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aa:lab:07 [2020/11/23 23:07] claudiu.dorobantu |
aa:lab:07 [2020/11/23 23:12] (current) claudiu.dorobantu |
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| Consider the following search algorithm of a value v in a sorted array arr: | Consider the following search algorithm of a value v in a sorted array arr: | ||
| - | int search (int arr[], int lo, int hi, int v){ | + | int search(int arr[], int lo, int hi, int v) |
| - | int mid = (lo+hi)/2; | + | { |
| + | int mid = (lo + hi) / 2; | ||
| if (arr[mid] == v) | if (arr[mid] == v) | ||
| return mid; | return mid; | ||
| Line 56: | Line 57: | ||
| return search(arr, mid, hi, v); | return search(arr, mid, hi, v); | ||
| } | } | ||
| - | | + | |
| **2.1** Determine the recurrence for the search algorithm above. | **2.1** Determine the recurrence for the search algorithm above. | ||
| Line 68: | Line 69: | ||
| Consider the following modification to 'search' (which may not make sense in practice): | Consider the following modification to 'search' (which may not make sense in practice): | ||
| - | | + | |
| - | int search (int arr[], int lo, int hi, int v){ | + | int search(int arr[], int lo, int hi, int v) |
| + | { | ||
| if (!is_sorted(arr, lo, hi)) | if (!is_sorted(arr, lo, hi)) | ||
| return -1; | return -1; | ||
| - | int mid = (lo+hi)/2; | + | int mid = (lo + hi) / 2; |
| if (arr[mid] == v) | if (arr[mid] == v) | ||
| return mid; | return mid; | ||
| Line 82: | Line 84: | ||
| return search(arr, mid, hi, v); | return search(arr, mid, hi, v); | ||
| } | } | ||
| - | | + | |
| **3.1** In what time can we check if an array is sorted? | **3.1** In what time can we check if an array is sorted? | ||
| Line 100: | Line 102: | ||
| **4.5** Consider the following algorithm: | **4.5** Consider the following algorithm: | ||
| - | + | ||
| - | int fibo(int n){ | + | int fibo(int n) |
| + | { | ||
| if (n <= 1) | if (n <= 1) | ||
| return n; | return n; | ||
| - | return fibo(n-1) + fibo(n-2); | + | return fibo(n - 1) + fibo(n - 2); |
| } | } | ||
| - | + | ||
| - | Determine its complexity with regard to the size of the input. | + | Determine its complexity with regard to the size of the input. |
| **4.6** Solve $math[T(n) = \sqrt n * T(\sqrt n) + n]. | **4.6** Solve $math[T(n) = \sqrt n * T(\sqrt n) + n]. | ||