1335A - Candies and Two Sisters.cpp

/*
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.

Input
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.

Output
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.

Example
inputCopy
6
7
1
2
3
2000000000
763243547
outputCopy
3
0
0
1
999999999
381621773
Note
For the test case of the example, the 3 possible ways to distribute candies are:

a=6, b=1;
a=5, b=2;
a=4, b=3.
*/





#include<bits/stdc++.h>
using namespace std;

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    
    int t;
    cin >> t;
    
    while (t--) {
    	int n;
    	cin >> n;
    	
    	if (n % 2) 
    		cout << n / 2 << endl;
    	else cout << n / 2 - 1 << endl;
	}
    
    

    return 0;
}