Sequential search

Content summary

This lesson introduces the sequential search algorithm.

Idea

Imagine a deck of cards all face down. You need to find where one of the 3s is (any of the four 3s).

The natural way is to flip the cards one by one, starting from the top, until you see a 3.

We apply the same idea to an array:

We compare each element with the target value k, from the beginning to the end, and stop as soon as we find it.

Here’s how it works step by step:

How the sequential seach algorithm works

1. Go through the array from the first element to the last (A[i]), and for each position i:

   • If A[i] == k, return i — that’s the index where the value was found.

2. If we finish checking all elements and never found k, return -1 (meaning: not found).

   (-1 is a common convention for "not found" because array indices start at 0 — there are no negative indices.)

Terminology

Sequential search is also known as linear search.

Both terms can be used interchangeably. Internationally, linear search is the more common term. In Vietnamese textbooks, however, it is usually translated as sequential search (tìm kiếm tuần tự).

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Flowchart

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Visualization

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Writing the program

1. Import the numpy library.

import numpy as np

2. Write the function linear_search() to implement the sequential search algorithm.

The function takes two input parameters:

• The array A
• The target value k

It returns:

• The index i where k is found, or
• -1 if k is not found.

def linear_search(A, k):
    # Lấy số lượng phần tử của mảng A
    n = len(A)

    # Duyệt từng phần tử từ đầu đến cuối mảng
    for i in range(n):
        if A[i] == k:
            # Nếu A[i] nào đó bằng k thì trả về chỉ số i
            return i

    # Không tìm thấy, trả về -1
    return -1

3. Write the main program.

For simplicity in this example, we will skip asking the user to input the entire array. Instead, we create a fixed array in the code, and the user only needs to enter the value they want to search for.

if __name__ == '__main__':
    # Khởi tạo mảng Array
    Array = np.array([1, 7, 4, 0, 9, 4, 8, 8, 2, 4, 5, 5])

    # Cho người dùng nhập giá trị cần tìm
    key = int(input('Nhập giá trị cần tìm: '))

Call the linear_search() function and store the result (the found index or -1) in a variable named found.

if __name__ == '__main__':
    # Khởi tạo mảng Array
    Array = np.array([1, 7, 4, 0, 9, 4, 8, 8, 2, 4, 5, 5])

    # Cho người dùng nhập giá trị cần tìm
    key = int(input('Nhập giá trị cần tìm: '))

    # Gọi hàm linear_search()
    found = linear_search(Array, key)

Use the variable found to print an appropriate message:

• If found is not -1, display that the value was found and show its position.
• If found is -1, display that the value was not found.

if __name__ == '__main__':
    # Khởi tạo mảng Array
    Array = np.array([1, 7, 4, 0, 9, 4, 8, 8, 2, 4, 5, 5])

    # Cho người dùng nhập giá trị cần tìm
    key = int(input('Nhập giá trị cần tìm: '))

    # Gọi hàm linear_search()
    found = linear_search(Array, key)

    if found == -1:
        # Nếu chỉ số trả về là -1 thì in ra không tìm thấy
        print(f'Không tìm thấy {key}')
    else:
        # Ngược lại, khác -1, thì in ra tìm thấy tại found
        print(f'Tìm thấy {key} tại vị trí {found}')

4. Run the program above and enter 9. The output will be:

Nhập giá trị cần tìm: 9
Tìm thấy 9 tại vị trí 4

Run the program again and enter 6 as the value to search for. The output will be:

Nhập giá trị cần tìm: 6
Không tìm thấy 6

Note

If the value k appears multiple times in the array, the sequential search algorithm will return only the first occurrence (the one found earliest during the traversal).

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Source code

The complete code is available at:

• Google Colab

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Some English words

Vietnamese	Tiếng Anh
so sánh	compare
thuật toán tìm kiếm	search algorithm
tìm kiếm tuần tự	sequential search, linear search
tìm thấy, không tìm thấy	found, not found

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