Created
November 12, 2017 23:45
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[超棒的二項展開式實現] binomial formula implementation
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/* 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; | |
} |
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