost 9.

  5. 5

    In the graph P–Q 3, P–R 7, Q–R 2, Q–S 6, R–S 1, R–T 9, S–T 4, what is the shortest distance from P to T?

    Model answer

    The shortest distance from P to T is 10, along P to Q to R to S to T. The route P to Q to R to T would cost 14.

  6. 6

    In the graph P–Q 3, P–R 7, Q–R 2, Q–S 6, R–S 1, R–T 9, S–T 4, state the order in which the nodes are settled from P.

    Model answer

    The nodes settle in the order P, Q, R, S and then T. The corresponding distances are 0, 3, 5, 6 and 10.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book
2Open book
3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Data Structures: Arrays, Records and Hash Tables
Stacks, Queues, Linked Lists and Trees
Boolean Logic and Simplification
Algorithms, Pseudo-Code and Programming Constructs

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

KDW to HAT.
decryptsencryptscompresses

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe two are not the same.
BOpen source refers to the availability of the code.
CMuch open source software is free of charge.

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

Backup means the copy of the data.
TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Searching and Shortest-Path Algorithms, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Or £46 a year, about £3.83 a month. Cancel anytime.