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.

Python write an expression that executes the loop body as long as the user enters a non-negative number. note: if the submitted code has an infinite loop, the system will stop running the code after a few seconds and report "program end never reached." the system doesn't print the test case that caused the reported message. sample outputs with inputs: 9 5 2 -1

People with high self-esteem: accept their strengths and weaknesses. believe that failed experiences are failures of their whole self. feel good about who they are only when they reach total success. need positive external experiences to counteract negative feelings that constantly plague them.

Write a program that inserts the digits of an integer into an array in originalorderfollowed by reverse order. first, promptthe user to enter a positive integer(> 0). determine the number of digits of the integer. create a dynamically allocated integer arrayof a size twice the number of digits. now insert the digits in original order which will occupy half of the array. then, insert the digits in reverse order. finally, output thedigits in thearray. use at least two functions to organize your program.