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(ai)，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(ai)-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 }
