B. Pasha and Tea
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Pasha decided to invite his friends to a tea party. For that occasion, he has a large teapot with the capacity ofwmilliliters and2ntea cups, each cup is for one of Pasha’s friends. Thei-th cup can hold at mostaimilliliters of water.
It turned out that among Pasha’s friends there are exactlynboys and exactlyngirls and all of them are going to come to the tea party. To please everyone, Pasha decided to pour the water for the tea as follows:
Pasha can boil the teapot exactly once by pouring there at mostwmilliliters of water;Pasha pours the same amount of water to each girl;Pasha pours the same amount of water to each boy;if each girl getsxmilliliters of water, then each boy gets2xmilliliters of water.
In the other words, each boy should get two times more water than each girl does.
Pasha is very kind and polite, so he wants to maximize the total amount of the water that he pours to his friends. Your task is to help him and determine the optimum distribution of cups between Pasha’s friends.
Input
The first line of the input contains two integers,nandw(1≤n≤105,1≤w≤109)— the number of Pasha’s friends that are boys (equal to the number of Pasha’s friends that are girls) and the capacity of Pasha’s teapot in milliliters.
The second line of the input contains the sequence of integersai(1≤ai≤109,1≤i≤2n)—the capacities of Pasha’s tea cups in milliliters.
Output
Print a single real number — the maximum total amount of water in milliliters that Pasha can pour to his friends without violating the given conditions. Your answer will be considered correct if its absolute or relative error doesn’t exceed10-6.
Sample test(s)
input
2 41 1 1 1
output
3
input
3 184 4 4 2 2 2
output
18
input
1 52 3
output
4.5
二分答案即可
#include <stdio.h>#include <ctime>#include <math.h>#include <limits.h>#include <complex>#include <string>#include <functional>#include <iterator>#include <algorithm>#include <vector>#include <stack>#include <queue>#include <set>#include <map>#include <list>#include <bitset>#include <sstream>#include <iomanip>#include <fstream>#include <iostream>#include <ctime>#include <cmath>#include <cstring>#include <cstdio>#include <time.h>#include <ctype.h>#include <string.h>#include <assert.h>using namespace std;int n, w;double p[200010];int main(){while (cin >> n){cin >> w;for (int i = 1; i <= n * 2; i++)scanf("%lf",&p[i]);sort(p + 1, p + 1 + 2 * n);int t1 = p[1];int t2 = p[n + 1];double ans;if (t2 >= t1 * 2) //yes{double left = 0;double right = w;double mid;while (left + 0.000000001 <right){mid = (left + right) / 2;//n*X + n*X/2 <= middouble x = mid / n / 3;if (x <= t1){left = mid;ans = mid;}elseright = mid;}}else{double left = 0;double right = w;double mid;while (left + 0.000000001 <right){mid = (left + right) / 2;//n*X + n*X/2 <= middouble x = mid * 2 / n / 3;if (x <= t2){left = mid;ans = mid;}elseright = mid;}}printf("%.8lf\n",ans);}return 0;}
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