Write a method called isConsecutive that accepts a PriorityQueue of integers as a parameter and returns true if the queue contains a sequence of consecutive integers starting from the front of the queue. Consecutive integers are integers that come one after the other, as in 5, 6, 7, 8, 9, etc., so if the queue stores [7, 8, 9, 10, 11], your method should return true. (Also return true if passed an empty queue.) If your method modifies the state of the queue during its computation, it should restore the queue before it returns. You may use one stack or queue as auxiliary storage.

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.

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The average cost of one year at a private college in 2012-2013 is $43,289. the average grant aid received by a student at a private college in 2012-2013 is $15,680.   what is the average student contribution for one year at a private college in 2012-2013?