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 }