AtCoder Regular Contest 058--E - 和風いろはちゃん / Iroha and Haiku（转化01串+状态压缩）

E - 和風いろはちゃん / Iroha and Haiku

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Time Limit: 4 sec / Memory Limit: 512 MB

Score : 700700 points

Problem Statement

Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.

Iroha is looking for X,Y,ZX,Y,Z-Haiku (defined below) in integer sequences.

Consider all integer sequences of length NN whose elements are between 11 and 1010, inclusive. Out of those 10N10N sequences, how many contain an X,Y,ZX,Y,Z-Haiku?

Here, an integer sequence a0,a1,...,aN−1a0,a1,...,aN−1 is said to contain an X,Y,ZX,Y,Z-Haiku if and only if there exist four indices x,y,z,w(0≦x

• ax+ax+1+...+ay−1=Xax+ax+1+...+ay−1=X
• ay+ay+1+...+az−1=Yay+ay+1+...+az−1=Y
• az+az+1+...+aw−1=Zaz+az+1+...+aw−1=Z

Since the answer can be extremely large, print the number modulo 109+7109+7.

Constraints

• 3≦N≦403≦N≦40
• 1≦X≦51≦X≦5
• 1≦Y≦71≦Y≦7
• 1≦Z≦51≦Z≦5

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Input

The input is given from Standard Input in the following format:

NN XX YY ZZ

Output

Print the number of the sequences that contain an X,Y,ZX,Y,Z-Haiku, modulo 109+7109+7.

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Sample Input 1 Copy

Copy

3 5 7 5

Sample Output 1 

这个题完全没有思路......然后看了看题解也不是特别明白，讨论一下稍后再写一下。

大题解法是看做01串，1就是1,2 就是10，那么n就是1后面n-1个0，然后看后面的x+y+z位是否包含x+y+z，包含的话就是不符合情况的，统计这些。最后减去。

#include
#include
using namespace std;
int n,x,y,z,nw;
const int mod=1e9+7;
int S,f[45][1<<17],ans=1;
int main()
{
    scanf("%d",&n);
    scanf("%d%d%d",&x,&y,&z);
    for (int i=1;i<=n;i++) ans=1ll*ans*10%mod;
    nw=(1<