913 - Joana and the Odd Numbers

🌕🌗🌑🌑🌑

# 題目連結

• 題目連結
• Online Judge
• uDebug

# 題目說明

Time limit: 3.000 seconds

# 題目

Joana loves playing with odd numbers. In the other day, she started writing, in each line, an odd number of odd numbers. It looked as follows:

$$\begin {matrix} &1 & & & & & & \\ &3 &5 &7 & & & &\\ &9 &11 &13 &15 &17 & &\\ &19 &21 &23 &25 &27 &29 &31\\ &... & & & & & & \end {matrix}$$

On a certain line Joana wrote 55 odd numbers. Can you discover the sum of the last three numbers written in that line? Can you do this more generally for a given quantity of odd numbers?

Given the number N of odd numbers in a certain line, your task is to determine the sum of the last three numbers of that line.

# Input

The input is a sequence of lines, one odd number N (1 < N < 1000000000) per line

# Output

For each input line write the sum of the last three odd numbers written by Joana in that line with N numbers. This sum is guaranteed to be less than 2⁶³.

# Sample Input

3
5
7

# Sample Output

15
45
87

# 解題技巧

這題雖然不難，但是要想得到運算的方法:

• line : 計算出 N 是第幾行
• totalNum : 再利用行數計算出，到該行總共有幾個數字
• lastNum : 最後利用總數字個數計算出該行最後一個奇數
• ans : 藉由最後一個數字算出答案

提示: 因為 1 < N < 1000000000 ，所以要利用 long 。

# Solution

import java.util.*;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);

        while (sc.hasNextLong()) {

            long N = sc.nextLong();

            long line = (N + 1) / 2;

            long totalNum = line * line;

            long lastNum = 2 * (totalNum) - 1;

            long ans = (lastNum - 2) * 3;

            System.out.println(ans);

        }

        sc.close();

    }

}