A error occurs when the program's grammar and punctuation is correct, but something happens to halt the program before it is finished. 1. Runtime
2. Syntax
3. Logical

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 even~s--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

Alook-up table used to convert pixel values to output values on a monitor. essentially, all pixels with a value of 190 or above are shown as white (i. e. 255), and all values with a value of 63 or less are shown as black (i. e. 0). in between the pixels are scaled so that a pixel with a value p is converted to a pixel of value 2/127 −+3969). if a pixel has a value of 170 originally, what value will be used to display the pixel on the monitor? if a value of 110 is used to display the pixel on the monitor, what was the original value of the pixel?

Least square fit to polynomial write a function leastsquarefit3pol that solves a linear system of equations to find a least squares fit of a third order polynomial to an experimental data set given as two row arrays. the function leastsquarefit3pol must explicitly solve a set of linear equations and cannot use polyfit. there should be no restriction on the size of the problem that can be solved.