BNUOJ-29358 Come to a spring outing 搜索,DP

最新推荐文章于 2025-09-06 09:33:29 发布

转载最新推荐文章于 2025-09-06 09:33:29 发布 · 86 阅读

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原文链接：http://www.cnblogs.com/zhsl/p/3282081.html

文章标签：

#java #c/c++ #php

本文探讨了一种特定的背包问题，通过深度优先搜索（DFS）和动态规划（DP）两种方法解决物品分配到三个相同容量背包的问题，并确保所有物品能够被合理分配。文章提供了完整的C++代码实现。

　　题目链接：http://www.bnuoj.com/bnuoj/problem_show.php?pid=29358

　　状态虽然很多，但是非常稀疏，dfs搜索然后剪下枝。。

　　或者DP，f[i][j][k]表示前 i 个物品能否到达第一个背包和第二个背包容量分别为 j 和 k 的状态，然后判断第3个背包是否能装下剩下的。f[i][j][k]=f[i-1][j][k] | f[i-1][j-v[i]][k] | f[i-1][j][k-v[i]]..

　　搜索：

 1 //STATUS:C++_AC_10MS_1308KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 //#include <map>
23 using namespace std;
24 //#pragma comment(linker,"/STACK:102400000,102400000")
25 //using namespace __gnu_cxx;
26 //define
27 #define pii pair<int,int>
28 #define mem(a,b) memset(a,b,sizeof(a))
29 #define lson l,mid,rt<<1
30 #define rson mid+1,r,rt<<1|1
31 #define PI acos(-1.0)
32 //typedef
33 //typedef __int64 LL;
34 //typedef unsigned __int64 ULL;
35 //const
36 const int N=35;
37 const int INF=0x3f3f3f3f;
38 const int MOD=100000,STA=8000010;
39 //const LL LNF=1LL<<60;
40 const double EPS=1e-8;
41 const double OO=1e15;
42 const int dx[4]={-1,0,1,0};
43 const int dy[4]={0,1,0,-1};
44 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
45 //Daily Use ...
46 inline int sign(double x){return (x>EPS)-(x<-EPS);}
47 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
48 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
49 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
50 template<class T> inline T Min(T a,T b){return a<b?a:b;}
51 template<class T> inline T Max(T a,T b){return a>b?a:b;}
52 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
53 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
54 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
55 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
56 //End
57 
58 int v[N];
59 int T,n,m;
60 
61 int dfs(int d,int a,int b,int c)
62 {
63     if(d==n)return 1;
64     if(a>=v[d] && dfs(d+1,a-v[d],b,c))return 1;
65     if(b>=v[d] && dfs(d+1,a,b-v[d],c))return 1;
66     if(c>=v[d] && dfs(d+1,a,b,c-v[d]))return 1;
67     return 0;
68 }
69 
70 int main(){
71  //   freopen("in.txt","r",stdin);
72     int i,j,ca=1,ok,sum;
73     scanf("%d",&T);
74     while(T--)
75     {
76         scanf("%d%d",&n,&m);
77         sum=0;
78         for(i=0;i<n;i++){
79             scanf("%d",&v[i]);
80             sum+=v[i];
81         }
82         printf("Case %d: ",ca++);
83         if(m*m*m<sum){
84             printf("No\n");
85             continue;
86         }
87 
88         ok=dfs(0,m,m,m);
89 
90         printf("%s\n",ok?"Yes":"No");
91     }
92     return 0;
93 }

　　DP：

 1 //STATUS:C++_AC_730MS_24308KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 //#include <map>
23 using namespace std;
24 //#pragma comment(linker,"/STACK:102400000,102400000")
25 //using namespace __gnu_cxx;
26 //define
27 #define pii pair<int,int>
28 #define mem(a,b) memset(a,b,sizeof(a))
29 #define lson l,mid,rt<<1
30 #define rson mid+1,r,rt<<1|1
31 #define PI acos(-1.0)
32 //typedef
33 typedef long long LL;
34 typedef unsigned long long ULL;
35 //const
36 const int N=35;
37 const int INF=0x3f3f3f3f;
38 const int MOD=100000,STA=8000010;
39 const LL LNF=1LL<<60;
40 const double EPS=1e-8;
41 const double OO=1e15;
42 const int dx[4]={-1,0,1,0};
43 const int dy[4]={0,1,0,-1};
44 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
45 //Daily Use ...
46 inline int sign(double x){return (x>EPS)-(x<-EPS);}
47 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
48 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
49 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
50 template<class T> inline T Min(T a,T b){return a<b?a:b;}
51 template<class T> inline T Max(T a,T b){return a>b?a:b;}
52 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
53 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
54 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
55 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
56 //End
57 
58 int f[N][410][410],v[N];
59 int T,n,m,sum;
60 
61 bool solve()
62 {
63     int i,j,k;
64     mem(f,0);
65     f[0][0][0]=1;
66     for(i=1;i<=n;i++){
67         for(j=0;j<=m;j++){
68             for(k=0;k<=m;k++){
69                 f[i][j][k]|=f[i-1][j][k];
70                 if(j>=v[i])f[i][j][k]|=f[i-1][j-v[i]][k];
71                 if(k>=v[i])f[i][j][k]|=f[i-1][j][k-v[i]];
72                 if(f[i][j][k] && sum-j-k<=m)return true;
73             }
74         }
75     }
76     return false;
77 }
78 
79 int main(){
80  //   freopen("in.txt","r",stdin);
81     int i,j,ca=1;
82     scanf("%d",&T);
83     while(T--)
84     {
85         scanf("%d%d",&n,&m);
86         sum=0;
87         for(i=1;i<=n;i++){
88             scanf("%d",&v[i]);
89             sum+=v[i];
90         }
91 
92         printf("Case %d: %s\n",ca++,solve()?"Yes":"No");
93     }
94     return 0;
95 }