[超棒的二項展開式實現] binomial formula implementation

PrimeSoccer_binomial.cpp

/*  given p as the probability of this team winning, 
 *  what's the probability for this team have a prime number as it's final score
 */
double solve(int p){
  vector<int> prob(0, 20);
  prob[0]=1;
  
  // 短短七行讓你省去寫C(n, k) 又可以拿到第k項展開後的結果
  // generate binomial coefficient (x+y)^n : C(n, k) * (x^n-k) * (x^k)
  // pascal triangle 
  // 1
  // 0.8        0.2
  // 0.8^2  2*(0.8*0.2)  0.2^2
  // 1      3            3         1
  // 1      4            6         4        1
  //...
  for(int t = 0;t < 18; ++ t){
    for(int i = 18; i >= 0; -- i){
      prob[i] *= (100 - p) / 100.0;
      if(i > 0){
        probi] += prob[i-1] * p / 100.0;
      }
    }
  }
  
  double sum = 0.0;
  for(int i=1;i<=18;++i){
    if(isPrime(i)){
      sum += p[i];
    }
  }
  return sum;
}