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(dp专题004)hdu 2955Robberies(01背包变形)

·552 字·2 分钟

题目链接

题意: 给出n个银行 ,以及抢劫每个银行可以得到的价值和被抓的概率,不同银行之间被抓的概率是相互独立的,现在给出安全概率p,只有当概率从小于安全概率时才是安全的,问最多能抢劫多少价值。

思路:一开始很直接就想到把概率算成容量,

于是就成了经典的01背包,然后发现概率是double型。。。想当然得以为最多是2位小数,于是都*100转化成了整数做01背包。

然而正确思路是,把银行价值看成背包容量,而背包价值是概率!

将危险的概率转化成安全概率(1-危险概率=安全概率)

然后做01背包。

然后从大到小扫一遍价值,第一个大于安全概率的就是答案。

注意精度。

代码实现
 1/* ***********************************************
 2Author :111qqz
 3Created Time :Tue 15 Nov 2016 06:53:53 PM CST
 4File Name :code/hdu/2955.cpp
 5************************************************ */
 6#include <cstdio>
 7#include <cstring>
 8#include <iostream>
 9#include <algorithm>
10#include <vector>
11#include <queue>
12#include <stack>
13#include <set>
14#include <map>
15#include <string>
16#include <cmath>
17#include <cstdlib>
18#include <deque>
19#include <ctime>
20#define fst first
21#define sec second
22#define lson l,m,rt<<1
23#define rson m+1,r,rt<<1|1
24#define ms(a,x) memset(a,x,sizeof(a))
25typedef long long LL;
26#define pi pair < int ,int >
27#define MP make_pair
28using namespace std;
29const double eps = 1E-8;
30const int dx4[4]={1,0,0,-1};
31const int dy4[4]={0,-1,1,0};
32const int inf = 0x3f3f3f3f;
33const int N=105;
34double dp[N];
35double p;
36int n,V;
37int value[N];
38double cost[N];
39void solve(double Cost,int Value)
40{
41        for ( int i = V ; i >= Value ; i--)
42                dp[i] = max(dp[i],dp[i-Value]*Cost);
43}
44int dblcmp( double d)
45{
46    return d<-eps?-1:d>eps;
47}
48int main()
49{
50  #ifndef  ONLINE_JUDGE
51    freopen("code/in.txt","r",stdin);
52  #endif
53   int T;
54   cin>>T;
55   while (T--)
56   {
57
58
59        scanf("%lf%d",&p,&n);
60        p = 1 - p;
61	V = 0 ;
62        for ( int i = 1; i <= n ; i++)
63        {
64                scanf("%d%lf",&value[i],&cost[i]);
65                cost[i] = 1 - cost[i];
66		V = V + value[i];
67        }
68	for ( int i = 0 ; i <= V ; i++) dp[i] =  0;
69        for ( int i = 1 ; i <= n ; i++)
70                solve(cost[i],value[i]);
71
72        for ( int i = V ; i >= 0 ; i--)
73	{
74	    if (dblcmp(dp[i]-p)>0)
75	    {
76		printf("%d\n",i);
77		break;
78	    }
79	}
80   }
81#ifndef ONLINE_JUDGE
82  fclose(stdin);
83  #endif
84    return 0;
85}

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