[Introduction to Algorithms, CLRS] Problems 1.1

This is a solution for Introduction to Algorithms. I write this for my study purpose.

Problems 1-1 Comparison of running times

For each function f .n/ and time t in the following table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f .n/ microseconds.

Answer:

We assume a 30 day month and 365 day year. I use '^' for 'to the'.

	1 second	1 minute	1 hour	1 day	1 month	1 year	1 century
lg n	2^(10^6)	2^(6*(10^7))	2^(3.6*(10^9))	2^(8.64*(10^10))	2^(2.592*(10^12))	2^(3.1536*(10^13))	2^(3.15576*(10^15))
sqrt(n)	1*(10^12)	3.6*(10^15)	1.29*(10^19)	7.46*(10^21)	6.72*(10^24)	9.95*(10^26)	9.96*(10^30)
n	1*(10^6)	6*(10^7)	3.6*(10^9)	8.64*(10^10)	2.59*(10^12)	3.15*(10^13)	3.16*(10^15)
n lg n	189481	8.64*(10^6)	4.18*(10^8)	8.69*(10^9)	2.28*(10^11)	2.54*(10^12)	2.2*(10^14)
n^2	1000	7745	60000	293938	1609968	5615692	56176151
n^3	100	391	1532	4420	13736	31593	146679
2^n	19	25	31	36	41	44	51
n!	9	11	12	13	15	16	17

source: http://sites.math.rutgers.edu/~ajl213/CLRS/Ch1.pdf