Write a Monte Carlo code for a system of \(N\) hard spheres of diameter \(D\) on a one-dimensional ring of length \(L\) with periodic boundary conditions. Calculate the pair correlation function and compare it to equations (13.1.6) and (13.1.7). The pressure of the system is given by \(P / n k T=1+n D g\left(D^{+}\right)\); see equation (10.7.12). Compare your pressure to the one obtained for the exact configurational partition function \(Z_{N}=L(L-N D)^{N-1} / N\) !; see equation (13.1.2).