A set of coins makes change for n if the sum of the values of the coins is n. For example, if you have 1- cent, 2-cent and 4-cent coins, the following sets make change for 7: . 71-cent coins 5 1-cent, 1 2-cent coins. 31-cent, 2 2-cent coins 31-cent, 1 4-cent coins 11-cent, 3 2-cent coins 11-cent, 1 2-cent, 1 4-cent coins Thus, there are 6 ways to make change for 7. Write a function count_change that takes a positive integer n and a list of the coin denominations and returns the number of ways to make change for n using these coins (Hint: You will need to use tree recursion):
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- Computer Science You are playing the popular card game “Inscribings”. In this game, your opponent places n monster cards onto the board, the ith of which has hi health points. You in turn have m ≥ n hero cards in your hand, the jth of which deals dj damage per turn. To begin the game, you will choose n heroes from your hand and assign each of them to a different enemy monster. Each turn, your heroes will deal damage equal to their damage power to the opposing enemy. If at any point an opponent’s monster reaches 0 health or less, then it is destroyed. You are given a limited number of turns k to destroy all enemy monsters. Design an algorithm which runs in O(m + n log n) time and determines whether it is possible to assign your heroes in such a way as to destroy all enemy monsters in k turns or fewer. If it is possible, your algorithm must also return any such assignment. Need an algorithm which runs in Θ(m log m) time.Stone Pit is a game in historic roman time, that involves removing stones from tower of stones. The rules of this game are mentioned under: At first there are X group of stones, numbered 1 through X. Two warriors can play and they take alternate turns. If the bitwise XOR of all group equals 0 before a warrior's chance, then that warrior is declared winner. When warrior's turn comes, they must choose one of the remaining groups and remove it. Develop a C++ program to decide which warrior wins, given that both warriors are expert at this game. Sample Input: 4 4271 Sample Output: Second WarriorStone Pit is a game in historic roman time, that involves removing stones from tower of stones. The rules of this game are mentioned under: • At first there are X group of stones, numbered 1 through X. Two warriors can play and they take alternate turns. If the bitwise XOR of all group equals 0 before a warrior's chance, then that warrior is declared winner. When warrior's turn comes, they must choose one of the remaining groups and remove it. Develop a JAVA program to decide which warrior wins, given that both warriors are expert at this game. Sample Input: 1 3 561 Sample Output: First Warrior
- In an astronomy board game, N planets in an imaginary universe do not follow the normal law of gravitation. All the planets are positioned in a row. The planetary system can be in a stable state only if the sum of the mass of all planets at even positions is equal to the sum of the mass of planets at the odd positions. Initially, the system is not stable, but a player can destroy one planet to make it stable. Find the planet that should be destroyed to make the system stable. If no such planet exists, then return -1. If there are multiple such planets, then destroy the planet with the smallest index and return the index of the destroyed planet. Example Let N-5 and planets = [2,4,6,3,4]. Destroying the fourth planet of mass 3 will result in planets = [2,4,6,4], and here, the sum of odd positioned planets is (2+6)=8, and the sum of even positioned planets is (4+4)=8, and both are equal now. Hence, we destroy the fourth planet. 11 MNBASK19922 13 14 15 16 17 18 20 * The function is…In a card game, your opponent places n monster cards onto the board, the i th of which has hi health points. You in turn have m ≥ n hero cards in your hand, the j th of which deals dj damage per turn. To begin the game, you will choose n heroes from your hand and assign each of them to a different enemy monster. Each turn, your heroes will deal damage equal to their damage power to the opposing enemy. If at any point an opponent’s monster reaches 0 health or less, then it is destroyed. You are given a limited number of turns k to destroy all enemy monsters. Design an algorithm which runs in O(m + n log n) time and determines whether it is possible to assign your heroes in such a way as to destroy all enemy monsters in k turns or fewer First develop a Θ(m log m) time algorithm, then improve it to Θ(m + n log n) Do not write the code, give steps and methods. Explain the steps of algorithm, time complexity, and the logic behind these steps in plain English Input is the number of monsters…In a card game, your opponent places n monster cards onto the board, the i th of which has hi health points. You in turn have m ≥ n hero cards in your hand, the j th of which deals dj damage per turn. To begin the game, you will choose n heroes from your hand and assign each of them to a different enemy monster. Each turn, your heroes will deal damage equal to their damage power to the opposing enemy. If at any point an opponent’s monster reaches 0 health or less, then it is destroyed. You are given a limited number of turns k to destroy all enemy monsters. Design an algorithm which runs in O(m + n log n) time and determines whether it is possible to assign your heroes in such a way as to destroy all enemy monsters in k turns or fewer First develop a Θ(m log m) time algorithm, then improve it to Θ(m + n log n) Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English input is The number of monsters n, the health…
- Tennis is a racket sport that is played by two opposing players on S sets. Each set consists of at least Kgames. A set is won by a player if that player wins at least K games and at least 2 games more than theopponent. Once a set is won, the set is ended and the match continues to a new set (if any) where bothplayers start from 0 game won for that new set.For example, let K = 6, then a set can be ended with any of the following.• P1 (Player 1) wins 6 games while P2 (Player 2) wins 3 games → P1 wins the set.• P1 wins 7 games while P2 wins 9 games → P2 wins the set.On the other hand, a set cannot be ended with any of the following.• P1 wins 6 games while P2 wins 5 games → no player wins at least 2 games more than the opponent.• P1 wins 0 game while P2 wins 5 games → no player wins K = 6 games.• P1 wins 7 games while P2 wins 0 games → the set is already ended when P1 won the first 6 games.• P1 wins 8 games while P2 wins 5 games → the set must already be ended before it reaches this…3. Card Flipper: You walk into a room, and see a row of n cards. Each one has a number x; written on it, where i ranges from 1 to n. However, initially all the cards are face down. Your goal is to find a local minimum: that is, a card i whose number is less than or equal to those of its neighbors, xj-1 = X; <= Xj+1. The first and last cards can also be local minima, and they only have one neighbor to compare to. There can be many local minima, but you are only responsible for finding one of them. Obviously you can solve this problem by turning over all n cards, and scanning through them. However, show that you can find such a minimum by turning over only O(log n) cards.Bus timetables specify to the second the exact arrival and departure time of each bus on each stop. You need to pay for the full fare of every bus you ride and different bus lines charge different fees , but they are flat fees (independent of distance travelled on the line) A travel plan is a sequence of stop-time pairs where stop is a location of a bus stop and time is when we arrive at that stop. The plan is feasible if for any two consecutive pairs (a, t) and (b, t′) in the plan there exists a bus that departs after t and arrives at b at exactly t′. That is, a travel plan does not allow us to walk between stops. Assuming that no two buses arrive at the same time at the same stop, a feasible plan uniquely identifies the bus lines that we need to take to realize the plan. The cost of the plan is the sum of the fares we need to pay. Your task is to design an efficient algorithm that given a departure time t, an arrival time t′, an origin stop a and a destination stop b, finds the…
- IN JAVA Alice and Bob are playing a board game with a deck of nine cards. For each digit between 1 to 9, there is one card with that digit on it. Alice and Bob each draw two cards after shuffling the cards, and see the digits on their own cards without revealing the digits to each other. Then Alice gives her two cards to Bob. Bob sees the digits on Alice’s cards and lays all the four cards on the table in increasing order by the digits. Cards are laid facing down. Bob tells Alice the positions of her two cards. The goal of Alice is to guess the digits on Bob’s two cards. Can Alice uniquely determine these two digits and guess them correctly? Input The input has two integers p,q (1≤p<q≤9) on the first line, giving the digits on Alice’s cards. The next line has a string containing two ‘A’s and two ‘B’s, giving the positions of Alice’s and Bob’s cards on the table. It is guaranteed that Bob correctly sorts the cards and gives the correct positions of Alice’s cards. Output If Alice can…Let A = {a, b, c} and B = {u, v}. Write a. A × B b. B × AIn a candy store, there are N different types of candies available and the prices of all the N different types of candies are provided to you. You are now provided with an attractive offer. You can buy a single candy from the store and get at most K other candies ( all are different types ) for free. Now you have to answer two questions. Firstly, you have to find what is the minimum amount of money you have to spend to buy all the N different candies. Secondly, you have to find what is the maximum amount of money you have to spend to buy all the N different candies. In both the cases you must utilize the offer i.e. you buy one candy and get K other candies for free. Example 1: Input: N = 4 K = 2 %3D candies[] = {3 2 1 4} Output: 3 7