68 lines
1.7 KiB
C++
68 lines
1.7 KiB
C++
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#include<stdio.h>
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#include<math.h>
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// using newton interpolation
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int main(){
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int n,m;
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double x[100],y[100];
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double t[100];
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double xt;
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scanf("%d",&n);
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scanf("%d",&m);
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for(int i=0;i<n;i++){
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scanf("%lf %lf",&x[i],&y[i]);
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for(int j=0;j<i;j++){
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// if points are too close, just keep one of them.
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if(fabs(x[i]-x[j])<1e-6){
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i--;
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n--;
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continue;
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}
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}
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}
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// newton interpolation
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for(int i=0;i<n;i++){
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for(int j=i-1;j>=0;j--){
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double p=1;
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for(int k=j-1;k>=0;k--){
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p=p*(x[i]-x[k]);
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}
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y[i]=y[i]-p*t[j];
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}
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double p=1;
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for(int k=i-1;k>=0;k--){
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p=p*(x[i]-x[k]);
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}
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/*
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if value is precise enough then higher terms are not necessary (sometimes even
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troublesome, when x[k] is too close to x[0], x[1],...,x[k-1] (distance < 1)
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then p=(x[k]-x[0])*(x[k]-x[1])*...*(x[k]-x[k-1]) is too small, this will result
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in a super large t[k] even when the residual error of a k-1 degree polynomial
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is small enough.)
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*/
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if(fabs(y[i])<1e-9){
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y[i]=0;
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}
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t[i]=y[i]/p;
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}
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int k=0;
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for(int i=0;i<n;i++){
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// if a coefficient is too small, then regard it as zero.
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if(fabs(t[i])>1e-6){
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k=i;
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}
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}
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// degree of the polynomial
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printf("%d\n",k);
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n=k+1;
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for(int i=0;i<m;i++){
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scanf("%lf",&xt);
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double yt=0;
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double p=1;
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for(int j=0;j<n;j++){
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yt+=t[j]*p;
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p*=(xt-x[j]);
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}
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printf("%lf\n",yt);
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}
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return 0;
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}
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