UVALive 6184 - One-Dimensional Cellular Automaton 高斯消元模板题 (2012 Tokyo)

题意:

设f(x)多项式的最大幂为d...现在告诉f(0)~f(d+2)的值..其中有一个是错的..问哪个是错的...

题解:

直接枚举+高斯消元暴力..

Program:

#include<iostream>
#include<stdio.h>
#include<cmath>
#include<queue>
#include<stack>
#include<algorithm>
#define ll long long
#define MAXN 15
using namespace std; 
//----------------gauss消元,从0开始矩阵为matrix-------- 
double matrix[MAXN][MAXN+1],ans[MAXN];
void exchange_col(int p1,int p2,int n)
{ 
        for (int i=0;i<=n;i++) swap(matrix[p1][i],matrix[p2][i]);
}
bool gauss(int n)
{
        int i,j,k,p;
        double r;
        for (i=0;i<n-1;i++)
        {
               p=i;
            //   output(n);
               for (j=i+1;j<n;j++)
                  if (abs(matrix[j][i])>abs(matrix[p][i])) p=j; 
               if (p!=i) exchange_col(i,p,n);               
               if (abs(matrix[i][i])<1e-3) return false;
               for (j=i+1;j<n;j++)
               {
                     r=matrix[j][i]/matrix[i][i];
                     for (k=i;k<=n;k++) matrix[j][k]-=r*matrix[i][k];
               }
        }
        for (i=n-1;i>=0;i--)
        {
               ans[i]=matrix[i]
;
               for (j=n-1;j>i;j--) ans[i]-=matrix[i][j]*ans[j];
               if (abs(matrix[i][i])<1e-3) return false;
               ans[i]/=matrix[i][i];
        }
        return true;
}
//---------------------gauss消元模板--------------------------
double data[MAXN];
int main()
{ 
        int d,i,j,t,m,p;
    //    freopen("input.txt","r",stdin),freopen("output.txt","w",stdout); 
        while (~scanf("%d",&d) && d)
        {
                for (i=0;i<=d+2;i++) scanf("%lf",&data[i]);
                for (t=0;t<=d+2;t++)
                { 
                   //     t=2;
                        m=0;
                        for (i=0;i<=d+2;i++)
                        {
                               if (i==t) continue;
                               p=1;
                               for (j=0;j<=d;j++) matrix[m][j]=p,p*=i;
                               matrix[m][d+1]=data[i];                              
                               m++; 
                        }
                        if (!gauss(m)) break;
                }
                printf("%d\n",t);
        }
        return 0;
}