There are n ≥ 2 married couples who need to cross a river. They have a boat that can hold no more than two people at a time. To complicate matters, all the husbands are jealous and will not agree on any crossing procedure that would put a wife on the same bank of the river with another woman's husband without the wife's husband being there too, even if there are other people on the same bank. Can they cross the river under such constraints? Solve the problem for n = 2.
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- Four individuals wish to traverse an unstable bridge; they all start on the same side. You have 17 minutes to get everyone to the opposite side. Night has fallen, and they have only one torch. Two individuals may cross the bridge at once at most. Any crossing party, whether one or two individuals, must carry a torch. The torch must be carried back and forth; it cannot, for instance, be hurled. Person 1 crosses the bridge in one minute, person 2 in two minutes, person 3 in five minutes, and person 4 in ten minutes. A dyad must trek together at the slower individual's cadence. Create the algorithm specification that solves the problem.A ancient magnate is failing. His want is to have solely ONE of his descendant’s receive ALL of his treasure, however which one? He has N quantity of decendants. He works out a answer to locate the one fortunate baby who inherits his wealth. He will get N tokens, label every token with an integer fee and assign every token to a descendant. Each token receives a cost solely once. He locations all the tokens in a circle round him, numbered 1 to N, and begins removing one in K till there is solely one left... Write a software that takes two integer values N and K and prints the token wide variety of the fortunate decendant. Input Format The first line of the entry includes the two integers N and K. Constraints . zeroThe Harvard robotics club has organized a Robothon. n robots are placed alongthe edge of a circular area at the middle of the OAT(open air theatre). Each robot will move along arbitrary tracksinside the circle while leaving behind a heat signature along its trail. However, they have beenprogrammed not to cross their own trail or the trail of another robot, neither will they ever moveout of the circle. In case a pair of robots i and j meet at any point, they are removed from the sceneand the club will pay a reward sum of M[i, j] to the owners of these robots. Note that some robotscan keep moving infinitely without ever meeting another one. Given the reward matrix M whereM[i, j] = M[j, i], design a polynomial time algorithm that determines the maximum money theclub might potentially end up spending. For this particular problem, give a very brief justificationof the recurrence. Give pseudo-code for a dynamic program which solves the recurrence efficiently Youdo not need to prove…
- In a prison, there is a door b/w any pair of adjacent cells and one exit guarded by a guard G. One prisoner is a maniac M which kills anybody he can see when he enters a cell. If M returns to the cell with his victim, then he loses consciousness and stops. In the evening all inmates and the guard went to sleep in their cells. In the morning, maniac M is gone and all other prisoners with the guard were found dead in their cells. Show the route of the maniac.Three prisoners have been sentenced to long terms in prison, but due to over crowed conditions, one prisoner must be released. The warden devises a scheme to determine which prisoner is to be released. He tells the prisoners that he will blindfold them and then paint a red dot or blue dot on each forehead. After he paints the dots, he will remove the blindfolds, and a prisoner should raise his hand if he sees at least one red dot on the other two prisoners. The first prisoner to identify the color of the dot on his own forehead will be release. Of course, the prisoners agree to this. (What do they have to lose?) The warden blindfolds the prisoners, as promised, and then paints a red dot on the foreheads of all three prisoners. He removes the blindfolds and, since each prisoner sees a red dot (in fact two red dots), each prisoner raises his hand. Some time passes when one of the prisoners exclaims, "I know what color my dot is! It's red!" This prisoner is then released. Your problem…On a chess board of r rows and c columns there is a lone white rook surrounded by a group of opponent's black knights. Each knight attacks 8 squares as in a typical chess game, which are shown in the figure - the knight on the red square attacks the 8 squares with a red dot. The rook can move horizontally and vertically by any number of squares. The rook can safely pass through an empty square that is attacked by a knight, but it must move to a square that is not attacked by any knight. The rook cannot jump over a knight while moving. If the rook moves to a square that contains a knight, it may capture it and remove it from the board. The black knights. never move. Can the rook eventually safely move to the designated target square? The figure illustrates how the white rook can move to the blue target square at the top-right corner in the first sample case. The rook captures one black knight at the bottom-right of the board on its way. Rok nd kight lcoes by Chunen Input The first line…
- This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".an Office consisting of m cabins enumerated from 1 to m. Each cabin is 1 meter long. Sadly, some cabins are broken and need to be repaired.You have an infinitely long repair tape. You want to cut some pieces from the tape and use them to cover all of the broken cabins. To be precise, a piece of tape of integer length t placed at some positions will cover segments 5,5+1-sit-1.You are allowed to cover non-broken cabins, it is also possible that some pieces of tape will overlap.Time is money, so you want to cut at most k continuouspieces of tape to cover all the broken cabins. What is theminimum total length of these pieces?Input FormatThe first line contains three integers n,m and k(1sns10°, namsloº, Isksn) - the number of broken cabins, the length of the stick and the maximum number of pieces you can useThe second line contains n integers bl,b2,bn (Isbism) - the positions of the broken cabins. These integers are given in increasing order, that is, blOutput Format:Print the minimum total…Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.
- 3. To defeat Electro, Spider-Man needs to connect all of the pylons (vertices) in the graph below, with the numbers representing the difficulty of making the connection. Use Kruskal's algorithm to determine a minimum cost spanning tree for the following graph. Briefly describe the algorithm and how it works, and include the total cost as part of your answer. 1 3 1 1 5 3 3 4. 4 2 2 4 3 4. The Green Goblin has set up a spooky (and deadly) scavenger hunt around New York City, starting and ending at LaGuardia airport. Gobby has taken Spider-Man's web shooters, so he is stuck using public transit, where the listed times below are the average number of minutes to travel between locations. In order to save Aunt May, Peter must find a circuit that will take 155 or fewer minutes. If he can find a path that takes 140 or fewer minutes, he can save Aunt May AND stop the Green Goblin (AND you hi 2.Correct answer will be upvoted else Multiple Downvoted. Computer science. Gildong has a square board comprising of n lines and n sections of square cells, each comprising of a solitary digit (from 0 to 9). The cell at the j-th section of the I-th line can be addressed as (i,j), and the length of the side of every cell is 1. Gildong prefers enormous things, so for every digit d, he needs to find a triangle with the end goal that: Every vertex of the triangle is in the focal point of a cell. The digit of each vertex of the triangle is d. Somewhere around one side of the triangle is corresponding to one of the sides of the board. You might expect that a side of length 0 is corresponding to the two sides of the board. The space of the triangle is boosted. Obviously, he can't simply be content with tracking down these triangles with no guarantees. Along these lines, for every digit d, he will change the digit of precisely one cell of the board to d, then, at that point, track…Correct answer will be upvoted else multiple downvoted. Computer science. Alice and Bob got n confections from their folks. Each candy weighs either 1 gram or 2 grams. Presently they need to split all confections between themselves reasonably so the all out weight of Alice's confections is equivalent to the all out weight of Bob's confections. Check in the event that they can do that. Note that confections are not permitted to be sliced down the middle. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Then, at that point, t experiments follow. The primary line of each experiment contains an integer n (1≤n≤100) — the number of confections that Alice and Bob got. The following line contains n integers a1,a2,… ,an — the loads of the confections. The heaviness of each candy is either 1 or 2. It is ensured that the amount of n over all experiments doesn't surpass 105. Output For each experiment, output on a different line:…