Assume that there exist m locations numbered 1 to m while you travel downstream. at any location i you can rent a boat to be returned at any of the downstream locations j > i. you are given a cost array cost(i, j) which provides the cost of these rentals for all 1≤i j). for example, the cost array with m= 4 might be the following: to jcost(i, j) 1 2 3 4 1 0 2 3 7from i 2 - 0 2 4 3 - - 0 2 4 - - - 0you need to find a dynamic programming algorithm that computes the cheapest sequence of rentals taking you from location 1 all the way down to location m.

Write a program that displays the following menu: geometry calculator 1. calculate the area of a circle 2. calculate the area of a rectangle 3. calculate the area of a triangle 4. quit enter your choice (1-4): if the user enters 1, the program should ask for the radius of the circle and then display its area. use the following formula: area = ď€(the square of r) use 3.14159 for ď€ and the radius of the circle for r. if the user enters 2, the program should ask for the length and width of the rectangle and then display the rectangle’s area. use the following formula: area = length * width if the user enters 3, the program should ask for the length of the triangle’s base and its height, and then display its area. use the following formula: area = base * height * .5 if the user enters 4, the program should end. input validation: display an error message if the user enters a number outside the range of 1 through 4 when selecting an item from the menu. do not accept negative values for the circle’s radius, the rectangle’s length or width, or the triangle’s base or height. note: if the user enters an improper menu choice (1-4), the program prints "the valid choices are 1 through 4. run the program again and select one of those." if the user enters a negative radius, the program prints "the radius can not be less than zero." if the user enters a negative value for height or base, the program prints "only enter positive values for base and height."