Xiao Zhang is often distressed because there are too many things to arrange. Now he has n tasks at hand, and each task has a starting times, and an ending time e ₁. To complete a task, he must do it from the starting time to the ending time, and Xiao Zhang can only perform one task at the same time. Xiao Zhang wants to know how many tasks he can accomplish at most. Input The first line is an integer n (1sns300000), indicating the number of tasks Xiao Zhang has at hand. In the next n lines, each line contains two integers s₁, e. (1ss;
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- In order to beat AlphaZero, Grandmaster Hikaru is improving her chess calculation skills.Today, Hikaru took a big chessboard with N rows (numbered 1 through N) and N columns (numbered 1 through N). Let's denote the square in row r and column c of the chessboard by (r,c). Hikaru wants to place some rooks on the chessboard in such a way that the following conditions are satisfied:• Each square of the board contains at most one rook.• There are no four rooks forming a rectangle. Formally, there should not be any four valid integers r1, c1, r2, c2 (≠r2,c1≠c2) such that there are rooks on squares (r1,c1), (r1,c2 (r2,c1)and (r2,c2).• The number of rooks is at least 8N.Help Hikaru find a possible distribution of rooks. If there are multiple solutions, you may find any one. It is guaranteed that under the given constraints, a solution always exists.InputThe first line of the input contains a single integer T denoting the number of test cases. The first and only line of each test case contains…we consider a problem where we are given a set of coins andour task is to form a sum of money n using the coins. The values of the coins arecoins = {c1, c2,..., ck}, and each coin can be used as many times we want. Whatis the minimum number of coins needed?For example, if the coins are the euro coins (in cents){1,2,5,10,20,50,100,200}and n = 520, we need at least four coins. The optimal solution is to select coins200+200+100+20 whose sum is 520.program in python the following problem We ask that you assist the ITPC by indicating the maximum total number of letters that can be printed on a set of N shirts that are valid to be worn by both teams. For example, if “PÉREZ”, “GONZÁLEZ” and “LÓPEZ” play in the U-18 team, while “GARCIA”, “PERALTA” and “RODRÍGUEZ” play in the U-21 team, the best thing is that a jersey has the prefix "G" with 1 letter (for "GONZALEZ" and "GARCIA" to use), another has the prefix "PER" with 3 letters (for "PÉREZ" and "PERALTA" to use), and another has a 0-letter prefix (to be used by “LOPEZ” and “RODRIGUEZ”). Thus, the answer in this case is 1 + 3 + 0 = 4. Entry Each test case is described using three lines. The first line contains an integer N that indicates the number of players in each of the two teams (1≤N≤104). The second line contains the surnames of the N players of the U-18 team. The third line contains the surnames of the N players of the U21 team. Each last name is a non-empty string of at…
- I need help figuring out the following HW questionProblem1Given a value `value`, if we want to make change for `value` cents, and we have infinitesupply of each of coins = {S1, S2, .. , Sm} valued `coins`, how many ways can we make the change?The order of `coins` doesn't matter.For example, for `value` = 4 and `coins` = [1, 2, 3], there are four solutions:[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3].So output should be 4. For `value` = 10 and `coins` = [2, 5, 3, 6], there are five solutions: [2, 2, 2, 2, 2], [2, 2, 3, 3], [2, 2, 6], [2, 3, 5] and [5, 5].So the output should be 5. Time complexity: O(n * m) where n is the `value` and m is the number of `coins`Space complexity: O(n)""" def count(coins, value): """ Find number of combination of `coins` that adds upp to `value` Keyword arguments: coins -- int[] value -- int """ # initialize dp array and set base case as 1 dp_array = [1] + [0] * value.. (+.Let l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept. If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀). If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁). Instructions Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order: Input x₁ Input y₁ Input x₂
- Consider the functionf :: Int -> Intf n = if n==0then 0else 1 + (f(n-1))Use induction to show that the function f returns the value of n for all possible inputs n ≥0.Here are the steps:1. Verify that f 0 returns 0 to show the base case.2. Show that if f(n-1) returns n −1 then f n returns n.3. Since you have shown the base case and the induction step, you can confidentlystate that the function works for all possible nonnegative input values.Hint: To show that ”if f(n-1) returns n −1 then f n returns n” is valid you need toassume that f(n-1) returns n −1 and then argue that it must follow that f n returnsn. Use the definition of the function and just a little bit of algebra.Criteria for Success: You have clearly written down all three steps of the inductive proof. Your proof contains complete sentences which explain all the steps andthe algebra. I don’t want to see just a bunch of symbols on a page!Imagine you have a strip of highway connecting n towns in a line. Each town is being evaluated as a possible location for building a cellular phone tower. Each cell tower will provide coverage to the town it’s built in, but no other towns. However, due to the way that cell towers interfere with one another, it’s not possible to build cell phone towers in two adjacent towns.Describe an algorithm that, given the populations of each of the towns, reports the maximum number of people you can provide cell phone coverage to, subject to the restriction that no two adjacent towns can each have cell towers in them. Use dynamic programming to dramatically speed up your solution over a na ̈ıve recursive algorithm.a). The classical Tower of Hanoi (ToH) puzzle is well-known. It consists of three pegs and disks of sizes 1,2, . . . , n arranged on one of the pegs as a “tower”, in decreasing order of size, from bottom to top. The goal of the puzzle is to transfer all disks to another peg, placed in the same order. At each step, a single disk is moved from (the top of) one peg to (the top of) another, subject to the “divine” rule: to never have a larger disk above a smaller one. Write an algorithm ad draw the flow chart for moving all the disks from Peg A to Peg C. b). Write an algorithm and draw a flow chart for a software solution that can solve the equation below problem. Where ai = {a1,a2,a3,...an} marks
- Considering the function f(x) = x – cos(x), what is the value of x7 after performing fixed point iteration. Assume an initial guess of 1. Use the equation form that will seem fit according to the choices provided.Group of answer choices 0.72210 0.71537 0.76396 0.72236Correct answer will be upvoted else downvoted. Computer science. Polycarp recalled the 2020-th year, and he is content with the appearance of the new 2021-th year. To recall such a great second, Polycarp needs to address the number n as the amount of a specific number of 2020 and a specific number of 2021. For instance, if: n=4041, then, at that point, the number n can be addressed as the total 2020+2021; n=4042, then, at that point, the number n can be addressed as the total 2021+2021; n=8081, then, at that point, the number n can be addressed as the total 2020+2020+2020+2021; n=8079, then, at that point, the number n can't be addressed as the amount of the numbers 2020 and 2021. Assist Polycarp with seeing if the number n can be addressed as the amount of a specific number of numbers 2020 and a specific number of numbers 2021. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Then, at that point, t experiments follow.…Bruno gives his son P100 on one day, P50 on the second day, P25 on third day and so on. What will be total amount given by Ram to his son starting from the first day, if he lives forever?