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  • POJ3111 K Best —— 01分数规划 二分法

    题目链接:http://poj.org/problem?id=3111

    K Best
    Time Limit: 8000MS   Memory Limit: 65536K
    Total Submissions: 11380   Accepted: 2935
    Case Time Limit: 2000MS   Special Judge

    Description

    Demy has n jewels. Each of her jewels has some value vi and weight wi.

    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 = {i1i2, …, ik} 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 — vi and wi (0 ≤ vi ≤ 106, 1 ≤ wi ≤ 106, both the sum of all vi and the sum of all wi 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:
     
     
    代码一:
     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 int n, k;
    29 
    30 bool test(double L)
    31 {
    32     for(int i = 1; i<=n; i++)
    33         q[i].d = 1.0*q[i].a - L*q[i].b;
    34 
    35     sort(q+1, q+1+n);
    36     double sum = 0;
    37     for(int i = 1; i<=k; i++)   //取前k大的数
    38         sum += q[i].d;
    39     return sum>=0;
    40 }
    41 
    42 int main()
    43 {
    44     while(scanf("%d%d", &n, &k)!=EOF)
    45     {
    46          //一次性把所有信息都录入结构体中,当排序时,即使打乱了顺序,仍然还记得初始下标。
    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("
    ");
    66     }
    67 }
    View Code
     
    代码二:
     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 id;
    24     bool operator<(const node x)const{
    25         return d>x.d;
    26     }
    27 }q[MAXN];
    28 
    29 int n, k;
    30 int a[MAXN], b[MAXN];
    31 
    32 bool test(double L)
    33 {
    34     for(int i = 1; i<=n; i++)   //每一次q[i]都重新更新,与a[i],b[i]独立开来
    35     {
    36         q[i].id = i;
    37         q[i].d = 1.0*a[i] - L*b[i];
    38     }
    39     sort(q+1, q+1+n);
    40     double sum = 0;
    41     for(int i = 1; i<=k; i++)
    42         sum += q[i].d;
    43     return sum>=0;
    44 }
    45 
    46 int main()
    47 {
    48     while(scanf("%d%d", &n, &k)!=EOF)
    49     {
    50         for(int i = 1; i<=n; i++)
    51             scanf("%d%d", &a[i], &b[i]);
    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("
    ");
    66     }
    67 }
    View Code

    错误代码:

     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 id;
    24     bool operator<(const node x)const{
    25         return d>x.d;
    26     }
    27 }q[MAXN];
    28 
    29 int n, k;
    30 int a[MAXN], b[MAXN], ans[MAXN];
    31 
    32 bool test(double L)
    33 {
    34     //经过一次排序后,q[i].id不再等于i,所以出错。应该同时更新q[i].id
    35     for(int i = 1; i<=n; i++)
    36         q[i].d = 1.0*a[i] - L*b[i];
    37 
    38     sort(q+1, q+1+n);
    39     double sum = 0;
    40     for(int i = 1; i<=k; i++)
    41         sum += q[i].d;
    42     return sum>0;
    43 }
    44 
    45 int main()
    46 {
    47     while(scanf("%d%d", &n, &k)!=EOF)
    48     {
    49         for(int i = 1; i<=n; i++)
    50         {
    51             scanf("%d%d", &a[i], &b[i]);
    52             q[i].id = i;       
    53         }
    54 
    55         double l = 0, r = 1e7;
    56         while(l+EPS<=r)
    57         {
    58             double mid = (l+r)/2;
    59             if(test(mid))
    60                 l = mid + EPS;
    61             else
    62                 r = mid - EPS;
    63         }
    64 
    65         for(int i = 1; i<=k; i++)
    66             printf("%d ", q[i].id);
    67         printf("
    ");
    68     }
    69 }
    View Code
     
     
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  • 原文地址:https://www.cnblogs.com/DOLFAMINGO/p/7571434.html
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