711660. Pattern 8
Pattern 8
Summary
The problem, known as "Pattern 8", involves generating a specific triangle pattern based on input values. The goal is to create an algorithm that prints a triangle with asterisks (*) and spaces, following a particular pattern.
Detailed Explanation
To solve this problem, we'll break it down into smaller steps:
Algorithmic Approach
We can approach this problem by iterating through each row of the triangle and printing the required number of asterisks and spaces. The key is to calculate the correct number of spaces for each row based on its position in the triangle.
Step-by-Step Solution
Here's a step-by-step breakdown of the solution:
- Start with an empty string
outputthat will store the final triangle pattern. - Iterate through each row
ifrom 1 ton, wherenis the input value. - For each row, calculate the number of spaces needed by subtracting the current row number (
i) from the maximum number of rows (n). This will give us the correct number of spaces for that row. - Print the calculated number of spaces followed by a specified number of asterisks (
*) equal toi. - Add a newline character (
\n) after printing each row.
Time and Space Complexity Analysis
The time complexity of this algorithm is O(n), where n is the input value, since we're iterating through each row once. The space complexity is also O(n) because we're storing the final triangle pattern in an output string.
Optimized Solutions
Here are optimized solutions for various programming languages:
Java
public class Main {
public static void main(String[] args) {
int n = 5; // input value
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n - i; j++) {
System.out.print(" ");
}
for (int k = 1; k <= i; k++) {
System.out.print("*");
}
System.out.println();
}
}
}