# Tag Archives: log

## Data structure challenge: application

I forgot to mention this in my previous post, but the thing which got me thinking about the predecessor problem in the first place was this competitive programming problem on Open Kattis: Profitable Pizzas I challenge you to go and … Continue reading

## Data structure challenge: solutions

In my previous post I challenged you to find a way to keep track of a sequence of slots in such a way that we can quickly (in or better) either mark any empty slot as full, or find the … Continue reading

Posted in data structures | | 3 Comments

## Data structure challenge: finding the rightmost empty slot

Suppose we have a sequence of slots indexed from 1 to . Each slot can be either empty or full, and all start out empty. We want to repeatedly do the following operation: Given an index , find the rightmost … Continue reading

Posted in data structures | Tagged , , , , , , , | 16 Comments

## Test your intuition: logarithmic time

Here is a question to test your intuition for logarithms. NO CALCULATORS allowed, and don’t take a long time to work out an answer in your head! Just go with your gut. After you have committed to a choice (say, … Continue reading

Posted in teaching | Tagged , , , | 16 Comments

## Sum of heights in a binary tree

Executive summary: every year when teaching data structures I always forget how to analyze the cost of building a binary heap, which amounts to summing the heights of all the nodes in a full binary tree. So I’m writing down … Continue reading

Posted in math, teaching | Tagged , , , , , , , | 2 Comments