杭电ACm，problem1001的疑问，为什么不能用高斯算法

Question

Input
The input will consist of a series of integers n, one integer per line.

Output
For each case, output SUM(n) in one line, followed by a blank line. You may assume the result will be in the range of 32-bit signed integer.

很疑惑
#include <iostream>
using namespace std;
void main()
{int n;
while(cin>>n)
{
int i,sum=0;
for(i=1;i<=n;i++) sum=sum+i;
cout<<sum<<endl<<endl;
}
}
成功ac但是
#include <iostream>
using namespace std;
void main()
{int n;
while(cin>>n)
{
cout<<n*(n+1)/2<<endl<<endl;
}
}
就老是报错，求教是为何，按照道理结果是一样的啊。

Answer 1

因为n很大的时候n*(n+1)的值会溢出。可以判断奇偶然后先做除法。
注意这句：You may assume the result will be in the range of 32-bit signed integer.
要求是你的结果要在32位有符号整型范围内。假设n*(n+1)/2的结果刚好满足32位。但是在做除法前
n*(n+1)的结果就超过了32位。