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See Also [[Further Maths - Graphs]]S [[Further Maths - Kruskal's Algorithm]]S Flashcards What is the first step of Prim’s algorithm?? Choosing any start vertex. What do you do after choosing a first vertex for Prim’s algorithm?? Repeatedly choose the shortest edge that connects a new vertex. What is the worst-case complexity of Prim’s algorithm?? $$ O(n^3) $$ 2021-11-10 What is the first step if you’ve been told to start at $A$?

Flashcards What does Avagadro’s constant represent?? The number of atoms in $12$ grams of Carbon-12. What is one mole of a substance?? An amount in which the number of atoms/molecules is equal to Avogadro’s constant. What is the molar mass of a substance?? The mass per mole of a substance. How do you find the mass of one atoms from its mass number/nucleon number?? Divide the mass number by Avogadro’s constant. What is a nucleon?? A proton or a neutron.

See Also [[Further Maths - Graphs]]S [[Further Maths - Prim's Algorithm]]S Flashcards What is a spanning tree?? A tree that includes all the vertices of a graph. What is a minimum spanning tree?? A tree that includes all the vertices of a graph at the minimum possible cost. What is the first step of Kruskal’s algorithm?? List the edges in the order of weight, smallest first. What step comes after listing out the edges of a graph in weight order for Kruskal’s algorithm?

See Also Flashcards What is a Eulerian trail?? A trail that goes along every edge exactly once. Why isn’t a trail that visits every edge multiple times a Eulerian trail?? Because it visits an edge more than once. What is a Eulerian trail that joins up to the beginning called?? A Eulerian cycle. How many edges does entering a vertex and then exiting a vertex “use up” when constructing a Eulerian trail?? 2 Why must all vertices be even for a Eulerian trail to be possible?

See Also Flashcards What is a Hamiltonian cycle?? A cycle that visits all the vertices of a graph. How many times should a Hamiltonian cycle visit a vertex?? Just one, apart from at the end. What must be true about the start and end vertex of a Hamiltonian cycle?? It must be the same. What is the formula for the number of Hamiltonian cycles for a complete graph $K_n$?? $$ \frac{(n - 1)!}{2} $$ Backlinks [[Further Maths - Syllabus]]S [[Further Maths - Graphs]]S Metadata date: 2021-11-04 12:14 tags: - '@?

Flashcards 2021-11-02 If you know two roots of a cubic equation $ax^3 + bx^2 + cx + d = 0$, how can you find the final one?? Use the sum of the roots or product of the roots formulas. Backlinks [[MAT Questions]]N Metadata date: 2021-11-02 19:08 summary: "" tags: - '@?public' - '@?mat' - '@?notes' - '@?maths' title: MAT - Paper 2020 - Q2

Flashcards 2021-11-02 When given a seemingly opaque equation like $$\beta^4 + 2\beta^3 - 4\beta - 2$$ what should you do?? Try and plot it. What’s a common technique for showing that if something holds for a special case of a graph/function, it also holds more generally?? The properties are preserved under geometric transformations. Backlinks [[MAT Questions]]N Metadata date: 2021-11-02 18:01 summary: "" tags: - '@?public' - '@?mat' - '@?notes' - '@?maths' title: MAT - Paper 2019 - Q3

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