recursion programming projects design and implement program to solve the -queens problem your program should prompt the user for the size of the boardsearch for solutionand print the resulting board if solution was found instead of finding single solution to the -queens problemwe can compute the total number of solutions for given value of modify the solvenqueens(function from listing to count the number of solutions for given value of instead of simply determining if solution exists test your program on the following values of (the number of solutions for the given board size is indicated in parentheses( ( ( ( ( ( ( ( ( ( ( ( implement new version of the maze solving program from to use recursion instead of software stack design and implement program to play tic-tac-toe against the computer using recursive function to build game tree for deciding the computer' next move the knight' tour problem is another chessboard puzzle in which the objective is to find sequence of moves by the knight in which it visits every square on the board exactly once the legal moves of knight are shown in the diagram to the right design and implement program that uses recursive backtrack ing algorithm to solve the knight' tour your program should extract from the user starting position for the knight and produce list of moves that solves the knight' tour the knapsack problem is classic problem in computer science you are given knapsack and collection of items of different weights and your job is to try to fit some combination of the items into the knapsack to obtain target weight all of the items do not have to fit in the knapsackbut the total weight cannot exceed the target weight for examplesuppose we want to fill the knapsack to maximum weight of pounds from collection of seven items where the weights of the seven items are and for small number of itemsit' rather easy to solve this problem one such solutionfor examplewould be to include the items that have weights and but what if we had several thousand items of varying weights and need to fit them within large knapsackdesign and implement recursive algorithm for solving this problem