题目描述
Given function f(x,y)=ax2+bxy+cy2f(x, y) = a x^2 + b xy + c y^2f(x,y)=ax2+bxy+cy2, check if f(x,y)≥0f(x, y) \geq 0f(x,y)≥0 holds for all x,y∈Rx, y \in \mathbb{R}x,y∈R.
输入描述:
The input contains zero or more test cases and is terminated by end-of-file.
Each test case contains three integers a, b, c.
- −10≤a,b,c≤10-10 \leq a, b, c \leq 10−10≤a,b,c≤10
- The number of tests cases does not exceed 10410^4104.
输出描述:
For each case, output “Yes
” if f(x,y)≥0f(x, y) \geq 0f(x,y)≥0 always holds. Otherwise, output “No
”.
输入
1 -2 1
1 -2 0
0 0 0
输出
Yes
No
Yes
分类讨论,分别讨论a大于小于等于0的情况,然后逐个分析,,当然,这题数据范围小,暴力打表也能过。
#include <iostream>
using namespace std;
void yes()
{
cout << "Yes" << endl;
}
void no()
{
cout << "No" << endl;
}
int main()
{
int a, b, c;
while(cin >> a>> b>> c)
{
if(a < 0)
no();
else if(a == 0)
{
if(b == 0)
{
if(c < 0)
no();
else
yes();
}
else
no();
}
else
{
if(b * b - 4 * a * c <= 0)
yes();
else
no();
}
}
return 0;
}