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Offical+Review+Quesiton+W2009

# Offical+Review+Quesiton+W2009 - CS115 Final Exam Review...

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CS115 Final Exam Review Session Solution last update Apr 19 th , 2009 copy right 2009 Oda_Ea gle Production, all right reserved C S115/116/125/134/135/136/241/240/341/343 Tutor odaea [email protected] 1. Write a recursive function sum-powers-one-half, which consumes a natural number n and computes 1+ ½ + ½ 2 + … + (½) n-1 + (½) n ( define ( sum-powers-one-half n) ( cond ( ( zero? n ) 1 ) ( else ( + ( expt 1/2 n ) ( sum-powers-one-half ( sub1 n ) ) ) ) ) ) 2. Write a function to return the largest key in a non-empty association list. ( define ( largest-key aal ) ( local ( ( define ( largest-key-help aal msf) ( cond ( ( empty? aal ) msf ) ( ( < ( first ( first aal ) ) ( first msf ) ) ( largest-key-help ( rest aal ) msf ) ) ( else ( largest-key-help ( rest aal ) ( first aal ) ) ) ) ) ) ( cond ( ( empty? aal ) empty ) ( else ( largest-key-help aal ( first aal ) ) ) ) ) ) 3. bsts can be used to store dictionaries as well. Write a function to return the largest key stored in a bst. Note: make use of the property of the bst. ( define ( largest-key-bst bst ) ( cond ( ( empty? ( tree-right bst ) ) ( tree-key bst ) ) ( else ( largest-key-bst ( tree-right bst ) ) ) ) )

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4. Consider finding the longest string which is stored as an associated value in a dictionary. Write this method for both implementations of dictionaries discussed in class.
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