Day 21: mat385

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Today:

• Announcements:
  • Your Section 6.3 homework is graded (#4, 10, 17):
    4. Sorted list of four elements, binary search yields a best worst-case depth of $floor(n)+1$ (=3).
    10. If we have to stuff $n$ things into a binary search tree, the best we can do at a given depth is a power of two (minus 1). So, since 8 is greater than $7=2^3-1$, we have to go to depth three ($15=2^(3+1)-1$) to hold our eight elements.
    17. In this problem we don't care whether the coin is heavier or lighter; we simply want to find the counterfeit one.

        Turns out you can do it as a binary tree, therefore. But most of you did it as ternary.

        With only two comparisons, you can find it. See the key.

• Today: Section 7.4: Traversal Algorithms

  Once again on the rather simple algorithmic front, with algorithms for traversing (visiting each node) of a graph.

  We might be simply indicating what's stored at each node of the graph, or we may be performing some operation based on those nodes. Whatever we're doing, we want to do it efficiently.

  • Traversal algorthms include breadth first, depth first, and I include one that a student proposed. Maybe you can find a better one!:)
    1. depth first
    2. breadth first

  • The marked up pdf for Section 7.4.

• Links:
  • Depth first and Breadth first algorithms for problems from Gersting (in lisp)
  • Here's a traversal which was a student's idea, based on the breadth-first algorithm. It computes the distances between all pairs of vertices (like Floyd's algorithm).

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  Website maintained by Andy Long. Comments appreciated.