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19-Section-Handout

# 19-Section-Handout - CS106X Autumn 2010 Handout 19 October...

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CS106X Handout 19 Autumn 2010 October 11 th , 2010 Section Handout Problem 1: Generating Expressions Write the computeAllPossibilities function, which given a collection of one-digit numbers, expressed as a digit string (i.e. "14728" ), returns the set of all integers that can be generated by combining all of the one-digit numbers using + , - , * , / , and parentheses. For instance, computeAllPossibilities("1447") would return a set that includes -8 : 1 – 4 * 4 + 7 3 : 4 * 1 – 7 / 4 34 : 7 * 4 – 1 + 7 39 : 7 * (1 + 4) + 4 33 : (7 + 4) * (4 - 1) (Of course, the set of possibilities is larger than the four listed above.) Some clarifications and suggestions: o The digit string will only consist of the characters '0' through '9' , although there may be multiple instances of each digit. o The original digit string will never be empty. o Division is integer division, so that 5 / 4 * 4 equals 4 , not 5 . o Care must be taken to avoid division by zero so that it never contributes to any expression evaluation. o You must use all of the digits in the digit string, including duplicates.

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