HDU-4655 Cut Pieces 数学,贪心

　　题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4655

　　先不考虑相临的有影响，那么总数就是n*prod(a_i)，然后减去每个相邻的对总数的贡献Σ( Min(a[i],a[i+1])*prod(i-1)*prod(i+2) )，其中prod(i)为[1,i-1]这个区间a[i]的积，prod(i+2)表示的是[i+2,n]这个区间，答案就是n*prod(a_i)-Σ( Min(a[i],a[i+1])*prod(i-1)*prod(i+2) )，可以得到取得最大值是ai的排列就是最小，最大，次小，次大，例如:1 2 3 4 -> 1 4 2 3。然后就是一个DP转移了，方程很好写。。

 1 //STATUS:C++_AC_468MS_19068KB
 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=1000010;
37 const int INF=0x3f3f3f3f;
38 const int MOD= 1000000007,STA=8000010;
39 const LL LNF=1LL<<55;
40 const double EPS=1e-9;
41 const double OO=1e30;
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 LL num[N],s[N];
59 LL f[N],p[N];
60 int T,n;
61 
62 int main(){
63  //   freopen("in.txt","r",stdin);
64     int i,j,mid;
65     LL low,hig;
66     scanf("%d",&T);
67     while(T--)
68     {
69         scanf("%d",&n);
70         for(i=1;i<=n;i++)
71             scanf("%I64d",&num[i]);
72         sort(num+1,num+n+1);
73         mid=(n+1)>>1;
74         for(i=1;i<=n;i+=2){
75             s[i]=num[(i+1)>>1];
76             s[i+1]=num[n-((i+1)>>1)+1];
77         }
78         p[0]=1;
79         for(i=1;i<=n;i++)p[i]=(p[i-1]*s[i])%MOD;
80         f[1]=s[1];
81         for(i=2;i<=n;i++){
82             low=Min(s[i-1],s[i]);
83             hig=Max(0LL,s[i]-s[i-1]);
84             f[i]=( low*(f[i-1]+p[i-1]-p[i-2])%MOD+hig*(f[i-1]+p[i-1])%MOD )%MOD;
85         }
86 
87         printf("%I64d\n",(f[n]+MOD)%MOD);
88     }
89     return 0;
90 }

HDU-4655 Cut Pieces 数学,贪心

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