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The Complexity of Songs By Rohan Sharma
Disclaimer
“ The Ideal Talk”
Introduction
Informative
Accessible
< 10 minutes
My Talk
No introduction
Uninformative
Arcane
Possibly > 10 minutes
Possibly > 10 minutes
</Disclaimer>
Computer Science
Computer Science
Computer Science
 
Computer Science
 
Astronomy
 
Warning: Boring Stuff Ahead!
(Removed picture of friend sleeping.)
Computational  Complexity
Largest Member
3 2 7 9 1
3 2 7 9 1
3 2 7 9 1
3 2 7 9 1
3 2 7 9 1
3 2 7 9 1
3 2 7 9 1
3 2 7 9 1
Linear Time O(n)
Binary Search
3 7 10 21 33 39 46 Search for  10
3 7 10 Search for  10
10 Found  10
Logarithmic time O(lg n)
(Removed picture of friend opening his mouth wide open like the Grand Canyon.)
 
 
 
The Complexity of Songs
 
How?
Letters?
Tedious!
Words?
Yes!
Toughest:   O(n)   Easiest:  O(1)
 
Never gonna give you up Never gonna let you down Never gonna run around and desert you Never gonna make you cry Never gonna say goodbye Never gonna tell a lie and hurt you
Never gonna give you up Never gonna let you down Never gonna run around and desert you Never gonna make you cry Never gonna say goodbye Never gonna tell a lie and hurt you FAIL
Breakthrough
 
O(n 1/2 )
The Twelve Days of Christmas On the first day of Christmas my true love sent to me   A partridge in a pear tree.  On the second day of Christmas my true love sent to me   Two turtle doves,  and a partridge in a pear tree.  On the third day of Christmas, my true love sent to me  Three French hens, two turtle doves, and a partridge in a pear tree.
The Twelve Days of Christmas On the first day of Christmas my true love sent to me   gift 1 On the second day of Christmas my true love sent to me   gift 1, gift 2 On the third day of Christmas, my true love sent to me  gift 1, gift 2, gift 3 ... On the n th  day of Christmas, my true love sent to me  gift 1, gift 2, gift 3, ..., gift n
The Twelve Days of Christmas gift 1 gift 1, gift 2 gift 1, gift 2, gift 3 ... gift 1, gift 2, gift 3, ..., gift n
The Twelve Days of Christmas gift 1 gift 1, gift 2 gift 1, gift 2, gift 3 ... gift 1, gift 2, gift 3, ..., gift n
O(n 1/2 )
Breakthrough #2
N  Bottles of Beer n  bottles of beer on the wall n  bottles of beer! You take one down, and pass it around n - 1  bottles of beer on the wall!
O(lg n)
 
O(1)
Questions?

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The Complexity of Songs