Python Program to Print Spiral Pattern of Numbers

Introduction

A spiral pattern of numbers is an interesting exercise where numbers are printed in a spiral shape. This pattern starts from the top-left corner and moves inwards in a clockwise direction. The challenge is to control the direction of movement (right, down, left, and up) and ensure the numbers are placed correctly.

Problem Statement

Create a Python program that:

• Accepts the size of the spiral (an n x n grid).
• Prints a spiral pattern of numbers.

Example:

• Input: size = 4
• Output:

  1  2  3  4
  12 13 14 5
  11 16 15 6
  10 9  8  7
  

Solution Steps

1. Input the Size of the Grid: The user specifies the size of the grid (n x n).
2. Initialize the Grid: Create an empty n x n grid to store the numbers.
3. Use Loops to Control Movement: Use loops and direction changes to place the numbers in the grid in a spiral pattern (right, down, left, up).
4. Print the Grid: After filling the grid with numbers, print the grid in the spiral format.

Python Program

# Step 1: Input the size of the spiral (n x n)
n = int(input("Enter the size of the spiral (n x n): "))

# Step 2: Initialize the n x n grid with zeros
spiral = [[0] * n for _ in range(n)]

# Step 3: Initialize variables for movement direction and boundaries
num = 1
top, bottom, left, right = 0, n - 1, 0, n - 1

# Step 4: Fill the grid in a spiral pattern
while top <= bottom and left <= right:
    # Move right across the top row
    for i in range(left, right + 1):
        spiral[top][i] = num
        num += 1
    top += 1

    # Move down the right column
    for i in range(top, bottom + 1):
        spiral[i][right] = num
        num += 1
    right -= 1

    # Move left across the bottom row
    if top <= bottom:
        for i in range(right, left - 1, -1):
            spiral[bottom][i] = num
            num += 1
        bottom -= 1

    # Move up the left column
    if left <= right:
        for i in range(bottom, top - 1, -1):
            spiral[i][left] = num
            num += 1
        left += 1

# Step 5: Print the spiral pattern
for row in spiral:
    print(' '.join(map(str, row)))

Explanation

Step 1: Input the Size of the Spiral

• The program starts by asking the user to input the size of the spiral (n x n).

Step 2: Initialize the Grid

• An n x n grid is created and initialized with zeros using list comprehension.

Step 3: Initialize Movement Variables

• Variables top, bottom, left, and right define the boundaries of the current movement.
• num starts at 1 and increments as the spiral is filled.

Step 4: Fill the Grid in a Spiral Pattern

• The loop continues until the boundaries meet or cross. The numbers are filled in a spiral order:
  • Move right across the top row.
  • Move down the right column.
  • Move left across the bottom row.
  • Move up the left column.
• After each movement, the boundaries (top, bottom, left, right) are adjusted.

Step 5: Print the Spiral Pattern

• After filling the grid, the spiral pattern is printed row by row.

Output Example

For size = 4, the output will be:

1 2 3 4
12 13 14 5
11 16 15 6
10 9 8 7

For size = 5, the output will be:

1  2  3  4  5
16 17 18 19 6
15 24 25 20 7
14 23 22 21 8
13 12 11 10 9

Conclusion

This Python program prints a spiral pattern of numbers in an n x n grid using loops and directional changes. The numbers are placed in a spiral order (right, down, left, and up) while adjusting the boundaries after each movement. This exercise is useful for practicing loop control, grid manipulation, and output formatting in Python.