The following program example can be used to sum the array values of size N elements in parallel on a system containing N computing cores (there is a separate processor for each array element): for j = 1 to log_2(N) {
for k = 1 to N {
if ((k + 1) % pow(2,j) == 0) {
values[k] += values[k - pow(2,(j-1))]
}
}
}
This has the effect of summing the elements in the array as a series of partial sums After the code has executed, the sum of all elements in the array is stored in the last array location. Are there any race conditions in the above code example? If so, identify where they occur and illustrate with an example. If not, demonstrate why this algorithm is free from race conditions.

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.