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Lecture Data Structures & Algorithms: Chapter 3

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Lecture Data Structures & Algorithms: Chapter 3 (Searching Techniques prens) presented linear (sequential) search, binary search, complexity of algorithms.

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Nội dung Text: Lecture Data Structures & Algorithms: Chapter 3

DONG NAI UNIVERSITY OF TECHNOLOGY Data Structures & Algorithms 1
DONG NAI UNIVERSITY OF TECHNOLOGY Searching Techniques 2
DONG NAI UNIVERSITY OF TECHNOLOGY LINEAR (SEQUENTIAL) SEARCH BINARY SEARCH COMPLEXITY OF ALGORITHMS 3
DONG NAI UNIVERSITY OF TECHNOLOGY • To finding out whether a particular element is present in the list. • 2 methods: linear search, binary search • The method we use depends on how the elements of the list are organized – unordered list: • linear search: simple, slow – an ordered list: • binary search or linear search: complex, faster 4
DONG NAI UNIVERSITY OF TECHNOLOGY LINEAR (SEQUENTIAL) SEARCH • How? – Proceeds by sequentially comparing the key with elements in the list – Continues until either we find a match or the end of the list is encountered. – If we find a match, the search terminates successfully by returning the index of the element – If the end of the list is encountered without a match, the search terminates unsuccessfully. 5
DONG NAI UNIVERSITY OF TECHNOLOGY LINEAR (SEQUENTIAL) SEARCH int lsearch(int arr[], int n, int value) { for(int i=0;i
DONG NAI UNIVERSITY OF TECHNOLOGY BINARY SEARCH • List must be a sorted one • We compare the element with the element placed approximately in the middle of the list • If a match is found, the search terminates successfully. • Otherwise, we continue the search for the key in a similar manner either in the upper half or the lower half. 7
DONG NAI UNIVERSITY OF TECHNOLOGY 8
void bsearch(int arr[],int n,int value) NAI UNIVERSITY OF TECHNOLOGY DONG { int low,up,mid; low = 0; up = n-1; while(low
By Recursion DONG NAI UNIVERSITY OF TECHNOLOGY int Search (int arr[], int value, int low, int up) { if (low
DONG NAI UNIVERSITY OF TECHNOLOGY COMPLEXITY OF ALGORITHMS • In Computer Science, it is important to measure the quality of algorithms, especially the specific amount of a certain resource an algorithm needs • Resources: time or memory storage (PDA?) • Different algorithms do same task with a different set of instructions in less or more time, space or effort than other. • The analysis has a strong mathematical background. • The most common way of qualifying an algorithm is the Asymptotic Notation, also 11
DONG NAI UNIVERSITY OF TECHNOLOGY COMPLEXITY OF ALGORITHMS • It is generally written as • Polynomial time algorithms, – O(1) --- Constant time --- the time does not change in response to the size of the problem. – O(n) --- Linear time --- the time grows linearly with the size (n) of the problem. – O(n2) --- Quadratic time --- the time grows quadratically with the size (n) of the problem. In big O notation, all polynomials with the same degree are equivalent, so O(3n2 + 3n + 7) = O(n2) • Sub-linear time algorithms – O(logn) -- Logarithmic time • Super-polynomial time algorithms O(n!) ; O(2n) 12
DONG NAI UNIVERSITY OF TECHNOLOGY COMPLEXITY OF ALGORITHMS • Example1: complexity of an algorithm void func ( int a[], int n ) { 2 * O(1) + O(N) cout
DONG NAI UNIVERSITY OF TECHNOLOGY COMPLEXITY OF ALGORITHMS • Example2: complexity of an algorithm void func ( int a[], int n ) { cout
DONG NAI UNIVERSITY OF TECHNOLOGY COMPLEXITY OF ALGORITHMS • Linear Search – O(n). • Binary Search – O(log2 N) 15
DONG NAI UNIVERSITY OF TECHNOLOGY END 16

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