Luogu3162 CQOI2012 组装 贪心
作者:互联网
如果提供每一种零件的生产车间固定了,那么总时间\(t\)与组装车间的位置\(x\)的关系就是
\(t = \sum (x-a_i)^2 = nx^2-2\sum a_ix + \sum a_i^2\)
而显然的一点,提供某一种零件的生产车间一定会是\(|x-a_i|\)最小的那个\(i\),所以如果一个生产车间\(i\)会向组装车间提供零件,那么对应的\(x\)会在一段区间之内。
把这些区间拿出来,从左往右扫一遍,这个过程中记录提供每一种零件的生产车间的变化并动态维护\(\sum a_i\)、\(\sum a_i^2\)以及\(x\)的取值范围,这样就可以算出当前状态下组装车间的最优选址。
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<ctime>
#include<cctype>
#include<algorithm>
#include<cstring>
#include<iomanip>
#include<queue>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<vector>
#include<cmath>
//This code is written by Itst
using namespace std;
inline int read(){
int a = 0;
char c = getchar();
bool f = 0;
while(!isdigit(c) && c != EOF){
if(c == '-')
f = 1;
c = getchar();
}
if(c == EOF)
exit(0);
while(isdigit(c)){
a = a * 10 + c - 48;
c = getchar();
}
return f ? -a : a;
}
#define ld long double
#define PLI pair < ld , int >
const int MAXN = 10010;
vector < int > lj[MAXN];
int N , M , p[MAXN];
priority_queue < PLI > q;
int main(){
#ifndef ONLINE_JUDGE
freopen("in","r",stdin);
//freopen("out","w",stdout);
#endif
N = read();
M = read();
ld pre = -1e40 , cur = -1e40 , sum = 0 , pfh = 0 , ans = 1e40 , minInd;
for(int i = 1 ; i <= M ; ++i){
int a = read() , b = read();
lj[b].push_back(a);
}
for(int i = 1 ; i <= N ; ++i){
sum += lj[i][0];
pfh += 1ll * lj[i][0] * lj[i][0];
if(lj[i].size() > 1)
q.push(PLI(-(lj[i][1] + lj[i][0]) / 2.0 , i));
}
while(!q.empty()){
PLI t = q.top();
q.pop();
pre = cur;
cur = -t.first;
int i = t.second;
ld minN = sum / N;
if(pre > minN){
if(ans > N * pre * pre - 2 * sum * pre + pfh){
ans = N * pre * pre - 2 * sum * pre + pfh;
minInd = pre;
}
}
else
if(cur < minN){
if(ans > N * cur * cur - 2 * cur * sum + pfh){
ans = N * cur * cur - 2 * cur * sum + pfh;
minInd = cur;
}
}
else
if(ans > (N * pfh - sum * sum) / N){
ans = (N * pfh - sum * sum) / N;
minInd = minN;
}
sum -= lj[i][p[i]];
pfh -= 1ll * lj[i][p[i]] * lj[i][p[i]];
sum += lj[i][++p[i]];
pfh += 1ll * lj[i][p[i]] * lj[i][p[i]];
if(p[i] + 1 != lj[i].size())
q.push(PLI(-(lj[i][p[i] + 1] + lj[i][p[i]]) / 2.0 , i));
}
pre = cur;
cur = 1e40;
ld minN = sum / N;
if(pre > minN){
if(ans > N * pre * pre - 2 * sum * pre + pfh){
ans = N * pre * pre - 2 * sum * pre + pfh;
minInd = pre;
}
}
else
if(cur < minN){
if(ans > N * cur * cur - 2 * cur * sum + pfh){
ans = N * cur * cur - 2 * cur * sum + pfh;
minInd = cur;
}
}
else
if(ans > (N * pfh - sum * sum) / N){
ans = (N * pfh - sum * sum) / N;
minInd = minN;
}
cout << fixed << setprecision(4) << minInd;
return 0;
}
标签:pre,Luogu3162,cur,pfh,sum,include,ans,CQOI2012,贪心 来源: https://www.cnblogs.com/Itst/p/10341948.html