You have a set of k small balls of three colors: black, white, and red arranged randomly in a row as illustrated in the figure below: [Note: the number of balls may not be equal, where, there is at least one ball of each color]. In This game it is requested to get all the black balls to the left-hand end, all the red balls to the right-hand at the end, with keeping all while balls in the middle. The only moves you are allowed to make are those that interchange the positions (swap) of two neighboring balls. ... The question is : 1) Design an algorithm for solving this puzzle. 2) What is the name of the algorithm you used to do the sorting balls ?
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- You have a fence post located at the point (x,y) where a goat is tethered by a rope. You also have a house, which is a rectangle with diagonally opposite corners at the points bottom-left: (x1,y1) and top-right: (x2,y2). You want to pick a length of rope that guarantees the goat cannot reach the house. Determine the minimum distance from the fence post to the house, so that you can make sure to use a shorter rope. Recall that the distance formula is: sqrt( (x2−x1)^2+(y2−y1)^2 ) The input consists of a single line containing six space-separated integer values: x, y, x1, y1, x2, and y2. You are guaranteed that x1<x2 and y1<y2, and that (x,y) is strictly outside the axis-aligned rectangle with corners at (x1,y1) and (x2,y2). Return the minimum distance from the goat’s post to the house as a floating-point value from main(). Learning Objectives Be able to create a program with a lesser template. Be able to calculate the min/max of integers. Be able to write a mathematical…The Penny Pitch game is popular in amusement parks. Pennies are tossed onto aboard that has certain areas marked with different prizes. For example: The prizes available on this board are puzzle, game, ball, poster, and doll. At the end ofthe game, if all of the squares that say BALL are covered by a penny, the player gets theball. This is also true for the other prizes. The board is made up of 25 squares (5 x 5).Each prize appears on three randomly chosen squares so that 15 squares contain prizes.Create a penny_pitch application that displays a Penny Pitch board (use [ and ] toindicate squares) with prizes randomly placed and then simulates ten pennies being randomly pitched onto the board. After the pennies have been pitched, the applicationshould display a message indicating which prizes have been won, it any.The number of permutations of a set of n items taken r at a time is given by the followingformulan!/r!(n−r)!: where n! is the factorial of n, r! is the factorial of r, and (n-r)! is thefactorial of the result of n-r. The factorial of a number n can be solved using the followingformula: n!=e−nnn√ 2πn.If there are 18 people in your class and you want to divide the class into programming teams of 3members, you can compute the number of different teams that can be arranged using this formula(n!/r!(n−r)!).Write a C++ program that determines the number of potential team arrangements. You will needto use the double type for this computation. Use the Lab Template you set-up last week, properformatting, and appropriate comments in your code. The output must be labeled clearly andformatted neatly.
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