luogu 3423 [POI2005]BAN-Bank Notes

Posted 2022-09-11 mandy-h-y

分析

多重背包优化，输出方案

二进制优化 / 单调队列优化

输出方案只需要记录是否转移，用bool类型存

这题好像卡空间

代码

1.二进制优化

 1 /************************
 2 User:Mandy.H.Y
 3 Language:c++
 4 Problem:luogu
 5 Algorithm:
 6 Date:2019.8.30
 7 ************************/
 8 
 9 #include<bits/stdc++.h>
10 
11 using namespace std;
12 
13 const int maxn = 205;
14 const int maxk = 2e4 + 5;
15 int b[maxn],c[maxn],new_b[4005],new_c[4005],new_id[4005];
16 int dp[maxk],ans[maxn];
17 int n,k,cnt;
18 bool vis[4005][maxk];
19 
20 template<class T>inline void read(T&x)
21     x = 0;bool flag = 0;char ch = getchar();
22     while(!isdigit(ch)) flag |= ch == ‘-‘,ch = getchar();
23     while(isdigit(ch)) x = (x << 1) + (x << 3) + (ch ^ 48),ch = getchar();
24     if(flag) x = -x;
25 
26 
27 template<class T>void putch(const T x)
28     if(x > 9) putch(x / 10);
29     putchar(x % 10 | 48);
30 
31 
32 template<class T>void put(const T x)
33     if(x < 0) putchar(‘-‘),putch(-x);
34     else putch(x);
35 
36 
37 void file()
38     freopen("3423.in","r",stdin);
39     freopen("3423.out","w",stdout);
40 
41 
42 void readdata()
43     read(n);
44     for(int i = 1;i <= n; ++ i) read(b[i]);
45     for(int i = 1;i <= n; ++ i) read(c[i]);
46     read(k);
47 
48 
49 void work()
50     for(int i = 1;i <= n; ++ i)
51         c[i] = min(c[i],k/b[i]);
52         for(int j = 1;j <= c[i]; j <<= 1)
53             new_b[++cnt] = b[i] * j;
54             new_c[cnt] = j;
55             new_id[cnt] = i;
56             c[i] -= j;
57         
58         
59         if(c[i])
60             new_b[++cnt] = b[i] * c[i];
61             new_c[cnt] = c[i];
62             new_id[cnt] = i;
63             c[i] = 0;
64         
65      
66     memset(dp,0x3f3f3f3f,sizeof(dp));
67     dp[0] = 0;
68     for(int i = 1;i <= cnt; ++ i)
69         for(int j = k;j >= new_b[i]; -- j)
70             if(dp[j] > dp[j - new_b[i]] + new_c[i])
71                 dp[j] = dp[j - new_b[i]] + new_c[i];
72                 vis[i][j] = 1;
73             
74         
75     
76     
77     put(dp[k]);
78     putchar(‘\\n‘);
79     int i = cnt,j = k;
80     while(i >= 1)
81         if(vis[i][j])
82             j = j - new_b[i],ans[new_id[i]] += new_c[i];
83         --i;
84     
85     for(int i = 1;i <= n; ++ i)
86         put(ans[i]);
87         putchar(‘ ‘);
88     
89 
90 
91 int main()
92 //    file();
93     readdata();
94     work();
95     return 0;
96 

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