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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#687019#6620. Linear Fractional TransformationY_J_YWA 219ms16240kbC++202.5kb2024-10-29 16:47:592024-10-29 16:47:59

Judging History

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  • [2024-10-29 16:47:59]
  • 评测
  • 测评结果:WA
  • 用时:219ms
  • 内存:16240kb
  • [2024-10-29 16:47:59]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define root 1,n,1
#define ls (rt<<1)
#define rs (rt<<1|1)
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define pd __gnu_pbds
inline ll read() {
	ll x=0,w=1;char ch=getchar();
	for(;ch>'9'||ch<'0';ch=getchar()) if(ch=='-') w=-1;
	for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
	return x*w;
}
inline void print(__int128 x){
	if(x<0) {putchar('-');x=-x;}
	if(x>9) print(x/10);
	putchar(x%10+'0');
}
#define maxn 1000010
const double eps=1e-8;
#define	int_INF 0x3f3f3f3f
#define ll_INF 0x3f3f3f3f3f3f3f3f
complex<long double>a[200][200];
int n;
int gauss() {
	int c,r;
	for(c=0,r=0;c<n;c++) {
		int t=r;
		for(int i=r;i<n;i++) {
			if(abs(a[i][c])>abs(a[t][c])) {
				t=i;
			}
		}
		if(abs(a[t][c])<eps) continue;
		for(int i=c;i<=n;i++) swap(a[t][i],a[r][i]);
		for(int i=n;i>=c;i--) a[r][i]/=a[r][c];
		for(int i=r+1;i<n;i++) {
			if(abs(a[i][c])>eps) {
				for(int j=n;j>=c;j--) {
					a[i][j]-=a[r][j]*a[i][c];
				}
			}
		}
		r++;
	}
	if(r<n) {
		for(int i=r;i<n;i++) {
			if(abs(a[i][n])>eps) {
				return 2;//无解
			}
		}
		return 1;//有无穷多解
	}
	for(int i=n-1;i>=0;i--) {
		for(int j=i+1;j<n;j++) {
			a[i][n]-=a[i][j]*a[j][n];
		}
	}
	return 0;//有唯一解
}
complex<long double>z[maxn],w[maxn];
long double p[maxn],q[maxn],r[maxn],s[maxn];
int main() {
	int T=read();
	while(T--) {
		n=3;
		for(int i=1;i<=3;i++) {
			scanf("%Lf%Lf%Lf%Lf",&p[i],&q[i],&r[i],&s[i]);
			z[i].real(p[i]);z[i].imag(q[i]);
			w[i].real(r[i]);w[i].imag(s[i]);			
		}
		scanf("%Lf%Lf",&p[4],&q[4]);
		z[4].real(p[4]);z[4].imag(q[4]);
		complex<long double>A=(w[1]-w[2])/(z[1]-z[2]);
		complex<long double>B=w[1]-A*z[1];
		if(abs(A*z[3]+B-w[3])<eps) {//意味着此时c=0
			complex<long double>ans=A*z[4]+B;
			printf("%.7Lf %.7Lf\n",ans.real(),ans.imag());
			continue;
		}
		for(int i=0;i<3;i++) {
			a[i][0]={1,0};a[i][1]={1,0};
			a[i][2]=-w[i+1];
			a[i][3]=w[i+1]*z[i+1];
		}		
		int state=gauss();
//		cout<<state<<endl;
		complex<long double>ans=(a[0][3]+a[1][3])/(z[4]+a[2][3]);
		printf("%.7Lf %.7Lf\n",ans.real(),ans.imag());
//		cout<<a[2][3].real()<<" "<<a[2][3].imag()<<endl;
//		cout<<"check:"<<endl;
//		ans=(a[0][3]+a[1][3])/(z[1]+a[2][3]);
//		printf("%.7Lf %.7Lf\n",ans.real(),ans.imag());
//		
//		ans=(a[0][3]+a[1][3])/(z[2]+a[2][3]);
//		printf("%.7Lf %.7Lf\n",ans.real(),ans.imag());
//		
//		ans=(a[0][3]+a[1][3])/(z[3]+a[2][3]);
//		printf("%.7Lf %.7Lf\n",ans.real(),ans.imag());
	}
	return 0;
}

Details

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Test #1:

score: 100
Accepted
time: 0ms
memory: 16240kb

input:

2
-1 0 0 -1
0 1 -1 0
1 0 0 1
0 -1
-1 0 -1 0
0 1 0 -1
1 0 1 0
0 -1

output:

1.0000000 0.0000000
0.0000000 1.0000000

result:

ok 4 numbers

Test #2:

score: -100
Wrong Answer
time: 219ms
memory: 14128kb

input:

100000
0 0 -1 1
1 1 1 0
1 0 1 -1
-1 0
-1 -1 -1 1
1 -1 1 -1
-1 0 1 0
-1 -1
-1 -1 0 -1
-1 1 -1 -1
0 -1 0 0
1 1
1 0 0 -1
0 0 0 0
-1 -1 1 0
1 1
-1 -1 0 -1
0 1 1 -1
1 0 -1 -1
1 -1
0 1 1 -1
1 0 1 0
0 -1 0 1
-1 -1
1 1 -1 1
0 0 -1 -1
0 1 0 1
1 0
1 1 1 -1
0 1 -1 -1
1 0 -1 0
1 -1
1 0 -1 1
-1 -1 1 0
0 -1 0 1
0...

output:

0.1538462 0.2307692
-0.5000000 -0.5000000
0.3333333 -0.3333333
-0.3529412 -0.4117647
-0.6666667 -0.3333333
-0.7500000 0.5000000
-0.6000000 -0.8000000
0.3750000 -0.1250000
-0.2500000 1.2500000
0.4000000 -0.2000000
0.3846154 -0.0769231
-0.2800000 -0.0400000
-0.1538462 0.2307692
-0.0769231 -0.3846154
-...

result:

wrong answer 1st numbers differ - expected: '1.0000000', found: '0.1538462', error = '0.8461538'