Python: Get all strobogrammatic numbers that are of length n

Last update on December 21 2024 07:19:12 (UTC/GMT +8 hours)

Strobogrammatic Numbers

Write a Python program to get all strobogrammatic numbers that are of length n.

A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down (e.g., 69, 96, 1001).

For example,
Given n = 2, return ["11", "69", "88", "96"].
Given n = 3, return ['818', '111', '916', '619', '808', '101', '906', '609', '888', '181', '986', '689']

Visual Presentation:

Sample Solution:

Python Code:

# Define a function 'gen_strobogrammatic' that generates strobogrammatic numbers of length 'n'.
def gen_strobogrammatic(n):
    """
    :type n: int
    :rtype: List[str]
    """
    # Call the helper function with the given length 'n'.
    result = helper(n, n)
    return result

# Define a helper function 'helper' to recursively generate strobogrammatic numbers.
def helper(n, length):
    # Base case: when 'n' is 0, return an empty string.
    if n == 0:
        return [""]
    # Base case: when 'n' is 1, return the strobogrammatic digits for length 1.
    if n == 1:
        return ["1", "0", "8"]
    # Recursive case: generate strobogrammatic numbers for 'n-2'.
    middles = helper(n-2, length)
    result = []
    # Iterate over the generated middles and create strobogrammatic numbers.
    for middle in middles:
        # If 'n' is not equal to the original length, add "0" on both sides.
        if n != length:
            result.append("0" + middle + "0")
        # Add strobogrammatic numbers with "8" in the middle.
        result.append("8" + middle + "8")
        # Add strobogrammatic numbers with "1" in the middle.
        result.append("1" + middle + "1")
        # Add strobogrammatic numbers with "9" in the first half and "6" in the second half.
        result.append("9" + middle + "6")
        # Add strobogrammatic numbers with "6" in the first half and "9" in the second half.
        result.append("6" + middle + "9")
    return result

# Test the function with different values of 'n' and print the results.
print("n = 2: \n", gen_strobogrammatic(2))
print("n = 3: \n", gen_strobogrammatic(3))
print("n = 4: \n", gen_strobogrammatic(4))

Sample Output:

n = 2: 
 ['88', '11', '96', '69']
n = 3: 
 ['818', '111', '916', '619', '808', '101', '906', '609', '888', '181', '986', '689']
n = 4: 
 ['8008', '1001', '9006', '6009', '8888', '1881', '9886', '6889', '8118', '1111', '9116', '6119', '8968', '1961', '9966', '6969', '8698', '1691', '9696', '6699']

Explanation:

The above Python code generates strobogrammatic numbers of a given length 'n'. Strobogrammatic numbers are those that remain the same when rotated 180 degrees. Here's a brief explanation:

• The main function is "gen_strobogrammatic(n)", which takes an integer 'n' as input and returns a list of strobogrammatic numbers of length 'n'.
• The main function calls a helper function "helper(n, length)" to recursively generate strobogrammatic numbers.
• In the helper function:
• If 'n' is 0, it returns a list containing an empty string (base case).
• If 'n' is 1, it returns a list of strobogrammatic digits for length 1 ('1', '0', '8').
• For 'n' greater than 1, it recursively generates strobogrammatic numbers for 'n-2'.
• The "helper()" function builds strobogrammatic numbers by adding digits in the middle and considering rotations:
• If 'n' is not equal to the original length, it adds "0" on both sides.
• It adds strobogrammatic numbers with "8" in the middle.
• It adds strobogrammatic numbers with "1" in the middle.
• It adds strobogrammatic numbers with "9" in the first half and "6" in the second half.
• It adds strobogrammatic numbers with "6" in the first half and "9" in the second half.
• The main function returns the result generated by the helper function.
• The code then tests the gen_strobogrammatic function with different values of 'n' (2, 3, 4) and prints the results.

Flowchart:

Python Code Editor :

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