山东省第八届acm大赛 F题（SDUT 3898）

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quadratic equation

Time Limit: 2000MS Memory Limit: 131072KB

Problem Description

With given integers a,b,c, you are asked to judge whether the following statement is true: "For any x, if a⋅+b⋅x+c=0, then x is an integer."

Input

The first line contains only one integer T(1≤T≤2000), which indicates the number of test cases.
For each test case, there is only one line containing three integers a,b,c(−5≤a,b,c≤5).

Output

or each test case, output “YES” if the statement is true, or “NO” if not.

Example Input

31 4 40 0 11 3 1

Example Output

YESYESNO

可恶比赛的时候没A掉离散数学中的蕴含式只有当前件成立后件不成立时输出 "NO" 其他情况都输出 "YES" 本题就是当方程有解并且解不为整数时输出 "NO" 其他情况输出 "YES"

1 1 1

1 0 0

0 0 1

0 1 1

比赛的时候试了各种情况唯独没判断sqrt（b*b-4*a*c）是否为整数

AC代码：

#include<stdio.h>#include<cmath>int main (){    int t;    scanf ("%d",&t);    while (t--){        int a,b,c;        scanf ("%d%d%d",&a,&b,&c);        if (a==0&&b==0&&c==0){            printf ("NO\n");            continue;        }        if (a==0){            if(b!=0&&c!=0){                if((c%b)!=0){                    printf ("NO\n");                    continue;                }            }        }        else if (a!=0){            float temp=(b*b)-(4*a*c);            if (temp>=0){                if ((int)sqrt(temp)!=sqrt(temp)){                    printf ("NO\n");                    continue;                }                else{                    if ((-1*b-(int)sqrt(temp))%(2*a)!=0||(-1*b+(int)sqrt(temp))%(2*a)!=0){                    printf ("NO\n");                    continue;                }                }            }        }        printf ("YES\n");    }    return 0;}

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