A group of n guests shows up to a house for a party, but some pairs of guests are enemies. There are two rooms in the house, and the host wants to distribute guests among the rooms, breaking up as many pairs of enemies as possible. The guests are all waiting outside the house and are impatient to get in, so the host needs to assign them to the two rooms quickly, even if this means that it's not the best possible solution.
(a)We constructed a greedy 1/2-approximation algorithm for this problem that runs in time O(V +E) prior. Now give a randomized algorithm that achieves (in expectation) the same approximation guarantee in time O(V ).
(b) Your solution in part (a) probably had to flip O(V ) random coins, but coins are expensive, use hashing to give an algorithm that only flips O(logV) random coins.

Explain briefly why you cannot expect to find a previous version of every file with which you work.

This program should be a short piece of code that prints all of the positive integers from 1 to 100 as described more fully below. the program may contain multiple methods, and if using an oo language, should be contained within a single class or object. the program should be designed so that it begins execution when invoked through whichever mechanism is most common for the implementation language. â–ş print out all positive integers from 1 to 100, inclusive and in order. â–ş print messages to standard output, matching the sample output below. â–ş in the output, state whether the each integer is 'odd' or 'even' in the output. â–ş if the number is divisible by three, instead of stating that the number is odd or even, state that the number is 'divisible by three'. â–ş if the number is divisible by both two and three, instead of saying that the number is odd, even or divisible by three; state that the number is 'divisible by two and three'. â–ş design the logic of the loop to be as efficient as possible, using the minimal number of operations to perform the required logic. sample output the number '1' is odd. the number '2' is even. the number '3' is divisible by three. the number '6' is divisible by two and three.

Match the following errors with their definitions. a. #name b. #value c. #ref d. 1. when a formula produces output that is too lengthy to fit in the spreadsheet cell 2. when you enter an invalid cell reference in a formula 3. when you type text in cells that accept numeric data 4. when you type in a cell reference that doesn’t exist