a3 - McGill University COMP251 Assignment 3 Worth 10 Due...

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McGill University COMP251: Assignment 3 Worth 10%. Due October 29 at the beginning of lecture (10am sharp!) Question 1 Give an algorithm that sorts (into non-decreasing order) an input array of n integers in the range 0 to n 3 - 1. Your algorithm must run in O ( n ) time. Question 2 For this question, an arithmetic expression (or just expression) is built from integers and variables x 1 ,x 2 ,..., using the operations + , - , × , ÷ as follows: any number is an expression, any variable is an expression, if A and B are expressions, then so are ( A - B ) and ( A ÷ B ), if A 1 , A 2 , ... , A k are expression, then so are ( A 1 + A 2 + ... + A n ) and ( A 1 × A 2 × ... × A n ) For example, (( x 1 + 5 + ( x 2 × 3 × x 6 ) + ( x 2 ÷ x 1 )) - 4) is an expression. (a) Give a data structure for representing arithmetic expressions as trees of unbounded branch- ing. Clearly explain the fields you are using. (b) Give an algorithm that on input ( A,X ), where A is the root of the tree representing an expression which we also call A and X
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