NOTES.md

My Approach

We always use nested loops for printing the patterns.

1. For the outer loop, we count the number of lines/rows and loop for them.
2. Next, for the inner loop, we focus on the number of columns and somehow connect them to the rows by forming a logic such that for each row we get the required number of columns to be printed.
3. We print the "*" inside the inner loop.
4. Observe symmetry in the pattern or check if a pattern is a combination of two or more similar patterns.

Time Complexity

To analyze the time complexity of this program, let's break it down step by step:

1. The outer loop iterates 2 * N - 1 times (it runs N times for the first half of rows and N - 1 times for the second half).
2. Inside the outer loop, there are three parts that involve nested loops.
   • The first inner loop (for j in range(1, stars+1)) runs i times where i ranges from 1 to 2 * N - 1.
   • The second inner loop (for j in range(1, spaces+1)) runs 2 * N - 2 * i times for each i.
   • The third inner loop (for j in range(1, stars+1)) also runs i times.

When we put it all together, for each row:

• The time spent in the first inner loop is roughly proportional to i.
• The time spent in the second inner loop is roughly proportional to N - i.
• The time spent in the third inner loop is roughly proportional to i.

Considering these factors, the code's overall time complexity is quadratic, specifically $O(N^2)$, where N represents the number of rows or lines in the triangle.

where N is the number of rows/lines (horizontally).

Space Complexity

• The additional space used by the code is mainly for temporary variables and the input values.
• The memory used by the nested loops is constant and does not depend on the input size N.
• So, the space complexity of the code is $O(1)$, constant space complexity.