Is it possible to place eight Queens on a chessboard, so that none of the Queens occupy the same row, column, or diagonal? Depth-First & Breadth-First Search Take a number whose square root is to be calculated, any positive number. Take a guess at the numbers square root. Calculate the square root by improving on the current guess as indicated:Next guess = (number/ current guess + current guess)/ 2 Repeat this process until the difference between the next guess and the current is within the accepted level of accuracy. The better your guess, the fewer the number of iterations needed to get the square root. A good first guess is typically half the number whose square root is to be calculated. The process is ten repeated until the desired accuracy is achieved.Newton-Raphson MethodDetermine a root of the equation f(x) = x^3-x^2-9x+9 = 0 using the Newton-Raphson method if the initial guess is x1 = 1.5.Gauss-Siedel Method Solve the following set of linear simultaneous equations using the Gauss-Seidel method:10x1 + 2x2 + 3x3 = 11 X1 + 5x2 + 2x3 = 20 3x1 + 2x2 + 6x3 = -12 Theoretical SolutionsEight-Queens Puzzle1.Pick a position for the Queen2.If legal, go to next row.3.If illegal, pick the next position.4.If no legal position is found, back up to one row.If legal positions are found for all eight rows, the problem is solved.Binary SearchSearch the current node value to see if it equals the search value.If the search value is smaller than the current value, make the current node the left child node.Make the current node the right child node.Depth-First & Breadth-First SearchDepth-First Search: Searches as far down the left side of the binary tree.When it encounters, NULL, the search switches to the bottom-most right child and resumes.Breadth-First Search: Remove a node from the queue. This becomes the current node.Place all child nodes of the current node onto the queue.Newtons MethodGet a positive number whose square root is to be calcu...
