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Lecture 22: Arrays (cont)

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2 Lecture Contents: t Searching in array: linear search binary search t Multidimensional arrays t Demo programs t Exercises

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3 The problem Searching in array: to determine and return the location of a particular value (target) Classification of searching algorithms: t Linear search t Binary search t Search based on hash functions

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4 43 Linear Search t The idea of a linear search is to walk through the entire array until a target value is located t If the target is not located, specific type of indicator needs to be returned

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5 Linear search algorithm Problem: to search a target in array Given:1. array (populated collection of data items) 2. target Output:index of array element that matches the target OR -1 if there is no match

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6 Linear search algorithm 1. Assume the target has not been found. 2. Start with the initial array element. 3.Repeat while the target is not found and there are more array elements { 4. If the current element matches the target 5. Set a flag to indicate the target was found Else 6. Advance to the next array element } // end of repeat 7. If the target was found 8. Return the target index as a search result Else 9. Return 1 as a search result.

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7 Linear search implemented iteratively // Iterative Linear Search int LinSearchIterative(int target, int table[], int size) { int k = 0; while ( k < size ) { if (target == table[k]) return k; k++; } return -1; }

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8 Linear search implemented iteratively How to call the function? int LinSearchIterative(int target, int table[], int size); void main() { int tar; int m[] = { 10, 15, 8, 30, 50, 40 }; int res; tar = 20; // test other value as well res = LinSearchIterative(tar, m, 6); if (res== -1) cout low (low the target 9. Let high be mid1 Else 10. Let low be mid+1 } // end of repeat 11. return 1

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16 Binary search implemented iteratively // Iterative Binary search int BinSearchIterative(int target, int table[], int size) { int low, high, mid; low = 0; high = size - 1; while ( low table[mid]) low = mid + 1; } return -1; }

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17 Binary search implemented iteratively How to call the function?

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18 Binary search implemented recursively // Recursive Binary search int BinSearchRecursive(int target, int table[], int low, int high) { if (low > high) return -1; int mid; mid = (low + high) / 2; if (target == table[mid]) return mid; if (target < table[mid]) // low half of the table { // high = mid -1; return BinSearchRecursive(target, table, low, mid -1); } if (target > table[mid]) // high half of the table { // low = mid+1; return BinSearchRecursive(target, table, mid +1, high); }

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19 Binary search implemented recursively How to call the function?

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20 Binary search - Time performance Array size of n After 1 iteration array size of n/2 = n / 2^1 After 2 iterations array size of n / 4 = n / 2^2 After x iterations array size of 1 = n / 2^x n = 2 ^ xx = ln n

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21 More on arrays Extract from Friedman/Koffman, chapter 9

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Data Structures Arrays and Structs Chapter 9

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23 37 9.5 Searching and Sorting Arrays t Look at 2 common array problems Searching Sorting t How do we go about finding the smallest number in an array? Assume 1st is smallest and save its position Look for one smaller If you locate one smaller save its position

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24 38 ArrayOperations.cpp // File: arrayOperations.cpp // Finds the subscript of the smallest value in a // subarray. // Returns the subscript of the smallest value // in the subarray consisting of elements // x[startindex] through x[endindex] // Returns -1 if the subarray bounds are invalid. // Pre: The subarray is defined and 0