711655. Pattern 4
Pattern 4
Slug: triangle-number-1661428795 Difficulty: Easy Id: 711655
Summary
The Pattern 4 problem involves generating a pattern of numbers that resembles a triangle. The key concept involved is number generation based on the given input.
Detailed Explanation
The problem requires us to generate a pattern where each row consists of consecutive integers, and the sum of all integers in each row forms an arithmetic sequence. To achieve this, we can start by initializing a variable n which represents the number of rows required. Then, we use a loop that runs for n iterations.
Inside each iteration, we generate a new row where each element is equal to its index plus one. We also calculate the sum of all elements in the current row and store it in another variable. This stored value becomes the first element of the next row.
Here's a step-by-step breakdown of the solution:
- Initialize
nto the desired number of rows. - Start a loop that runs for
niterations. - Inside each iteration, generate a new row where each element is equal to its index plus one (
i + 1). - Calculate the sum of all elements in the current row and store it in another variable. This stored value becomes the first element of the next row.
Time Complexity Analysis: The time complexity of this algorithm is O(n), as we are performing a constant amount of work for each row generated.
Space Complexity Analysis: The space complexity is also O(n), as we need to store the generated rows and their sums in memory.
Optimized Solutions
Java
public class Main {
public static void main(String[] args) {
int n = 5; // number of rows
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= i; j++) {
System.out.print(j + " ");
}
System.out.println();
}
}
}