POJ3111 K Best —— 01分数规划 二分法

题目链接：http://poj.org/problem?id=3111

K Best

Description

Demy has n jewels. Each of her jewels has some value v_i and weight w_i.

Since her husband John got broke after recent financial crises, Demy has decided to sell some jewels. She has decided that she would keep k best jewels for herself. She decided to keep such jewels that their specific value is as large as possible. That is, denote the specific value of some set of jewels S = {i₁, i₂, …, i_k} as

.

Demy would like to select such k jewels that their specific value is maximal possible. Help her to do so.

Input

The first line of the input file contains n — the number of jewels Demy got, and k — the number of jewels she would like to keep (1 ≤ k ≤ n ≤ 100 000).

The following n lines contain two integer numbers each — v_i and w_i (0 ≤ v_i ≤ 10⁶, 1 ≤ w_i ≤ 10⁶, both the sum of all v_i and the sum of all w_i do not exceed 10⁷).

Output

Output k numbers — the numbers of jewels Demy must keep. If there are several solutions, output any one.

Sample Input

3 2
1 1
1 2
1 3

Sample Output

1 2

Source

Northeastern Europe 2005, Northern Subregion

题解：

代码如下：

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cmath>
 5 #include <algorithm>
 6 #include <vector>
 7 #include <queue>
 8 #include <stack>
 9 #include <map>
10 #include <string>
11 #include <set>
12 #define ms(a,b) memset((a),(b),sizeof((a)))
13 using namespace std;
14 typedef long long LL;
15 const double EPS = 1e-8;
16 const int INF = 2e9;
17 const LL LNF = 2e18;
18 const int MAXN = 1e5+10;
19
20 struct node
21 {
22     double d;
23     int a, b, id;
24     bool operator<(const node x)const{
25         return d>x.d;
26     }
27 }q[MAXN];
28
29 int n, k;
30
31 bool test(double L)
32 {
33     for(int i = 1; i<=n; i++)
34         q[i].d = 1.0*q[i].a - L*q[i].b;
35
36     sort(q+1, q+1+n);
37     double sum = 0;
38     for(int i = 1; i<=k; i++)
39         sum += q[i].d;
40     return sum>0;
41 }
42
43 int main()
44 {
45     while(scanf("%d%d", &n, &k)!=EOF)
46     {
47         for(int i = 1; i<=n; i++)
48         {
49             scanf("%d%d", &q[i].a, &q[i].b);
50             q[i].id = i;
51         }
52
53         double l = 0, r = 1e7;
54         while(l+EPS<=r)
55         {
56             double mid = (l+r)/2;
57             if(test(mid))
58                 l = mid + EPS;
59             else
60                 r = mid - EPS;
61         }
62
63         for(int i = 1; i<=k; i++)
64             printf("%d ", q[i].id);
65         printf("\n");
66     }
67 }