We always use nested loops for printing the patterns.
- For the outer loop, we count the number of lines/rows and loop for them.
- 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.
- We print the character inside the inner loop.
- Observe symmetry in the pattern or check if a pattern is a combination of two or more similar patterns.
To analyze the time complexity of this program, let's break it down step by step:
- Outer Loop (i): The outer loop runs N times, where N is the input parameter.
- Inner Loop (j): This loop runs from the ASCII value of
'A'to the ASCII value of'A' + i - 1. The maximum number of iterations for each iteration of the outer loop occurs when i is at its maximum value, which is N. In this case, the inner loop will iterate from'A'to'A' + N - 1, leading to N iterations.
Now, let's calculate the total number of iterations of the inner loop across all iterations of the outer loop:
1 + 2 + 3 + ... + N
This is the sum of the first N natural numbers, which can be represented as
Therefore, the overall time complexity of the program, using the frequency count method, is
where N is the number of rows/lines (horizontally).
- 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.