[JSOI2008]\u7403\u5f62\u7a7a\u95f4\u4ea7\u751f\u5668sphere<\/p>\n
Time Limit:1000MS Memory Limit:165536K
Total Submit:147 Accepted:89<\/p>\n
Description <\/strong><\/p>\n \u6709\u4e00\u4e2a\u7403\u5f62\u7a7a\u95f4\u4ea7\u751f\u5668\u80fd\u591f\u5728n\u7ef4\u7a7a\u95f4\u4e2d\u4ea7\u751f\u4e00\u4e2a\u575a\u786c\u7684\u7403\u4f53\u3002\u73b0\u5728\uff0c\u4f60\u88ab\u56f0\u5728\u4e86\u8fd9\u4e2an\u7ef4\u7403\u4f53\u4e2d\uff0c\u4f60\u53ea\u77e5\u9053\u7403\u9762\u4e0an+1\u4e2a\u70b9\u7684\u5750\u6807\uff0c\u4f60\u9700\u8981\u4ee5\u6700\u5feb\u7684\u901f\u5ea6\u786e\u5b9a\u8fd9 \u4e2an\u7ef4\u7403\u4f53\u7684\u7403\u5fc3\u5750\u6807\uff0c\u4ee5\u4fbf\u4e8e\u6467\u6bc1\u8fd9\u4e2a\u7403\u5f62\u7a7a\u95f4\u4ea7\u751f\u5668\u3002 <\/p>\n Input <\/strong><\/p>\n \u7b2c\u4e00\u884c\u662f\u4e00\u4e2a\u6574\u6570\uff0cn\u3002 Output <\/strong><\/p>\n \u6709\u4e14\u53ea\u6709\u4e00\u884c\uff0c\u4f9d\u6b21\u7ed9\u51fa\u7403\u5fc3\u7684n\u7ef4\u5750\u6807\uff08n\u4e2a\u5b9e\u6570\uff09\uff0c\u4e24\u4e2a\u5b9e\u6570\u4e4b\u95f4\u7528\u4e00\u4e2a\u7a7a\u683c\u9694\u5f00\u3002\u6bcf\u4e2a\u5b9e\u6570\u7cbe\u786e\u5230\u5c0f\u6570\u70b9\u540e3\u4f4d\u3002\u6570\u636e\u4fdd\u8bc1\u6709\u89e3\u3002\u4f60\u7684\u7b54\u6848\u5fc5\u987b\u548c\u6807\u51c6\u8f93\u51fa\u4e00 \u6a21\u4e00\u6837\u624d\u80fd\u591f\u5f97\u5206\u3002 <\/p>\n Sample Input <\/strong><\/p>\n 2 Sample Output <\/strong><\/p>\n 0.500 1.500<\/p>\n \u6570\u636e\u89c4\u6a21\uff1a Source \u672c\u9ad8\u4eae\u4ee3\u7801\u4f7f\u7528codeHl\u751f\u6210\uff0c<\/p>\n","protected":false},"excerpt":{"rendered":" [JSOI2008]\u7403\u5f62\u7a7a\u95f4\u4ea7\u751f\u5668sphere Time Limit:1000MS Memory Limit:165536KTotal Submit:147 Accepted:89 Description \u6709\u4e00\u4e2a\u7403\u5f62\u7a7a\u95f4\u4ea7\u751f\u5668\u80fd\u591f\u5728n\u7ef4\u7a7a\u95f4\u4e2d\u4ea7\u751f\u4e00\u4e2a\u575a\u786c\u7684\u7403\u4f53\u3002\u73b0\u5728\uff0c\u4f60\u88ab\u56f0\u5728\u4e86\u8fd9\u4e2an\u7ef4\u7403\u4f53\u4e2d\uff0c\u4f60\u53ea\u77e5\u9053\u7403\u9762\u4e0an+1\u4e2a\u70b9\u7684\u5750\u6807\uff0c\u4f60\u9700\u8981\u4ee5\u6700\u5feb\u7684\u901f\u5ea6\u786e\u5b9a\u8fd9 \u4e2an\u7ef4\u7403\u4f53\u7684\u7403\u5fc3\u5750\u6807\uff0c\u4ee5\u4fbf\u4e8e\u6467\u6bc1\u8fd9\u4e2a\u7403\u5f62\u7a7a\u95f4\u4ea7\u751f\u5668\u3002 Input \u7b2c\u4e00\u884c\u662f\u4e00\u4e2a\u6574\u6570\uff0cn\u3002 \u63a5\u4e0b\u6765\u7684n+1\u884c\uff0c\u6bcf\u884c\u6709n\u4e2a\u5b9e\u6570\uff0c\u8868\u793a\u7403\u9762\u4e0a\u4e00\u70b9\u7684n\u7ef4\u5750\u6807\u3002\u6bcf\u4e00\u4e2a\u5b9e\u6570\u7cbe\u786e\u5230\u5c0f\u6570\u70b9\u540e6\u4f4d\uff0c\u4e14\u5176\u7edd\u5bf9\u503c\u90fd\u4e0d\u8d85\u8fc720000\u3002 Output \u6709\u4e14\u53ea\u6709\u4e00\u884c\uff0c\u4f9d\u6b21\u7ed9\u51fa\u7403\u5fc3\u7684n\u7ef4\u5750\u6807\uff08n\u4e2a\u5b9e\u6570\uff09\uff0c\u4e24\u4e2a\u5b9e\u6570\u4e4b\u95f4\u7528\u4e00\u4e2a\u7a7a\u683c\u9694\u5f00\u3002\u6bcf\u4e2a\u5b9e\u6570\u7cbe\u786e\u5230\u5c0f\u6570\u70b9\u540e3\u4f4d\u3002\u6570\u636e\u4fdd\u8bc1\u6709\u89e3\u3002\u4f60\u7684\u7b54\u6848\u5fc5\u987b\u548c\u6807\u51c6\u8f93\u51fa\u4e00 \u6a21\u4e00\u6837\u624d\u80fd\u591f\u5f97\u5206\u3002 Sample Input 20.0 0.0-1.0 1.01.0 0.0 Sample Output 0.500 1.500 \u6570\u636e\u89c4\u6a21\uff1a\u5bf9\u4e8e40%\u7684\u6570\u636e\uff0c1<=n<=3\u5bf9\u4e8e100%\u7684\u6570\u636e\uff0c1<=n<=10\u63d0\u793a\uff1a\u7ed9\u51fa\u4e24\u4e2a\u5b9a\u4e49\uff1a1\u3001 \u7403\u5fc3\uff1a\u5230\u7403\u9762\u4e0a\u4efb\u610f\u4e00\u70b9\u8ddd\u79bb\u90fd\u76f8\u7b49\u7684\u70b9\u30022\u3001 \u8ddd\u79bb\uff1a\u8bbe\u4e24\u4e2an\u4e3a\u7a7a\u95f4\u4e0a\u7684\u70b9A, B\u7684\u5750\u6807\u4e3a(a1, a2, \u2026, an), (b1, b2, \u2026, bn)\uff0c\u5219AB\u7684\u8ddd\u79bb\u5b9a\u4e49\u4e3a\uff1adist = sqrt( (a1-b1)^2 + (a2-b2)^2 + \u2026 + (an-bn)^2 ) Source\u989d\u3002\u3002\u66fe\u7ecf\u6211\u975e\u5e38\u6267\u7740\u7684\u4e00\u5b9a\u8981\u7528\u6a21\u62df\u9000\u706bA\u8fd9\u4e2a\u9898\u76ee\u3002\u3002\u6ca1\u6210\u529f\u8fc7\u3002\u3002\u3002\u4eca\u5929\u770b\u5230\u8fd9\u4e2a\u6ca1\u8fc7\u89c9\u5f97\u5f88\u788d\u773c\u3002\u3002\u4e8e\u662f\u5199\u4e86\u4e2a\u89e3\u65b9\u7a0b\u56e7\u3002\u3002\u3002\u3002\u989d\u3002\u3002\u5b9e\u9645\u4e0a\u8fd9\u4e2a\u9898\u76ee\u53ea\u8981\u5728N+1\u4e2a\u70b9\u4e2d\u6bcf\u76f8\u90bb\u4e24\u4e2a\u70b9\u95f4\u505a\u4e2a\u5e73\u5206\u7ebf\u3002\u3002\u90a3\u4e48\u5f88\u663e\u7136\u7403\u5fc3\u5c31\u662fN\u4e2a\u5e73\u5206\u7ebf\u7684\u4ea4\u70b9\uff0c\u8fd9\u4e2a\u89e3\u65b9\u7a0b\u5c31OK\u4e86\u7011\u5e03\u6c57\u3002\u3002\u3002Code\uff1a#include <vector>#include <algorithm>#include <utility>#include <iostream>#include <cstdio>#include <cmath>#include <cstdlib>#include […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[10],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/349"}],"collection":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=349"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/349\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=349"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=349"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u63a5\u4e0b\u6765\u7684n+1\u884c\uff0c\u6bcf\u884c\u6709n\u4e2a\u5b9e\u6570\uff0c\u8868\u793a\u7403\u9762\u4e0a\u4e00\u70b9\u7684n\u7ef4\u5750\u6807\u3002\u6bcf\u4e00\u4e2a\u5b9e\u6570\u7cbe\u786e\u5230\u5c0f\u6570\u70b9\u540e6\u4f4d\uff0c\u4e14\u5176\u7edd\u5bf9\u503c\u90fd\u4e0d\u8d85\u8fc720000\u3002 <\/p>\n
0.0 0.0
-1.0 1.0
1.0 0.0<\/p>\n
\u5bf9\u4e8e40%\u7684\u6570\u636e\uff0c1<=n<=3
\u5bf9\u4e8e100%\u7684\u6570\u636e\uff0c1<=n<=10
\u63d0\u793a\uff1a\u7ed9\u51fa\u4e24\u4e2a\u5b9a\u4e49\uff1a
1\u3001 \u7403\u5fc3\uff1a\u5230\u7403\u9762\u4e0a\u4efb\u610f\u4e00\u70b9\u8ddd\u79bb\u90fd\u76f8\u7b49\u7684\u70b9\u3002
2\u3001 \u8ddd\u79bb\uff1a\u8bbe\u4e24\u4e2an\u4e3a\u7a7a\u95f4\u4e0a\u7684\u70b9A, B\u7684\u5750\u6807\u4e3a(a1, a2, \u2026, an), (b1, b2, \u2026, bn)\uff0c\u5219AB\u7684\u8ddd\u79bb\u5b9a\u4e49\u4e3a\uff1adist = sqrt( (a1-b1)^2 + (a2-b2)^2 + \u2026 + (an-bn)^2 )<\/p>\n
\u989d\u3002\u3002\u66fe\u7ecf\u6211\u975e\u5e38\u6267\u7740\u7684\u4e00\u5b9a\u8981\u7528\u6a21\u62df\u9000\u706bA\u8fd9\u4e2a\u9898\u76ee\u3002\u3002
\u6ca1\u6210\u529f\u8fc7\u3002\u3002\u3002\u4eca\u5929\u770b\u5230\u8fd9\u4e2a\u6ca1\u8fc7\u89c9\u5f97\u5f88\u788d\u773c\u3002\u3002\u4e8e\u662f\u5199
\u4e86\u4e2a\u89e3\u65b9\u7a0b\u56e7\u3002\u3002\u3002\u3002
\u989d\u3002\u3002\u5b9e\u9645\u4e0a\u8fd9\u4e2a\u9898\u76ee\u53ea\u8981\u5728N+1\u4e2a\u70b9\u4e2d\u6bcf\u76f8\u90bb\u4e24\u4e2a\u70b9\u95f4
\u505a\u4e2a\u5e73\u5206\u7ebf\u3002\u3002\u90a3\u4e48\u5f88\u663e\u7136\u7403\u5fc3\u5c31\u662fN\u4e2a\u5e73\u5206\u7ebf\u7684\u4ea4\u70b9\uff0c
\u8fd9\u4e2a\u89e3\u65b9\u7a0b\u5c31OK\u4e86\u7011\u5e03\u6c57\u3002\u3002\u3002
Code\uff1a
<\/strong>#include <vector>
#include <algorithm>
#include <utility>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <set>
#include <map>
#include <cstring>
#include <time.h>
#define rep(i,n) for(int i=0;i<n;i++)
const int inf=~0U>>1,maxn=10;
using namespace std;
double L[maxn+1][maxn];
double A[maxn][maxn+1];
int n;
inline double sqr(double x)
{
return x*x;
}
void Init()
{
cin>>n;
rep(i,n+1)
rep(j,n)cin>>L[i][j];
rep(i,n)
{
double*Line=A[i];
double*a=L[i],*b=L[i+1];
Line[n]=0;
rep(j,n)Line[n]+=sqr(a[j])-sqr(b[j]),Line[j]=2*(a[j]-b[j]);
}
}
void Solve()
{
rep(i,n)
{
double t=A[i][i];
rep(j,n+1)A[i][j]\/=t;
rep(j,n)if(j!=i)
{
double r=A[j][i];
rep(k,n+1)A[j][k]-=r*A[i][k];
}
}
rep(i,n)printf("%0.3lf ",A[i][n]);
}
int main()
{
\/\/freopen("in","r",stdin);
Init();
Solve();
}<\/p>\n