Pattern 4 - Repeated Number Triangle Pattern

Difficulty: Easy

Problem Statement

You are given an integer n. You need to recreate the pattern shown below for any value of N.

The pattern should be a right triangle of repeated numbers where each row i contains the number i repeated i times.

Examples

Example 1:
Input:  n = 4
Output:
1
22
333
4444

Example 2:
Input:  n = 5
Output:
1
22
333
4444
55555

Example 3:
Input:  n = 3
Output:
1
22
333

Example 4:
Input:  n = 1
Output:
1

Constraints

• 1 ≤ n ≤ 20
• Print the pattern in the function given to you.

1. Brute Force Approach

Algorithm / Intuition

Solution1: Nested Loop Approach

Intuition:

To create a repeated number triangle pattern, we need to print n rows, where row i contains the number i repeated i times. This forms a right triangle where each row displays the same number (equal to the row number) multiple times. This can be achieved using nested loops - the outer loop handles the rows and the inner loop handles the repetitions of the current row number.

Approach:

• Use an outer loop to iterate through rows (from 1 to n).
• Use an inner loop to iterate j times (from 1 to current row number i).
• In the inner loop, print the current row number i (not j).
• After completing each row (inner loop), print a newline to move to the next row.

DryRun:

Input: n = 5

Row 1: Print number 1, 1 time:  1
Row 2: Print number 2, 2 times: 22
Row 3: Print number 3, 3 times: 333
Row 4: Print number 4, 4 times: 4444
Row 5: Print number 5, 5 times: 55555

Final Output:
1
22
333
4444
55555

Code.

Java

class Solution {
  public void pattern4(int n) {
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= i; j++) {
        System.out.print(i);
      }
      System.out.println();
    }
  }
}

JavaScript

class Solution {
  pattern4(n) {
    for (let i = 1; i <= n; i++) {
      for (let j = 1; j <= i; j++) {
        process.stdout.write(i.toString());
      }
      console.log();
    }
  }
}

Python

class Solution:
    def pattern4(self, n):
        for i in range(1,n+1):
            for j in range(1,i+1):
                print(i, end="")
            print();

Complexity Analysis

Time Complexity: O(n²)

We have nested loops where the outer loop runs n times and the inner loop runs 1, 2, 3, ..., n times respectively. Total iterations = 1 + 2 + 3 + ... + n = n(n+1)/2 = O(n²).

Space Complexity: O(1)

We only use a constant amount of extra space for loop variables. The output space is not counted in auxiliary space complexity.

---

Alternative Approaches

Using String Multiplication

Java

class Solution {
    public void pattern4(int n) {
        for (int i = 1; i <= n; i++) {
            String row = String.valueOf(i).repeat(i);
            System.out.println(row);
        }
    }
}

JavaScript

class Solution {
  pattern4(n) {
    for (let i = 1; i <= n; i++) {
      const row = i.toString().repeat(i);
      console.log(row);
    }
  }
}

Python

class Solution:
    def pattern4(self, n):
        for i in range(1, n+1):
            row = str(i) * i
            print(row)

---

Edge Cases to Consider

1. n = 1: Should print a single "1"
2. Small Values (n = 2, 3): Verify correct triangle formation with repeated numbers
3. Larger Values: Ensure pattern maintains right triangle shape with proper repetitions
4. Maximum Constraint Value: n = 20 should work efficiently
5. Double Digit Numbers: For n > 9, ensure proper handling of multi-digit numbers

Pattern Analysis

Pattern Characteristics:

• Shape: Right Triangle
• Dimensions: n rows, with row i having i elements
• Fill: Repeated row numbers (1, 22, 333, ...)
• Growth: Each row adds one more occurrence of the row number

Key Observations:

• Row i contains the number i repeated i times
• Each row has exactly i characters (for single-digit numbers)
• Total numbers printed = 1 + 2 + 3 + ... + n = n(n+1)/2
• No spaces between repeated numbers in each row

Mathematical Pattern

For any row i:

• Number to Print: i
• Repetitions: i times
• Row Content: i repeated i times
• Row Length: i characters (for single digits)

Key Difference from Pattern 3

Aspect	Pattern 3	Pattern 4
Row 1	1	1
Row 2	12	22
Row 3	123	333
Logic	Print j (column index)	Print i (row index)
Sequence	Sequential numbers	Repeated same number

Follow-up Questions

1. Reverse Pattern: How would you create a decreasing version (n, n-1, ..., 1)?
2. Different Characters: How to use letters instead of numbers?
3. Spaced Version: How to add spaces between repeated numbers?
4. Multi-digit Handling: How does the pattern look for n > 9?

Related Patterns

This pattern builds upon triangular concepts:

• Pattern 1: Square of Stars (constant character, square shape)
• Pattern 3: Sequential Number Triangle (different numbers per row)
• Pattern 5: Reverse patterns
• Pattern 6: Alphabetical versions

Summary

Approach	Time Complexity	Space Complexity	Pros	Cons
Nested Loops	O(n²)	O(1)	Simple, direct, space optimal	Two loops needed
String Repeat	O(n²)	O(n)	More concise, built-in string functions	Uses extra space, language dependent

Recommended Solution: Use the nested loop approach for better understanding of pattern logic and optimal space complexity. This approach clearly shows the relationship between row number and repetitions.

Tips for Repeated Number Pattern Problems

1. Identify Repetition Logic: Understand what number repeats and how many times
2. Row-Column Relationship: Recognize when to use row index vs column index
3. Loop Control: Ensure inner loop runs exactly i times for row i
4. Output Format: Consider spacing and alignment requirements
5. Multi-digit Considerations: Plan for numbers greater than 9

Debugging Tips

1. Check Inner Loop Variable: Ensure you're printing i (row number), not j (column index)
2. Verify Repetition Count: Each row i should print number i exactly i times
3. Loop Boundaries: Confirm loops start from 1 and go to n and i respectively
4. Newline Placement: Ensure println() is called after completing each row

Pattern Variations to Practice

1. Pattern 4a: Same pattern but with spaces between repeated numbers
2. Pattern 4b: Right-aligned repeated number triangle
3. Pattern 4c: Repeated character triangle (A, BB, CCC, ...)
4. Pattern 4d: Reverse repeated number triangle (starting from n)
5. Pattern 4e: Hollow repeated number triangle (only borders)