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CS1020 Week 13: 16 th April 2015

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Contents Sit-in Lab #4 2

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Sit-in Lab #4 Set A – Word Scramble Set B – Numeric Sequence 3

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Objective Recursion Understanding the principles of recursion Understanding the basic requirements of a problem Formulating a recursive solution Figuring out the optimized way of solving a problem 4

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Problem Statement Word Scramble: Find a word in a character array Input 1.A character array 2.A word Objectives 1.Finding if the characters of the word are present in the character array as substring All the letters of the word must be in consecutive positions in the array 2.Finding if the characters of the word are present in the character array as subsequence All the letters of the word must be in same order in the array Things to learn: 1.Using recursion 2.Using recursion in combination with loop Set A: Word Scramble 5

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Search for the starting position of the word first Recursive Logic: Substring badtal k k re Character Array talk Word to search b b a a d d t t a a l l r r e e Recursively search for the next characters till end of array/word Set A: Word Scramble 6

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Recursive Logic: Substring adtalre read Search for the starting position of the word first e e a a d d i i n n g g r r e e Recursively search for the next characters till end of array/word r r Search again for the starting position of the word in the rest of the array Set A: Word Scramble Character Array Word to search 7

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Recursive Logic: Subsequence badtal k k re red Search for the starting position of the word first b b a a d d t t a a l l r r e e Recursively search for the next characters till end of array/word If a character mismatches, ignore it and continue to search in the remaining array Character Array Word to search Set A: Word Scramble 8

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Program Flow findWordInArray 1.Find the position of first character of the word in array i 2.Call a recursive method to find word in the array given the 1 st position findWordInArrayRec(ar ray,word,i,1) 3.If returns True Print i 4.Otherwise Continue from step 1 for remaining array findWordInArrayRec 1.Match array[i+1] and word[k] 2.If matches Call findWordInArrayRec( array,word,i+1,k+1) 3.Otherwise return false 4.Base Case: End of word has been reached return True findWordInArrayRec 1.Match array[i+1] and word[k] 2.If matches Call findWordInArrayRec( array,word,i+1,k+1) 3.Otherwise Continue from step 1 for remaining array 4.Base Case: End of word has been reached return True Substring search Subsequence search Set A: Word Scramble 9

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Problem Statement Numeric Sequence: Finding maximum value from a sequence Input 1.An array integers Objectives 1.Whether the array is sorted in increasing sequence or not Determine whether an array is sorted, if yes, then print the maximum element 2.Find the maximum value from a sequence which is at first increasing then decreasing Things to learn: 1.Using recursion 2.Using binary search appropriately Set B: Numeric Sequence 10

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Recursive Logic: Check if sorted To check whether a complete array is sorted or not you need to check whether every two consecutive elements are sorted or not Note that for this problem it is necessary to do linear scan – we need to check every element 5 10 15 25 2030 Not Sorted!! 11 Set B: Numeric Sequence

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Recursive Logic: Find maximum element Property of the array: 1.The sequence is increasing at first and then decreasing 2.There are no duplicate elements Maximum element is the peak element Last element of the increasing sequence/first element of decreasing element It is greater than the element before it It is also greater than the element after it There is always a single element in the array satisfying both the above properties 12 Set B: Numeric Sequence

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Recursive Logic: Find maximum element Binary search: 1.If the element is peak element return the element // base case 2.If the current element belongs to increasing sequence (arr[i-1] < arr[i] < arr[i+1]) search on the right side of array 3.If the current element belongs to decreasing sequence (arr[i-1] > arr[i] > arr[i+1]) search on the left side of array 1 3 5 9811 10 Belongs to increasing sequence – search on right Belongs to decreasing sequence – search on left Peak element! 13 Set B: Numeric Sequence

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Program Flow checkIfSorted 1.If array contains single element return true 2.If value at index < value at index+1, check the rest of the array (from index+1) 3.Otherwise return false findMax 1.If array contains single element return the element 2.If array contains 2 elements, return the greater element 3.Check mid-point of array i.If peak element, return the value ii.If belongs to increasing seq, findMax in right half iii.If belongs to decreasing seq, findMax in left half 14 Set B: Numeric Sequence

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