The Josephus problem is the following game: N people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After M passes, the person holding the hot potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. Thus, if M = 0 and N = 5, players are eliminated in order , and player 5 wins. If M = 1 and N = 5, the order of elimination is 2, 4, 1, 5.Write a program to solve the Josephus problem for general values of M and N. Try to make your program as efficient as possible. Make sure you dispose of cells.

Some of your friends have gotten into the burgeoning field of time-series data mining, in which one looks for patterns in sequences of events that occur over time. purchases at stock exchanges"what's being bought" are one source of data with a natural ordering in time. given a long sequence s of such events, your friends want an efficient way to detect certain "patterns" in them"for example, they may want to know if the four events buy yahoo, buy ebay, buy yahoo, buy oracle occur in this sequence s, in order but not necessarily consecutively. they begin with a collection of possible events (e.g., the possible transactions) and a sequence s of n of these events. a given event may occur multiple times in s (e.g., yahoo stock may be bought many times in a single sequence s). we will say that a sequence s is a subsequence of s if there is a way to delete certain of the events from s so that the remaining events, in order, are equal to the sequence s . so, for example, the sequence of four events above is a subsequence of the sequence buy amazon, buy yahoo, buy ebay, buy yahoo, buy yahoo, buy oracle their goal is to be able to dream up short sequences and quickly detect whether they are subsequences of s. so this is the problem they pose to you: give an algorithm that takes two sequences of events"s of length m and s of length n, each possibly containing an event more than once"and decides in time o(m + n) whether s is a subsequence of s.

4.11 painting a wall (1) prompt the user to input integers for a wall's height and width. calculate and output the wall's area (integer). note that in this case there is a new line after each prompt. (submit for 1 point). enter wall height (feet): 11 enter wall width (feet): 15 wall area: 165 square feet (2) extend to also calculate and output the amount of paint in gallons needed to paint the wall (floating point). assume a gallon of paint covers 350 square feet. store this value in a variable. output the amount of paint needed using the %f conversion specifier. (submit for 2 points, so 3 points total). enter wall height (feet): 11 enter wall width (feet): 15 wall area: 165 square feet paint needed: 0.471429 gallons (3) extend to also calculate and output the number of 1 gallon cans needed to paint the wall. hint: use a math function to round up to the nearest gallon. (submit for 2 points, so 5 points total). enter wall height (feet): 11 enter wall width (feet): 15 wall area: 165 square feet paint needed: 0.471429 gallons

Which spereadsheet type will determine how well a bussiness has done over the past year