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Table of Contents
Linear search
Binary search
Big O notation
Sorting algorithm
Select Sort
Bubble sort

CS-Week 3

Apr 04, 2025 am 06:06 AM
c language ai Data search Memory usage Bubble Sort

Algorithms are the set of instructions to solve problems, and their execution speed and memory usage vary. In programming, many algorithms are based on data search and sorting. This article will introduce several data retrieval and sorting algorithms.

Suppose there is an array [20, 500, 10, 5, 100, 1, 50] and you need to find the number 50. The linear search algorithm checks each element in the array one by one until the target value is found or the complete array is traversed.

CS-Week 3

The algorithm flow chart is as follows:

CS-Week 3

The pseudo-code for linear search is as follows:

<code>檢查每個元素:如果找到目標值:返回true返回false</code>

C language implementation:

 <code class="c">#include <cs50.h> #include <stdio.h> int main(void) { int numbers[] = {20, 500, 10, 5, 100, 1, 50}; int n = get_int("number: "); for (int i = 0; i </stdio.h></cs50.h></code>

The time complexity of linear search is O(n).

The binary search algorithm is suitable for sorted arrays. It improves efficiency by continuously narrowing the search range.

The pseudo-code for binary search is as follows:

<code>如果數(shù)組為空:返回false如果中間元素等于目標值:返回true如果中間元素大于目標值:在左半部分繼續(xù)查找否則:在右半部分繼續(xù)查找</code>

The time complexity of binary search is O(log n).

Big O notation

The large O notation is used to describe the time complexity of the algorithm. The following figure shows the curves of different time complexities:

CS-Week 3

The x-axis represents the input data volume, and the y-axis represents the solution time. O(log n) represents the optimal time complexity, and O(n2) represents the worst time complexity.

Sorting algorithm

The sorting algorithm is used to convert unordered data into ordered data. Sort data can improve search efficiency, such as binary search.

Select Sort

The pseudocode for selecting the sorting algorithm is as follows:

<code>對于每個元素:找到剩余元素中的最小值將最小值與當前元素交換</code>

Select the time complexity of sorting to be O(n2), regardless of whether the data has been sorted or not.

CS-Week 3

Bubble sort

The bubble sorting algorithm sorts data by repeatedly comparing and exchanging adjacent elements.

The pseudocode of the bubble sorting algorithm is as follows:

<code>重復(fù)n-1 次:對于每個元素:如果相鄰元素順序錯誤:交換它們?nèi)绻催M行任何交換:結(jié)束排序</code>

The time complexity of bubble sorting is O(n2) in worst case and O(n) in best case.

This article is based on the cs50x 2024 source code.

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