Inclusion–exclusion principle（动态规划）

int void F(string s, int prime){
    int R[s.length()][prime];
    memset(R, 0, sizeof(R));
    for(int i= s.length()-1;i>=0; i--){
       int first = s[i] - ‘0‘;
       for(int k = i+1; k < s.length(); j++){ //对R的第一维进行遍历
           for(int j = 0; j < primes; j ++){ //对R的第二维进行遍历
               R[i][j] += R[k][(prime+(j-first)%prime)%prime]; //i+...
               R[i][j] += R[k][(prime+(i-first)%prime)%prime]; //i-...
           }
           first = 10*first +s[k]; //i后面既没+也没-
        }
        R[i][first % p] += 1; //最后一个first
    }
    return return R[0][0];
}

int walprimes(const string& s) {
    return F(s, 2) + F(s, 3) + F(s, 5) + F(s, 7)
       - F(s, 2 * 3) - F(s, 2 * 5) - F(s, 2 * 7) - F(s, 3 * 5) - F(s, 3 * 7) - F(s, 5 * 7)
       + F(s, 3 * 5 * 7) + F(s, 2 * 5 * 7) + F(s, 2 * 3 * 7) + F(s, 2 * 3 * 5)
       - F(s, 2 * 3 * 5 * 7);
}