A. formulate a related decision problem for the independent-set problem, and prove that it is np-complete. (hint: reduce from the clique problem.)
b. suppose that you are given a "black-box" subroutine to solve the decision prob- lem you defined in part (a).
give an algorithm to find an independent set of max- imum size. the running time of your algorithm should be polynomial in jv j and jej, counting queries to the black box as a single step.

1.the index finger on your right hand types the f r v 4 j u m 7 h y 6 n lo.9 j u 7 m g t 5 b 2.if you need to multiply 400, 2, and 1 ½, what would you type on the numeric keypad? 400*2*1.5 400/2*1.5 400/2/1.5 400*2*1½ 3.select all examples of proper keyboarding technique. rest your fingers gently on the home row or home keys. slouch in your chair. rest your palms on the keyboard. relax your fingers. keep your hands lower than your elbows.

Which finger presses the h key on the keyboard? index finger on the left hand pinky finger on the right hand index finger on the right hand thumb on the left hand

Write a program that prints the day number of the year, given the date in the form month-day-year. for example, if the input is 1-1-2006, the day number is 1; if the input is 12-25-2006, the day number is 359. the program should check for a leap year. a year is a leap year if it is divisible by 4, but not divisible by 100. for example, 1992 and 2008 are divisible by 4, but not by 100. a year that is divisible by 100 is a leap year if it is also divisible by 400. for example, 1600 and 2000 are divisible by 400. however, 1800 is not a leap year because 1800 is not divisible by 400.