#1475: Array splitting

#1475: Array split time limit: 10000ms single point time limit: 1000ms memory limit: 256MB description

Little Ho got an array as a gift for his new year, and he liked this array very much!

After a few days of careful study, small Ho succeeded in splitting the array into segments, and each paragraph was not 0!

Now little Ho would like to know how many of these splitting methods are there?

The two split methods are treated differently when and only if the array is made up of all the locations where the arrays are broken.

Input

The first behavior of each set of inputs is a positive integer n, which indicates the length of the array

The second behaves n integers a1~an, describing the array that little Ho received

For 40% of data, meet 1<=n<=10

For 100% of data, meet 1<=n<=105, | ai|<=100

Output

For each set of inputs, the output is one line of ans, which represents the remainder of the split scheme divided by (109+7).

Sample input

51-1 0 2-2

Sample output

5
Analysis: Dp[i] Represents the previous I number scheme, Sum[i] represents the prefix and I;
DP[I]=∑DP[J] (1<=j<i)-∑dp[k] (1<=k<i&&sum[k]==sum[i]);
Code:

#include <iostream>#include<cstdio>#include<cstdlib>#include<cmath>#include<algorithm>#include<climits>#include<cstring>#include<string>#include<Set>#include<bitset>#include<map>#include<queue>#include<stack>#include<vector>#defineRep (I,m,n) for (i=m;i<=n;i++)#defineMoD 1000000007#defineINF 0x3f3f3f3f#defineVI vector<int>#definePB Push_back#defineMP Make_pair#defineFi first#defineSe Second#definell Long Long#definePi ACOs (-1.0)#definePII pair<int,int>#defineSYS system ("pause")Const intmaxn=1e5+Ten;Const intn=1e3+Ten;using namespacestd;ll gcd (ll p,ll q) {returnq==0? P:GCD (q,p%q);} ll Qpow (ll p,ll q) {ll F=1; while(q) {if(q&1) f=f*p;p=p*p;q>>=1;}returnF;}intn,m,k,t,a[maxn];ll Sum,dp[maxn];map<int,ll>p;intMain () {inti,j; p[0]=1; scanf ("%d",&N); Rep (I,1, N) scanf ("%d", &a[i]), a[i]+=a[i-1]; Rep (I,1, N) {Dp[i]+=sum+1; Dp[i]-=P[a[i]]; (Dp[i]+=MOD)%=MoD; Sum+=Dp[i]; Sum%=MoD; P[a[i]]+=Dp[i]; P[a[i]]%=MoD; } printf ("%lld\n", Dp[n]); return 0;}

#1475: Array splitting