Given the following recursive binary search algorithm for finding an element in a sorted array of integers: int recursivebinarysearch(int[] array, int target, int left, int right){ if (left > right) return -1; int middle = (left + right) / 2; if (array[middle] == target) return middle; if (array[middle] > target) return recursivebinarysearch(array, target, left, middle - 1); return recursivebinarysearch(array, target, middle + 1, right); }assume n is the length of the array. find the initial condition and recurrence equation that expresses the execution time for the worst case of this algorithm and then solve that recurrence.

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.