Topic summary · Decision maths (D1)

Algorithms on Graphs summary

Graph algorithms — shortest paths and minimum connectors — need careful labelling of vertices and growing sets.

Open Learning Sheet — Algorithms on Graphs Download Algorithms on Graphs answers PDF

Files: D1-Algorithms on Graphs.pdf · D1-Algorithms on Graphs answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

Dijkstra updates temporary labels until distances become permanent.
Prim and Kruskal build MSTs with different edge-selection rules.
Reject any MST edge that would create a cycle.
State the final route or tree with its total weight.

Worked example 1 — Gradient

Through $(1,2)$ and $(3,8)$ . Gradient?

Working

m=3

Rise over run.

Worked example 2 — Y-intercept

$y=3x-4$ meets the $y$ -axis where?

Working

(0,-4)

Set $x=0$ .

Worked example 3 — Evaluate

For $y=2x+1$ , find $y$ when $x=3$ .

Working

y=7

Substitute.

Worked example 4 — Kruskal

When does Kruskal reject an edge?

Working

\text{when it would form a cycle}

Always take the next lightest edge that keeps a forest.

Scaffolded Learning Sheet and answers (PDFs)

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