Zero One Triangle Pattern
Problem
Read n and print a triangle of 1 and 0. Every row ends with 1 and the digits change between 1 and 0 as you move left. Digits are separated by one space. Rule: a digit is 1 when row + column is even.
Constraints
- 1 <= n <= 20
Examples
Input
3
Output
1 0 1 1 0 1
Solutions
The digit depends only on the parity (even or odd) of row + column. The last digit of each row is at column = row, so row + column = 2 * row, which is always even, so every row ends with 1.
Java 8 has no String.repeat, so we use a small helper method. In Java 11 and newer you can write " ".repeat(count).
/*
* Problem : Triangle of 1 and 0.
* Input : One integer n (rows).
* Output : n lines of digits.
* Approach: Use the sum of row and column to choose 1 or 0.
* Time : O(n^2)
* Space : O(1)
* Java : 8 or newer.
*/
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
int rows = new Scanner(System.in).nextInt();
// Step 1: Repeat once for each row. Row numbers go from 1 to rows.
for (int row = 1; row <= rows; row++) {
StringBuilder line = new StringBuilder();
// Step 2: Visit each column of the row. Column numbers go from 1 to row.
for (int column = 1; column <= row; column++) {
// Step 3: If row + column is even, write 1. If it is odd, write 0.
int digit = (row + column) % 2 == 0 ? 1 : 0;
if (column > 1) {
line.append(" ");
}
line.append(digit);
}
// Step 4: Print the finished line.
System.out.println(line);
}
}
}
Hints (2)
- Look for a rule that uses row and column.
- What is the parity of row + column on the last column?