CareerCup

Logan answer is correct:
let p = a/b, n = a+b, and m = logn

1. you need to toss coin m times, and generate binary number: x
2 if x <= n
if x < p
return head
else
return tail
if x > n
repeat

This may waste many trials based on p. Not sure this is elegant solution.

Given in cormen solution's pdf...

While(1)
{
x = Biased_Toss();
y = Biased_Toss();
if(x!=y)
return x;
}

Pr { x=1 and y=0 } = P * (1-P)
Pr { x=0 and y=1 } = (1-P) * P

The solution proposed works great when we are running a computer program. But in the real world solution how does this work? In the question its not mentioned its a computer program.

Say Pr(H) and Pr(T) be the probability of getting head and tail from the biased coin.

then
we can say

toss coin twice
if it comes 'HT' then say its head ( Pr(HT) = Pr(H)*Pr(T) )
if it comes 'TH' then say its tail ( Pr(TH) = Pr(T)*Pr(H))

if it comes 'HH' or 'TT' then ignore the toss and repeat

Say the value of this coin is 1. If the p we are looking for is 0.7 for winning. To make this coin unfair, we simply toss it 10 times and if we have 7 heads, we win. If not, we lose. I don't see any reason to write code for this.

We can designate 1 event(toss) = 2 flips of the coin. Now, we can assign random variable {X=head} if the 2 flips give us HT,TH,HH and {X=tail} if we have TT. With this arrangement we have Pr{X=head} > Pr{X=tail}. Thus we have a biased coin. Now, if needed a specific p value we may have to consider the equation 1 event(toss) = y flips of the coin.

Mold the coin to make it a dice.. so if winning probability is .1... make the dice with 10 faces and it should work.. coding doesn't always help..:)

Say p is 60 here. So if we select a random number between 1-100 and it is <= 60 then we return heads and if >=60 we return tail.

For getting a random number between 1-100 we see that 100 in binary = 1100100, which has 7 digits, so we toss the fair coin 7 times and make a binary number out of it. Depending on the number we return head or tail (as described above).

A simple way of approaching the problem would be to specify certain constraints. In this case, let us specify the number of tosses n per game.
For a given unbiased coin, if n=2, the possible tosses will be:
HH
HT
TH
TT
Pr(H)=Pr(T)=1/2.
So n=2 will not work. Lets choose n=3, we get:
HHH
HHT
HTH
HTT
THH
TTH
TTT
Pr(H)=11/21 Pr(T)=10/21. Here the coin is biased towards getting a Head than a Tail.

Hope this example helps.