牛客网暑期ACM多校训练营（第五场）A gpa(01分数规划)

Description:

At the university where she attended, the final score of her is

Now she can delete at most k courses and she want to know what the highest final score that can get.

Input:

The first line has two positive integers n,k

The second line has n positive integers s[i]

The third line has n positive integers c[i]

Output:

Output the highest final score, your answer is correct if and only if the absolute error with the standard answer is no more than $10^{-5}$

Sample Input:

3 1
1 2 3
3 2 1

Sample Output:

2.33333333333

Hint:

Delete the third course and the final score is $\frac{2\times2+3\times1}{2+1}=\frac{7}{3}$

题目链接

$n$门课，每门课有两个属性$s$和$c$，删除$k$门课，使$\frac{\sum s[i]\times c[i]}{\sum s[i]}$最大。

01分数规划，设最终结果$max(\frac{\sum s[i]\times c[i]}{\sum s[i]})=x$，则$\sum s[i]\times c[i]-x\times\sum s[i]=0$，所以选择$(s\times c-x\times s)$最大的$n-k$门课，不断二分$x$直到找到最大值并达到合适的精度。

AC代码:

#include <bits/stdc++.h>
using namespace std;
#define mem(a,b) memset(a,b,sizeof(a))
#define pb push_back
#define mp make_pair
#define lowbit(x) (x&(-x))
#define XDebug(x) cout << #x << "=" << x << endl;
#define ArrayDebug(x,i) cout << #x << "[" << i << "]=" << x[i] << endl;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef pair<double,double> PDD;
typedef pair<ll,ll> PLL;
const int INF = 0x3f3f3f3f;
const int maxn = 1e7 + 5;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double pi = asin(1.0) * 2;
const double e = 2.718281828459;
template <class T>
inline bool read(T &ret) {
    char c;
    int sgn;
    if (c = getchar(), c == EOF) {
        return 0;
    }
    while (c != '-' && (c < '0' || c > '9')) {
        c = getchar();
    }
    sgn = (c == '-') ? -1 : 1;
    ret = (c == '-') ? 0 : (c - '0');
    while (c = getchar(), c >= '0' && c <= '9') {
        ret = ret * 10 + (c - '0');
    }
    ret *= sgn;
    return 1;
}
template <class T>
inline void out(T x) {
    if (x > 9) {
        out(x / 10);
    }
    putchar(x % 10 + '0');
}

int n, k;
vector<int> s, c;

bool check(double x) {
    vector<double> temp(n, 0.0);
    for (int i = 0; i < n; ++i) {
        temp[i] = 1.0 * s[i] * c[i] - x * s[i];
    }
    sort(temp.begin(), temp.end(), [&] (const double &a, const double &b) {
        return a > b;
    });
    double ans = 0;
    for (int i = 0; i < n - k; ++i) {
        ans += temp[i];
    }
    return ans > 0;
}

int main(int argc, char *argv[]) {
#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
#endif
    read(n); read(k);
    s.assign(n, 0);
    c.assign(n, 0);
    for (int i = 0; i < n; ++i) {
        read(s[i]);
    }
    for (int i = 0; i < n; ++i) {
        read(c[i]);
    }
    double left = 0, right = 1e3;
    while (right - left > eps) {
        double mid = (left + right) / 2;
        if (check(mid)) {
            left = mid;
        }
        else {
            right = mid;
        }
    }
    printf("%.8lf\n", left);
#ifndef ONLINE_JUDGE
    fclose(stdin);
    fclose(stdout);
    system("gedit out.txt");
#endif
    return 0;
}