Given a box of ethernet cables with dimensions rows x columns, choose a xa groups for all a such that 1 < a < min(rows, columns). Determine the number of ways the box of cables can be divided. Example rows = 5 columns = 3 There are 3*5 = 15 ways to choose a 1 x 1 area of cables. There are 2 * 4 = 8 ways to choose a 2 x 2 area of cables. There are 1 *3 = 3 ways to choose a 3 x 3 area of cables. In total, there are 15 +8 +3=26 ways the box can be divided. Function Description Complete the function numberOfWays in the editor below. numberOfWays has the following parameter(s): int queries[n][2]: a 2D array of integers, each represents box dimensions (rows x columns) for a query Returns: int[n] = array of long integers where element / denotes the result of the test queries[i] Constraints • 1 ≤ number of test cases < 2500 • 1 rows, columns ≤ 2500
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- Java codeA salesman would like to visit a set of n cities. The cities are connected pairwise by a direct trains. The cost of a train ticket varies depending on the cities it connects. This salesman would like to fly into one city, then use trains to visit each city exactly one, and then fly out of the last city on his trip. The cost of his trip is the total cost of all the train tickets (the plane tickets are not included). The salesman may chose any city to fly into and any city to fly out of. Let the problem of determining if there is a trip that costs at most k dollars be called T rainSalesman. Show that this problem is NP-complete.A town wishes to build a trail between city A, city B, city C, city D, and city E. The distances, in miles, between any two of the destinations are given in the table. Use the table to answer parts (a) and (b) below. A B C D E A * 154 134 216 129 B 154 * 195 51 243 C 134 195 * 225 220 D 216 51 225 * 308 E 129 243 220 308 * a) Use Kruskal's algorithm to determine the minimum-cost spanning tree that would link each location to create the least expensive trail. Choose the correct graph below. A. ABCD154216225E129 B. ABCD15419551E129 C. ABCD15413451E129 D. ABCD154134216E129 b) If the cost of building such a trail is $3700 per mile, what is the cost of building the trail determined in part (a)? The cost is:
- Wireless sensor networks (WSNs) refer to a domain of communication networks. In a WSN, small devices called sensor nodes are used for data transfer among each other and a base station. One limitation of a sensor node is that it has a very limited processing capability and very small memory. Consider a scenario in which you have an algorithm that can be subdivided into smaller problems. If you have to run these sub-problems in different sensor nodes, would you prefer to use divide & conquer approach or dynamic programming approach? Write briefly and precisely.Consider a billboard that consists of n vertical panels of width 1 and varying integer heights, hanged down and held by a horizontal roller from the top. The panel i has a height h For the objective of placing two banners, it is allowed to move each panel up by any integer length using the roller. Once the necessary moves are completed, you may place two banners completely inside of the panels. Based on the above description, what is the maximum total area that you can provide for the two posters? Output Print a single integer- the maximum total area the two posters can cover together. Example 1: 6 Input: Output: 18 Input The first line of input contains one integer n (1There are a set of courses, each of them requiring a set of disjoint time intervals. For example, a course could require the time from 9am to 11am and 2pm to 3pm and 4pm to 5pm. You want to know, given a number K, if it’s possible to take at least K courses. You can only take one course at any single point in time (i.e. any two courses you choose can’t overlap). Show that the problem is NP-complete, which means that choosing courses is indeed a difficult thing in our life. Use a reduction from the Independent set problem.If A={8,12,16,20} and B={12,16,20,24,28}, what is the value of P (A and B)?With T=4, n=12 and A=(3,5,8,8,9,16,29,41,50,63,64,67). Draw the corresponding walkthrough as shown in P.146.You are given a grid having N rows and M columns. A grid square can either be blocked or empty. Blocked squares are represented by a '#' and empty squares are represented by '.'. Find the number of ways to tile the grid using L shaped bricks. A L brick has one side of length three units while other of length 2 units. All empty squares in the grid should be covered by exactly one of the L shaped tiles, and blocked squares should not be covered by any tile. The bricks can be used in any orientation (they can be rotated or flipped). Input Format The first line contains the number of test cases T. T test cases follow. Each test case contains N and M on the first line, followed by N lines describing each row of the grid. Constraints 1 <= T <= 501 <= N <= 201 <= M <= 8Each grid square will be either '.' or '#'. Output Format Output the number of ways to tile the grid. Output each answer modulo 1000000007. Sample Input 3 2 4 .... .... 3 3 ...…TM M = (Q, E, I, 6, 90, 9a, qr), where Q = {90, 91, 92, 9a, 9r}, Σ = {0, 1}, r = {0, 1, L}, and 8 is: 8(qo, U) = (qr, U, R) 8(90, 0) = 8(go, 1) (91, 0, R) (qo, 1, R) = 8(g1, L) = (ga, U, R) 8(91,0) = (91, 0, R) 8(91, 1) = (92, 1, R) = (92, U, R) 8(92, U) 8(92, 0) = (90, 0, R) 8(92, 1) = (92, 1, R) i. Prove that M is NOT a decider. ii. Mathematically describe the language A that M recognises. Prove that A ≤ L(M). iii. Prove A = L(M). iv. Is A Turing-decidable? [Give clear reasons for your answer. No need for a formal proof.]Consider a billboard that consists of n vertical panels of width 1 and varying integer heights, hanged down and held by a horizontal roller from the top. The panel i has a height hi. hi For the objective of placing two banners, it is allowed to move each panel up by any integer length using the roller. Once the necessary moves are completed, you may place two banners completely inside of the panels. Based on the above description, what is the maximum total area that you can provide for the two posters? Input The first line of input contains one integer n (1a. Build an adjacency matrix ? for this map. b. How many paths of length 2 from V5 to V1 exist? c. How many paths of length 3 from V5 to V1 exist?SEE MORE QUESTIONSRecommended textbooks for youC++ Programming: From Problem Analysis to Program…Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage LearningC++ Programming: From Problem Analysis to Program…Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage Learning