Party All the Time+hdu+三分搜索

Party All the Time

Time Limit: 6000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 3501    Accepted Submission(s): 1115

Problem Description

In the Dark forest, there is a Fairy kingdom where all the spirits will go together and Celebrate the harvest every year. But there is one thing you may not know that they hate walking so much that they would prefer to stay at home if they need to walk a long way.According to our observation,a spirit weighing W will increase its unhappyness for S³*W units if it walks a distance of S kilometers. 
Now give you every spirit's weight and location,find the best place to celebrate the harvest which make the sum of unhappyness of every spirit the least.

 

Input

The first line of the input is the number T(T<=20), which is the number of cases followed. The first line of each case consists of one integer N(1<=N<=50000), indicating the number of spirits. Then comes N lines in the order that x_[i]<=x_[i+1] for all i(1<=i<N). The i-th line contains two real number : X_i,W_i, representing the location and the weight of the i-th spirit. ( |x_i|<=10⁶, 0<w_i<15 )

 

Output

For each test case, please output a line which is "Case #X: Y", X means the number of the test case and Y means the minimum sum of unhappyness which is rounded to the nearest integer.

 

Sample Input

140.6 53.9 105.1 78.4 10

 

Sample Output

Case #1: 832
解决方案：枚举best place，在某区间，随best place从小到大，总的spirit有一个从变小再变大的过程，所以三分搜索。
code：
#include<iostream>#include<cstdio>#include<cmath>#define MMAX 50005using namespace std;struct node{    double x,s;} spirit[MMAX];int N;double cal(double mid){    double sum=0.0;    for(int i=0; i<N; i++)    {        sum+=fabs((spirit[i].x-mid)*(spirit[i].x-mid)*(spirit[i].x-mid))*spirit[i].s;    }    return sum;}int main(){    int t,k=0;    scanf("%d",&t);    while(t--){        scanf("%d",&N);        double left=10e7,right=0.0,mid,midmid;        for(int i=0;i<N;i++){            scanf("%lf%lf",&spirit[i].x,&spirit[i].s);            left=min(spirit[i].x,left);            right=max(spirit[i].x,right);        }        double midv,midmidv;        while(right-left>0.0000001){            mid=(left+right)/2.0;            midmid=(mid+right)/2.0;            midv=cal(mid);            midmidv=cal(midmid);            if(midv<=midmidv) right=midmid;            else left=mid;        }        printf("Case #%d: %.0lf\n",++k,cal(left));    }    return 0;}