During Eid, it is a tradition for every father to give his children money to spend on entertainment. Chef has N coins; denote the value of the coin i by vi. Since today is Eid, Chef gives one coin to each of his two children. He wants the absolute value of the difference between the values of the coins given to the two children to be as small as possible to be as fair as possible. Help the chef by telling him the minimum possible difference between the values of the coins given to the two children. Of course, the chef cannot give the same coin to both children.
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- Tiling: The precondition to the problem is that you are given threeintegers n, i, j, where i and j are in the range 1 to 2n. You have a 2n by 2n squareboard of squares. You have a sufficient number of tiles each with the shape . Your goalis to place nonoverlapping tiles on the board to cover each of the 2n × 2n tiles except forthe single square at location i, j. Give a recursive algorithm for this problem in whichyou place one tile yourself and then have four friends help you. What is your base case?Q3: Interplanetary Spaceflight Milan Tusk is the richest person in the universe. After devoting decades of his life to further our space exploration technologies, he’s finally ready to retire. Being a space enthusiast, the first thing he wants to do is visit n planets p1, p2, …, pn, in this order. He’s currently on planet p0. Milan knows that the distance between planets pi and pi + 1 (for 0 ≤ i < n) is d[i]light years. His spaceship uses 1 tonne of fossil fuels per light year. He starts with a full tank and can fill up his tank at any of the n planets (but he must not run out in between two planets). There’s a huge cost to set up the spaceship for refuelling. Due to financial constraints (he’s not THAT rich), he can fill up his tank at most ktimes. In order to save money and make his spaceship lighter, Milan is looking for the smallest possible fuel tank that enables him to complete his space travel and reach planet pn. What is the smallest tank capacity that enables him to do so?…Little Frank loves mathematics. Every day, he solves some mathematical problems to improve his skill. A few days ago, he found a popular problem about turtles. The problem is as follows. Little Frank is given R rectangles, numbered 1 through R. The width and height of the i-th rectangle are Ni and M¡ unit respectively. There is a turtle located on the top-left corner of each rectangle. For each rectangle, count the number of ways the turtle can reach the bottom-right corner, if each turtle can only move right or down 1 unit at any time. The turtle is not allowed to move outside the rectangle, but, of course, the turtle can move on the boundary of the rectangle. In less than one second, this problem was solved for all rectangles. He felt that the problem was too easy. This morning, Little Frank wanted more challenges. Thus, for each rectangle į, he cut and removed a rectangle of A¡ x Bị unit from the top-right corner. See the following figure for detail. Bị Mi He could not solve this…
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