01分数规划

OI分数规划

首先，单纯的贪心是错误的(废话)

除了常见的二分之外还有一种调整法，不会.....

板题：POJ2976 Dropping tests

 1 #include <cstdio>
 2 #include <algorithm>
 3 
 4 typedef long long LL;
 5 const int N = 1010;
 6 const double INF = 1e11;
 7 
 8 struct Node {
 9     double a, b, c;
10     inline bool operator <(const Node &w) const {
11         return c < w.c;
12     }
13 }node[N];
14 
15 int n, k;
16 
17 inline bool check(double D) {
18     for(int i = 1; i <= n; i++) {
19         node[i].c = node[i].a - node[i].b * D;
20     }
21     std::sort(node + 1, node + n + 1);
22     //printf("k = %d \n", k);
23     double ans = 0;
24     for(int i = 1; i <= k; i++) {
25         ans += node[n + 1 - i].c;
26     }
27     return ans >= 0;
28 }
29 
30 inline void solve() {
31     k = n - k;
32     double l = INF, r = -INF;
33     for(int i = 1; i <= n; i++) {
34         scanf("%lf", &node[i].a);
35     }
36     for(int i = 1; i <= n; i++) {
37         scanf("%lf", &node[i].b);
38         double temp = node[i].a / node[i].b;
39         l = std::min(l, temp);
40         r = std::max(r, temp);
41     }
42 
43     for(int i = 1; i <= 50; i++) {
44         double mid = (l + r) / 2;
45         if(check(mid)) {
46             l = mid;
47         }
48         else {
49             r = mid;
50         }
51     }
52     printf("%lld\n", (LL)(r * 100 + 0.5));
53     return;
54 }
55 
56 int main() {
57     while(scanf("%d%d", &n, &k)) {
58         if(!n && !k) break;
59         solve();
60     }
61 
62     return 0;
63 }