Sigma (化简）牛客多校第一场 -- Integration

思路：

可以裂项化简，类似找规律，可以两项、三项代进去试试看。

  1 #define IOS ios_base::sync_with_stdio(0); cin.tie(0);
  2 #include <cstdio>//sprintf islower isupper
  3 #include <cstdlib>//malloc  exit strcat itoa system("cls")
  4 #include <iostream>//pair
  5 #include <fstream>
  6 #include <bitset>
  7 //#include <map>
  8 //#include<unordered_map>
  9 #include <vector>
 10 #include <stack>
 11 #include <set>
 12 #include <string.h>//strstr substr
 13 #include <string>
 14 #include <time.h>//srand(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
 15 #include <cmath>
 16 #include <deque>
 17 #include <queue>//priority_queue<long long, vector<long long>, greater<long long> > q;//less
 18 #include <vector>//emplace_back
 19 //#include <math.h>
 20 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
 21 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
 22 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
 23 #define mem(a,b) memset(a,b,sizeof(a))
 24 #define fo(a,b,c) for(a=b;a<=c;++a)//register long long i
 25 #define fr(a,b,c) for(a=b;a>=c;--a)
 26 #define pr printf
 27 #define sc scanf
 28 void swapp(long long &a,long long &b);
 29 double fabss(double a);
 30 long long maxx(long long a,long long b);
 31 long long minn(long long a,long long b);
 32 long long Del_bit_1(long long n);
 33 long long lowbit(long long n);
 34 long long abss(long long a);
 35 //const long long INF=(1LL<<60);
 36 const double E=2.718281828;
 37 const double PI=acos(-1.0);
 38 const long long inf=(1<<29);
 39 const double ESP=1e-9;
 40 const long long mod=(long long)1e9+7;
 41 const long long N=(long long)1e6+6;
 42 
 43 long long a[N];
 44 long long qpow(long long a,long long b,long long mod)
 45 {
 46     long long ans;
 47     a%=mod;
 48     ans=1;
 49     while(b!=0)
 50     {
 51         if(b&1)
 52             ans=(ans*a)%mod;
 53         b/=2;
 54         a=(a*a)%mod;
 55     }
 56     return ans;
 57 }
 58 
 59 int main()
 60 {
 61     long long n,i;
 62     while(~sc("%lld",&n))
 63     {
 64         for(i=1;i<=n;++i)
 65             sc("%lld",&a[i]);
 66         long long ans=0;
 67         for(i=1;i<=n;++i)
 68         {
 69             long long temp=a[i]*2;
 70             for(long long j=1;j<=n;++j)
 71             {
 72                 if(j==i)
 73                     continue;
 74                 temp*=((a[j]*a[j]-a[i]*a[i])%mod+mod)%mod;
 75                 temp%=mod;
 76             }
 77             ans+=qpow(temp,mod-2,mod);
 78             ans%=mod;
 79         }
 80         pr("%lld\n",ans);
 81     }
 82     return 0;
 83 }
 84 
 85 /**************************************************************************************/
 86 
 87 long long maxx(long long a,long long b)
 88 {
 89     return a>b?a:b;
 90 }
 91 
 92 void swapp(long long &a,long long &b)
 93 {
 94     a^=b^=a^=b;
 95 }
 96 
 97 long long lowbit(long long n)
 98 {
 99     return n&(-n);
100 }
101 
102 long long Del_bit_1(long long n)
103 {
104     return n&(n-1);
105 }
106 
107 long long abss(long long a)
108 {
109     return a>0?a:-a;
110 }
111 
112 double fabss(double a)
113 {
114     return a>0?a:-a;
115 }
116 
117 long long minn(long long a,long long b)
118 {
119     return a<b?a:b;
120 }