Write the iterative algorithm for reaching definition. Compute in and out for the following figure. dl:i-m-1 d2:j-n d3:a -ul BI d4:i-i+1 B2d5;j-j-1 d6: a - u2 B3 d7:i-u3 B4
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- Given the following function, what happens if a[] contains just one element that doesn't match val? int binarySearch(int a[], int first, int last, int val){ if (first > last) return -1; int middle = (first + last) / 2; if (a[middle] == val) return middle; if (a[middle] < val) return binarySearch(a, middle+1, last, val); else return binarySearch(a, first, middle-1, val);} Group of answer choices binarySearch never calls itself again and terminates (recursion never happens) binarySearch calls itself once then terminates (recursion happens once) binarySearch calls itself twice then terminates (recursion happens twice) binarySearch calls itself 3 times then terminates (recursion happens 3 times)Your task is to implement Depth-first search algorithm to solve the problem of placing 8 Queens on a chess board so none can “take” each other.• A code framework, supporting videos and html documentation of the provided code-base will be provided via Moodle in assignments section.• The implementation should accept one command-line argument at the time it is invoked for the starting position of the first queen.o It will be tested with a range of values for that input.o If the input is not an integer in the range of 0-7 it should report “Invalid Input” and exit. • You will be supplied with a partially completed file ‘main.c’ which contains the code need to read the command line and sets up the initial working candidate within the code framework.o Your task is to complete the code to implement depth-first search. o Your code must finish with a call to the function PrintFinalSolutionAndExit(); when a valid final solution stored in the variable “workingCandidate”. please solve full…Consider the following, E → E1#T{E.val := E,.val * T.val} E → T{E.val := T.val} T→ T 1 & F{T.val := T₁.val * F.val} T→ F{T.val := F.val} F→ num{F.val := num.Lexval} Draw an annotated parse tree for an expression: a # b & c# d & e.
- Write java program to Draw the binary search tree that results from adding the following integers (34 45 3 87 65 32 1 12 17). Assume our simple implementation with no balancing mechanism.Write a classifier algorithm for p(Y |X,α)Modify the producer-consumer implementation code bellow, so that it uses monitors to handle race conditions instead of semaphores or mutexes. Use the pthread library implementation #include <pthread.h> #include <semaphore.h> #include <stdio.h> #include <stdlib.h> #define BUFFER_SIZE 20 pthread_mutex_t mutex; int count = 0; int buffer[BUFFER_SIZE]; pthread_t tid; int producers = 0, consumers = 0; void insert(int item) { while (count == BUFFER_SIZE); if (count < BUFFER_SIZE) { buffer[producers] = item; producers++; producers=producers%BUFFER_SIZE; sleep(1); } return; } int remove_item() { int item; while (count == 0); if (count > 0) { item = buffer[consumers]; buffer[consumers] = buffer[consumers - 1]; consumers++; consumers=consumers%BUFFER_SIZE; sleep(1); } return item; } void * producer(void *param) { int item; while (1) { item = rand() % BUFFER_SIZE; while (count >= BUFFER_SIZE);…
- Show that the given argument is either valid or invalid using resolution. If Sally does her homework, people call Sally a wimp. However, nobody calls Sally a wimp. Therefore, Sally doesn’t do her homework.A grid needs a system for numbering the tiles in order to allow random-access lookup.For instance, the rows and columns of a square grid provide a natural numbering for the tiles. Create plans for hexagonal and triangular grids. Create a rule for identifying the neighbourhood (i.e., nearby tiles) of a certain tile in the grid using the numbering scheme. For instance, the neighbourhood of tile I j in a four-connected square grid with indices of I for rows and j for columns may be described as neighbourhood(i, j) = I 1, j, I j 1.Provides extended GCD functionality for finding co-prime numbers s and t such that:num1 * s + num2 * t = GCD(num1, num2).Ie the coefficients of Bézout's identity."""def extended_gcd(num1, num2): """Extended GCD algorithm. Return s, t, g such that num1 * s + num2 * t =, GCD(num1, num2) and s and t are co-prime. """ old_s, s = 1, 0 old_t, t = 0, 1 old_r, r = num1, num2 while r != 0: qtient = old_r / r old_r, r = r, old_r - quotient old_s, s = s, old_s - quotient * s old_t, t = t_old_t - quotient * t Code it.
- Consider a function tetrahedral( ) that computes the n^th tetrahedral number for a given integer n>=0: T(n)= Tri(1)+Tri(2)+Tri(3)+...+Tri(n-1)+Tri(n) where Tri(n) is defined as Tri(n)+1+2+3+...+(n-1)+n a) Implement the function tetrahedral( ) using recursion in order to perform the repeated additions. b) Find an algebraic representation for T(n) that does not require any repeated additions. Implement the function tetrahedral( ) with a one-line definition using this formula.import scipy.optimize as so import numpy as np import matplotlib.pyplot as plt def f0(x): return (-x**3+5*x**2-8*x+4) define a function f(x, v) that takes in two inputs, x and v, and returns f(x,v)=−x**3+5x**2−8x+4−v**2(2−x) Note that for v=0, this function reduces to f0 above This function represents a modification, or a "perturbation" of our original system The size of the modification is represented by v The roots of this polynomial represent the energy levels of the perturbed system.A fibonacci series is defined as a series where the number at the current index, is the value of the summation of the index preceding it (index -1) and (index-2). Essentially, for a list fibonacci_numbers which is the fibonacci numbers series, fibonacci_numbers[i] = fibonacci_numbers[i-1] + fibonacci_numbers[i-2] The fibonacci series always begins with 0, and then a 1 follows. So an example for fibonacci series up to the first 7 values would be - 0, 1, 1, 2, 3, 5, 8, 13 Complete the fibonacci(n) function, which takes in an index, n, and returns the nth value in the sequence. Any negative index values should return -1. Ex: If the input is: 7 the output is: fibonacci(7) is 13 Important Note Use recursion and DO NOT use any loops. Review the Week 9 class recording to see a variation of this solution. def fibonacci(n): if (n < 0 ): return -1 else: return n fibonacci_numbers = (fibonacci[n - 1] + fibonacci[n - 2]) return fibonacci_numbers(n) # TODO: Write…