There are two sisters Alice and Betty. You have n candies. You want to distribute these n candies between two sisters in such a way that:
Alice will get a (a>0) candies;
Betty will get b (b>0) candies;
each sister will get some integer number of candies;
Alice will get a greater amount of candies than Betty (i.e. a>b);
all the candies will be given to one of two sisters (i.e. a+b=n).
Your task is to calculate the number of ways to distribute exactly n candies between sisters in a way described above. Candies are indistinguishable.
Formally, find the number of ways to represent n as the sum of n=a+b, where a and b are positive integers and a>b.
You have to answer t independent test cases.
中文翻譯
有兩個姊妹 Alice 跟 Betty,現在你有 n 個糖果,你希望將這 n 個糖果按照以下方式分給兩姊妹:
Alice 會得到 a (a>0) 顆糖果
Betty 會得到 b (b>0) 顆糖果
姊妹都會得到某個整數顆糖果
Alice 會比Betty得到更多糖果 (a>b)
所有的糖果都會被給予其中一個人 (a+b=n)
你的任務是要計算有多少種方式來分配 n 顆糖果給這對姊妹(依照上面的規則)
具體地說,找到將 n 表示為 n=a+b 的方法數,其中 a 和 b 是正整數,且 a>b。
你需要回答 t 個獨立的測試案例。
輸入
The first line of the input contains one integer t (1≤t≤104) — the number of test cases. Then t test cases follow.
The only line of a test case contains one integer n (1≤n≤2⋅109) — the number of candies you have.
第一行輸入包含了一個整數 t (1≤t≤104) — 測試案例的數量,接下去有 t 個案例。
案例一行中包含了一個整數 n (1≤n≤2⋅109) — 你/妳有的糖果數量。
輸出
For each test case, print the answer — the number of ways to distribute exactly n candies between two sisters in a way described in the problem statement. If there is no way to satisfy all the conditions, print 0.
對每一個測試案例,印出答案 — 有多少種方法可以依照題目規則來分配 n 顆糖果給兩姊妹。要是沒有任何方法來滿足所有條件,則回傳 0。
範例
輸入
6 7 1 2 3 2000000000 763243547
輸出
3 0 0 1 999999999 381621773
筆記
For the test case of the example, the 3 possible ways to distribute candies are:
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int n = scanner.nextInt();
scanner.nextLine();
for (int i = 0; i < n; i++)
{
int tmp = scanner.nextInt();
scanner.nextLine();
if(tmp<3){
System.out.println(0);
}
else{
System.out.println(tmp%2==0 ? tmp/2-1 : tmp/2);
}
}
}
}
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