1. Dynamic Programming Problems
Birthday Paradox

2. Birthday Paradox There are 365 days in a year (no leap years)
You have N students in a classroom
How many students would you need so that the probability of there being at least one pair of students that have the same birthday, is greater than 50%
Well we know the answer is:
At least 2
Not more that 365

3. It must be: Number of Students Probability of at least one match 1 21 2
1/365 3
(1/365) + [1 – (1/365)] * [ (2/365 ] N
(prob match with N-1) + (prob no match) * (prob N will match other)
365

4. Shortest path example
Graph coming soon…come back later

5. Seats on an Airplane 100 seats on a plane
$59/seat and all sell  $5,900 and no empty seats
$100/seat and 80 sell  $8,000 and 20 empty seats
$200/seat and 50 sell  $10,000 and 50 empty seats
$300/seat and 30 sell  $9,000 and 70 empty seats

6. Seats on an Airplane
Suppose some customers would pay $299 but not $699
Some customers would pay $699 (or better $299)
We would like to reserve a seat for everyone willing to pay $699 and sell the rest for $299.
How many seats would be reserve for the $699 customers and the rest go to the $299 customers