• Continue to Read Chapter 13: Parallel Computation
• Quiz

• Assumes Sorted
• Like Telephone Book
• Logarithmic Time
• t = A * log(N)

• Note: here N is number of moves looking ahead.
• We Have an Algorithm!
• Layers of look ahead: If I do this, then he does this, ....
• Problem Solved (?!)
• Can Represent Possibilities by Tree
• Assume 10 Possibilities Each Move
• t = A * 10^N
• !!!!
• Exponential
• Sample Numbers

• Visit N Cities in Optimal Order
• Optimal By:
  • time
  • distance
  • cost
• N factorial (N!) Possibilities
• Look at Table
• N! is roughly N^N
• Typical of some very practical problems

3	2! = 2		5	4! = 24
abc			abcde
acb 			abced
			abdce
4	3! = 6		abdec
abcd			abecd
abdc			abedc
acbd		
acdb			acbde
adbc			acbed
adcb 			acdbe
			acdeb
			acebd
			acedb
		
			adbce
			adbec
			adcbe
			adceb
			adebc
			adecb

			aebcd
			aebdc
			aecbd
			aecdb
			aedbc
			aedcb

	t = 5.49 * 10**-3 * 2**n
n	t
5	.17s
10	5.62s
15	3.00m
20	1.6h
25	2.13d
30	68.23d
35	5.98y
40	191.3y
45	6120.y
50	196K y
55	6.27M y
60	201M y
65	6.42G y
70	205G y