Compute time complexity of the given program. The complexity computation should be for the complete program. Map it on its relevant standard function. Computation should be clear. For(i=1; i<=n; i++) For(j=i; j<=n;j++) For(k=1; k<=j; k++) Print Mark;
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Compute time complexity of the given program. The complexity computation should be for the complete program. Map it on its relevant standard function. Computation should be clear.
For(i=1; i<=n; i++)
For(j=i; j<=n;j++)
For(k=1; k<=j; k++)
Print Mark;
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Solved in 3 steps
- Instead of solving a problem using one large code segment, we can base that solution off of the solutions of smaller sub-problems. This is often referred to as modularity. This helps to manage the complexity of the program and can be done in the form of what type of abstraction? Consider the following procedures. PROCEDURE math (ans1, ans2){a ← INPUT() b ← INPUT()c ← math2(a, b)e ← a + ans1f ← b + ans2g ← math2(e, f)h ← c + gDISPLAY(h)}PROCEDURE math2 (res1, res2){d ← res1 + res2RETURN(d)} What is displayed as a result of executing the following program, if when prompted, the user enters a = 3 and b = 4? math(1, 2) PythonAnswer the given question with a proper explanation and step-by-step solution. Calculate the time complexity of the function: int a = 0; for(int i = 0; i < n; i++){ a += i; } int b = 0; for(int j = 0; j < m; j++){ b += j; }Question 3: What is the time complexity of following code. Show the time complexity of each statement below and the final running time. For computing the running time, you must show an example of tracing the algorithm as we did in the lecture. int a, b, c 0; for (a= n/2; a<= n; a++){ for (b = 2; b <= n; b= b* 2) { C= C+ n/ 2;
- Consider the following two functions. What are the time complexities of the functions? Please do explain and describe in details on how you derive the complexity of those two functions.int f1(int n) { if (n <= 1) return n; return 2 * f1(n/2);}int f2(int n) { if (n <= 1) return n; return f2(n/2) + f2(n/2);}1. Solve the Eight Tiled Puzzle Problem Using Hill-climbing algorithm with the help ofC++ programming language. Initial state and goal state are given below. 4 7 2 5 8 1 3 6 Initial State 1 2 3 4 5 7 8 6 Goal State Expected Outcome.a. The number of steps required to solve the puzzle.b. Print the best state after each iteration of hill-climbing requirements:no pre-defined functionsquee and algorithm library not allowedIostream only no otherint functionC (int n) { int i, j, sumC = 0; for (i=n; i > 0; i=i-5) for (j=1; j 0) { if (functionC(n) % 2 == 0) { for (i=m; i > 0; i=i/3) sumE++; } else (10) Asymptotic runtime of functionE { for (i=m; i > 0; i=i-3) sumE--; } n--; } return sumE;
- In programming, a recursive function calls itself. The classical example is factorial(n), which can be defined recursively as n*factorial(n-1). Nonethessless, it is important to take note that a recursive function should have a terminating condition (or base case), in the case of factorial, factorial(0)=1. Hence, the full definition is: factorial(n) = 1, for n = 0 factorial(n) = n * factorial(n-1), for all n > 1 For example, suppose n = 5: // Recursive call factorial(5) = 5 * factorial(4) factorial(4) = 4 * factorial(3) factorial(3) = 3 * factorial(2) factorial(2) = 2 * factorial(1) factorial(1) = 1 * factorial(0) factorial(0) = 1 // Base case // Unwinding factorial(1) = 1 * 1 = 1 factorial(2) = 2 * 1 = 2 factorial(3) = 3 * 2 = 6 factorial(4) = 4 * 6 = 24 factorial(5) = 5 * 24 = 120 (DONE) Exercise (Factorial) (Recursive): Write a recursive method called factorial() to compute the factorial of the given integer. public static int factorial(int n) The recursive algorithm is:…Compute time complexity of the given programs. The complexity computation should be for the complete program. Map it on its relevant standard function. Clear computation required. void swap(int *xp, int *yp) { int temp = *xp; *xp = *yp; *yp = temp; } // A function to implement bubble sort void bubbleSort(int arr[], int n) { int i, j; for (i = 0; i < n-1; i++) // Last i elements are already in place for (j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) swap(&arr[j], &arr[j+1]); } /* Function to print an array */ void printArray(int arr[], int size) { int i; for (i = 0; i < size; i++) cout << arr[i] << " "; cout << endl; }EXERCISE Choose two problem out of three questions for coding. 1. Write an inline function that will calculate 6x - 4y + xy + cos² (x-k). Assume that x and y may scalars, vectors or matrices and that all operations should be carried out element-wise. 2. Write a recursive MATLAB function to calculate the Fibonacci sequence and return the number with a specified index. 3. Write a short MATLAB function to find out whether a given number (up to 1,000,000 is a prime number. The function should return true or false. Bear in mind that 1 is not considered a prime number. (Hint: Use the brute force approach and divide the number (K) by all integers from 2 to K-1. Check the remainders for Os)
- A deadlock is the very unpleasant situation that may occur in very dynamic world of running processes, a situation that must be avoided at all costs. One famous algorithm for deadlock avoidance is the Banker's algorithm for deadlock avoidance. The version of this algorithm presented in this module's commentary gives just one solution (the Greedy approach). Consider the Greedy approach to the Banker's algorithm. Give an example of application of this algorithm for 7 processes (named P1, ... , P7) and 5 resource types (named R1, ... , R5). Start by listing the matrices involved in this algorithm, that constitute its input data; also, do not forget to mention the overall resources of each type available in this fictional system. Proceed by describing the algorithm, step by step; for each step, mention the test performed, which process was chosen, what is the old and new status of the Work array, etc. In the end, list the solution, that is the safe sequence of processes resulting from this…Exercise 3. For each of the following program fragments give a (.) estimation of the running time as a function of n. (a) sum = 0; (b) (c) (d) (e) for (int i = 0; i< n * n; i++) { for(int j = 0; j < n/2; j++) sum++; } sum = 0; for (int i sum++; +; } for (int j } sum = for = } = 0; j < n/2; j++) { sum++; } 0; (int i = 0; i< n * n; i++) { for (int j = 0; j < n * n; j++) sum++ sum = 0; for (int i = 0; iFor function log, write the missing base case condition and the recursive call. This function computes the log of n to the base b. As an example: log 8 to the base 2 equals 3 since 8 = 2*2*2. We can find this by dividing 8 by 2 until we reach 1, and we count the number of divisions we make. You should assume that n is exactly b to some integer power. Examples: log(2, 4) -> 2 and log(10, 100) -> 2 public int log(int b, int n ) { if <<Missing base case condition>> { return 0; } else { return <<Missing a Recursive case action>> }}SEE MORE QUESTIONS