Loop invariants Consider the following code, assuming that i, x, y, and n are integers, with n > 0. • State a non-trivial loop invariant for variable . • Prove the loop invariant. Be sure that the proof includes the final conditions after the loop has ended. • Note: a correct proof of an incorrect invariant will still receive partial credit. • Give the final value of a in terms of n. Hint: is the pattern close to (e.g. off by one) from some other pattern you might recognize? Hint: you might need to include a condition for y somewhere within your proof.
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- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. coordinating, we can observe the number of times some white string meets some dark string. We process the number of sets of distinctively shaded strings that cross rather than the number of convergence focuses, so one convergence point might be counted on numerous occasions if various sets of strings meet at a similar point. In case c is a legitimate shading, let f(c) mean the base number of such convergences out of all conceivable matchings. circle above is portrayed by the shading bwbbbwww. In the wake of coordinating with the spools as displayed, there is one convergence between contrastingly shaded strings. It tends to be demonstrated that it is the base conceivable, so f(bwbbbwww)=1. You are given a string s addressing an incomplete shading, with dark, white, and uncolored spools. A shading c is called s-reachable if you can accomplish it by allocating tones to the uncolored…Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. anglers have recently gotten back from a fishing excursion. The I-th angler has gotten a fish of weight man-made intelligence. Anglers will flaunt the fish they got to one another. To do as such, they initially pick a request where they show their fish (every angler shows his fish precisely once, in this way, officially, the request for showing fish is a stage of integers from 1 to n). Then, at that point, they show the fish they discovered by the picked request. At the point when an angler shows his fish, he may either become glad, become dismal, or stay content. Assume an angler shows a fish of weight x, and the most extreme load of a formerly shown fish is y (y=0 if that angler is quick to show his fish). Then, at that point: in the event that x≥2y, the angler becomes cheerful; in the event that 2x≤y, the angler becomes miserable; in the event that none of these two…Quadratic Root Solver For a general quadratic equation y = ax? + bx + c, the roots can be classified into three categories depending upon the value of the discriminant which is given by b2 - 4ac First, if the discriminant is equal to 0, there is only one real root. Then, if the discriminant is a positive value, there are two roots which are real and unequal. The roots can be computed as follows: -b+ Vb? – 4ac 2a Further, if the discriminant is a negative value, then there are two imaginary roots. In this case, the roots are given by b ь? - 4ас 2a 2a Programming tasks: A text file, coeff.txt has the following information: coeff.txt 3 4 4 4 1 4 Each line represents the values of a, b and c, for a quadratic equation. Write a program that read these coefficient values, calculate the roots of each quadratic equation, and display the results. Your program should perform the following tasks: • Check if the file is successfully opened before reading • Use loop to read the file from main…
- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Sasha likes exploring diverse mathematical articles, for instance, wizardry squares. However, Sasha comprehends that enchanted squares have as of now been examined by many individuals, so he sees no feeling of concentrating on them further. All things considered, he designed his own kind of square — a superb square. A square of size n×n is called prime if the accompanying three conditions are held all the while: all numbers on the square are non-negative integers not surpassing 105; there are no indivisible numbers in the square; amounts of integers in each line and every segment are indivisible numbers. Sasha has an integer n. He requests you to view as any great square from size n×n. Sasha is certain beyond a shadow of a doubt such squares exist, so help him! Input The principal line contains a solitary integer t (1≤t≤10) — the number of experiments. Every one…Python answer only. Correct answer will upvoted else downvoted. It is the ideal opportunity for your very first race in the game against Ronnie. To make the race intriguing, you have wagered a dollars and Ronnie has wagered b dollars. Yet, the fans appear to be frustrated. The fervor of the fans is given by gcd(a,b), where gcd(x,y) means the best normal divisor (GCD) of integers x and y. To make the race seriously invigorating, you can perform two kinds of activities: Increment both an and b by 1. Diminishing both an and b by 1. This activity must be performed if both an and b are more noteworthy than 0. In one action, you can play out any of these activities. You can perform self-assertive (potentially zero) number of moves. Decide the greatest energy the fans can get and the base number of moves needed to accomplish it. Note that gcd(x,0)=x for any x≥0. Input The principal line of input contains a solitary integer t (1≤t≤5⋅103) — the number of experiments.…True or False 1. Matrices are often represented by single small letters a, b, c... etc.2. Two m x n matrices A and B are equal if aij=bij for each i & j. (i.e., the two matrices havesame size, and all the corresponding elements are equal).3. Matrices A & B are said to be conformable in the order AB if, and only if, the number ofrows in A is equal to the number of columns in B.4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2columns. The product size of AB is a 4 x 2 matrix.5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in arow/column by a non-zero constant and adding the result to the corresponding entries inanother row/column. Then, det(B) = det(A).
- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Today the kindergarten has another gathering of n kids who should be situated during supper. The seats at the table are numbered from 1 to 4n. Two children can't sit on a similar seat. It is realized that two children who sit on seats with numbers an and b (a≠b) will enjoy if: gcd(a,b)=1 or, a partitions b or b separates a. gcd(a,b) — the greatest number x with the end goal that an is distinct by x and b is detachable by x. For instance, if n=3 and the children sit on seats with numbers 2, 3, 4, then, at that point, they will enjoy since 4 is isolated by 2 and gcd(2,3)=1. On the off chance that children sit on seats with numbers 4, 6, 10, they won't enjoy. The educator truly doesn't need the wreck at the table, so she needs to situate the children so there are no 2 of the child that can enjoy. All the more officially, she needs no pair of seats an and b that the children…Count divisibles in range def count_divisibles_in_range(start, end, n): Let us take a breather by tackling a problem simple enough that its solution needs only a couple of conditional statements and some arithmetic, but not even one loop or anything even more fancy. The difficulty is coming up with the conditions that cover all possible cases of this problem exactly right, including all of the potentially tricksy edge and corner cases, without being off-by-one. Given three integers start, end and n so that start <= end, count how many integers between start and end, inclusive, are divisible by n. Sure, you could solve this problem with the list comprehension one-linerreturn len([x for x in range(start, end+1) if x % n == 0]) but of course the automated tester is designed so that anybody trying to solve this problem in such a blunt fashion will only find themselves running out of both time and space! Your code should have no loops at all, but use only integer arithmetic and…Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Two cells are adjoining in the event that they share a side. Thusly, every cell (x, y) has precisely three neighbors: (x+1, y) (x−1, y) (x+1, y−1) in case x is even and (x−1, y+1) in any case. At first a few cells are contaminated, all the others are sound. The course of recuperation starts. Each second, for precisely one cell (despite the fact that there may be different cells that could change its state) one of the accompanying occurs: A sound cell with something like 2 contaminated neighbors likewise becomes tainted. A contaminated cell with something like 2 solid neighbors likewise becomes sound. In the event that no such cell exists, the course of recuperation stops. Patient is considered recuperated if the course of recuperation has halted and every one of the cells are solid. We're keen on a most dire outcome imaginable: is it conceivable that the patient…
- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. The new scholarly year has begun, and Berland's college has n first-year understudies. They are separated into k scholarly gatherings, in any case, a portion of the gatherings may be vacant. Among the understudies, there are m sets of associates, and every colleague pair may be both in a typical gathering or be in two unique gatherings. Alice is the custodian of the primary years, she needs to have an engaging game to make everybody know one another. To do that, she will choose two unique scholastic gatherings and afterward partition the understudies of those gatherings into two groups. The game requires that there are no colleague sets inside every one of the groups. Alice thinks about the number of sets of gatherings she can choose, with the end goal that it'll be feasible to play a game after that. All understudies of the two chose bunches should participate in the game.…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…Nuts and bolts You are given a collection of n bolts of different widths and n corresponding nuts. You are allowed to try a nut and bolt together, from which you can determine whether the nut is larger than the bolt, smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to its nut. Design an algorithm for this problem with average-case efficiency in (n log n).