Each of n keys in an array may have one of the values red, white, or blue. Give an efficient algorithm for rearranging the keys so that all the reds come before all the whites, and all the whites come before all the blues. (It may happen that there are no keys of one or two of the colors.) The only operations that are permitted on the keys are examination of a key to find out what color it is, and an exchange of two keys (specified by their indices). How many key examinations and exchanges does your algorithm perform in the worst case

In a heat transfer course, we can derive the equation for the temperature distribution in a flat rectangular plate. in this example, we will look at a plate at steadystate with three sides being held at t1, and one side held at t2. the temperature for any location on the plate, t(x, y), can be calculated by where create a function (prob3_5) that will take inputs of vectors x and y in feet, scalar n, scalars l and w in feet and scalars t1 and t2 in degrees fahrenheit. it will output a matrix t which is the temperature of each x and y locations. t will have the number of columns equal to the number of elements in x and rows equal to the number of elements in y. though this can be done without loops (perhaps more efficiently), your program must use a nested loop.