CodingGyan

Alternating Sign Series 1 - 2 + 3 - 4 ...

easy Series and Sequences

Problem

Read n and print the value of 1 - 2 + 3 - 4 + ... up to the number n. Odd numbers are added and even numbers are subtracted. For n = 0 the result is 0.

Constraints

  • 0 <= n <= 10^9

Examples

Input

5

Output

3

Solutions

Brute forceTime O(n)Space O(1)

We visit each number and decide the sign with the remainder of the division by 2.

Same code works in Java810172125Basic features only, so nothing changes between versions.
/*
 * Problem : Find 1 - 2 + 3 - 4 + ... up to n.
 * Input   : One integer n (n >= 0).
 * Output  : The result.
 * Approach: Add or subtract each number in a loop.
 * Time    : O(n)
 * Space   : O(1)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        int n = new Scanner(System.in).nextInt();

        // Step 1: The result starts at 0.
        long result = 0;

        // Step 2: Visit the numbers from 1 to n.
        for (int number = 1; number <= n; number++) {
            // Step 3: Add odd numbers and subtract even numbers.
            if (number % 2 == 1) {
                result = result + number;
            } else {
                result = result - number;
            }
        }

        // Step 4: Print the result.
        System.out.println(result);
    }
}
Hints (1)
  1. Which numbers get a plus sign?

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