Compsci 201 Recitation 12

Professor PeckJimmy Wei4/11/2014

In this Recitation• Greedy algorithms• Brief intro• Practice

• Memoization• Brief intro• Practice

• Submit via form: http://goo.gl/66Dhvn• Today’s problems are APTs!

Greedy Algorithms• What are they?• An algorithm where continuously selecting local

optima leads to a globally optimal solution• This is called “greedy” because we select the best

solution for every sub-problem• Will learn about greedy algorithms in more detail

in Compsci 330

Greedy Algorithms• As an example, consider the problem of making

change:• We want to use as few coins as possible that

amount to our total• What coins would you give for $0.63?• 2 quarters, 1 dime, 3 pennies

• How did you determine that solution?• Start by using as many quarters as possible, then

dimes, then nickels, then pennies• Can you see how this is “greedy”?

Greedy Algorithms – Answer 1-3• Read the VoteRigging APT and write the

following method:• Answer questions 1-3 before you write this

code• What the greedy choice?

/** * Returns the minimum number of votes to buy for candidate 0 to win * the election * @param votes is an array where the ith element represents * how many individuals were originally plan to vote for the ith candidate */public int minimumVotes(int[] votes);

Greedy Algorithms – Answer 4-6• Read the OlympicCandles APT and write the

following method:• Answer questions 4-6 before you write this

code• What the greedy choice?

/** * Returns the maximum number of nights you can light candles * @param candles is an array where the ith element represents the height of * the ith candle you have available */public int numberOfNights(int[] candles);

Because of the snow• We didn’t have to to discuss memoization in

class

• Help with BSTcount (you will not be penalized for not completing BSTcount for APT set 5)

Memoization• What is it?• No, it’s not “memorization”… no ‘r’• Refers to the idea that as we solve problems we

might sometimes need to reuse solutions to sub-problems, so we store them instead of recalculating them

• Also will learn more about this and dynamic programming in CS330

Memoization• As an example, think of recursive fibonacci:• What’s wrong with the recursive solution below?

• We recalculate fibonacci for low values of n• Instead, we could store those values in a data structure

(memoize) so that we don’t have to recalculate them!

public int fibonacci(int n) { return (n<=2) ? 1 : fibonacci(n-1) + fibonacci(n-2);}

Memoization• Read the BSTCount APT and write the following

method:

• Think about the sub-problems you need to solve here and how we can store the solutions to those subproblems to avoid having to recalculate them

/** * Returns the total number of possible BSTs with the given values * @param values is an array holding all values that need to be stored in * the BST */public long howMany(int[] values);

Have a good weekend!

Don’t forget to submit!