How do you write an algorithm to print a multiplication table?

 To write an algorithm to print a multiplication table, we need to decide on some basic details:

1. The size of the table: For example, if you want a table from 1x1 to 10x10, the table will have 10 rows and 10 columns.
2. The format: We will typically display each number with its product, arranged in a grid-like format.

Step-by-Step Algorithm:

Here’s how you can write an algorithm to print a multiplication table for a given size $N$:

1. Input: The size of the table $N$ (for example, $N = 10$).
2. Loop through rows (from 1 to $N$): Each row represents the multiplication of a number with all other numbers.
3. Loop through columns (from 1 to $N$): Each column corresponds to multiplying the row number by the column number.
4. Print the result for each cell: Each cell will show the product of the corresponding row and column values.
5. Format the output: Ensure the numbers are aligned neatly, especially if the table size grows larger.

Example: Multiplication Table for $N = 10$

Pseudocode:

Input: N (size of multiplication table)

For i from 1 to N:
    For j from 1 to N:
        Print i * j (format the output to be aligned)
    Print a newline after each row to move to the next line
End

Python Code Implementation:

def print_multiplication_table(N):
    # Loop through each row (1 to N)
    for i in range(1, N + 1):
        # Loop through each column (1 to N)
        for j in range(1, N + 1):
            # Print the product with some space for formatting
            print(f"{i * j:4}", end=" ")  # ":4" ensures alignment
        # Move to the next line after each row
        print()

# Example usage
N = 10  # Size of the multiplication table
print_multiplication_table(N)

Output for $N = 10$:

   1    2    3    4    5    6    7    8    9   10
   2    4    6    8   10   12   14   16   18   20
   3    6    9   12   15   18   21   24   27   30
   4    8   12   16   20   24   28   32   36   40
   5   10   15   20   25   30   35   40   45   50
   6   12   18   24   30   36   42   48   54   60
   7   14   21   28   35   42   49   56   63   70
   8   16   24   32   40   48   56   64   72   80
   9   18   27   36   45   54   63   72   81   90
  10   20   30   40   50   60   70   80   90  100

Explanation:

1. The outer loop (for i in range(1, N + 1)) iterates through the rows of the table.
2. The inner loop (for j in range(1, N + 1)) iterates through the columns for each row.
3. The expression i * j computes the product of the current row and column.
4. print(f"{i * j:4}", end=" ") ensures that each number takes up at least 4 characters, ensuring alignment for readability. You can adjust the :4 to fit your needs for larger or smaller numbers.
5. print() moves the output to the next line after each row.

This algorithm and implementation will print a nicely formatted multiplication table for any given size $N$.