C++:

Monte Carlo algorithms can be used to solve a wide range of problems by simulating a system using a type of random sampling. For example, we can use a Monte Carlo approach to estimate the value of pi (T). Consider the following quarter circle with radius r-1 inscribed within a square whose side is also 1 We know that the area of a circle is ur, so the area of the quarter circle aboveis a/4. Sincer-1, we have ac-/4. The side of the square is also 1, so the area of the square is as-12-1. The ratio of the area of the circle to the area of the square is R ada,-(/4) /-/4. If we can figure out a way to estimate the ratio R, we can find an estimate of Tt We can estimate by simulating throwing darts at the square above. We can do that by randomly generating two values, x and y, that are between 0 and 1. Then the point on the plane defined by the coordinates (xy) is the location of the dart on the unit square above. (Recall that you learned how to generate random values n a previous assignment) Let m = the number of darts thrown that land within the circle (represented by the green dots above) and n- the total number of darts thrown (represented by the sum of the green and red dots). Then the ratio of the area of the circle to the area of the square is R =