Analyze the runtime of c functions below and give a tight runtime bound for each. ....
PROBLEM 1 (24 points): For each of the recursive functions below and on the next page, give a correct recurrence relation expressing its runtime and then a tight runtime bound for the recurrence relation. Functions that take parameters lo and hi: n=hi-lo+1 RECURRENCE RELATION: int foo(int a[], int lo, int hi) { int x, i, j, m; X = 0; if(lo==hi) return a[10]; for(i=lo; i<=hi; i++) { for(j=i+1; j<=hi; j++) { if(a[i] % 2) x += a[i]; else x -=...
6. Using big-oh notation, give the runtime for each of the following recursive functions. You do not need to justify your answers: a) Int nonesense (int n) if (n <0) return 1; return nonsense (n-2) 1; b) int no nonesense (int n) if (n <0) return 1; return no_nonsense (n-1)+ no nonsense (n-1)
What is the worst-case asymptotic time complexity of the following divide-andconquer algorithm (give a Θ-bound). The input is an array A of size n. You may assume that n is a power of 2. (NOTE: It doesn’t matter what the algorithm does, just analyze its complexity). Assume that the non-recursive function call, bar(A1,A2,A3,n) has cost 3n. Show your work! Next to each statement show its cost when the algorithm is executed on an imput of size n abd give the...
What is the worst-case asymptotic time complexity of the following divide-andconquer algorithm (give a Θ-bound). The input is an array A of size n. You may assume that n is a power of 2. (NOTE: It doesn’t matter what the algorithm does, just analyze its complexity). Assume that the non-recursive function call, bar(A1,A2,A3,n) has cost 3n. Show your work! Next to each statement show its cost when the algorithm is executed on an imput of size n abd give the...
What is the runtime of each method? Give answer in Θ(big Theta) notation as a function of n, give a brief explanation. A. public static int method1(int n){ int mid = n/2; for (int i = mid; i >= 0; i--) System.out.println(i); for (int i = mid + 1; i <= n; i++) System.out.println(i); return mid; } B. public static int method2(int n){ for (int i = n; i >= 0; i / 3){ System.out.println(i ); } return mid; }...
Which big-O expression best characterizes the worst case time complexity of the following code? public static int foo(int N) ( int count = 0; int i1; while (i <N) C for (int j = 1; j < N; j=j+2) { count++ i=i+2; return count; A. O(log log N) B. O(log N2) C. O(N log N) D. O(N2)
Select all the valid asymptotic runtime bounds for the following function f2 in the worst case: public static int f1 (int n) { int x = 0; for (int i = 0; i < n; i++) { x++; } return x; } public static int f2 (int n) { if (n <= 1) { return 1; } return f1(n) + f2(n/2) + f2(n/2); } Θ(n^2) O(n^2) Θ(log(n)) Θ(log^2(n)) Θ(nlog(n)) Ω(n) Ω(n^2)
Need some help with finding the runtime of these java functions in the form of exact, tilde and big oh notation: Example of how: Func Exact Tilde O() Example 1 1 ~1 O(1) Example 2 2n+1 ~2n O(2n) Here are the functions: void funcA(int n) { step(); for (int i = 0; i < n; i++) { funcA(n-1); } } void funcB(int n) { step(); if (n > 0) funcB(n-1); ...
PYTHON: Im stuck here, big O notation and runtime. What is it and Why are they those? Please look at the pic, need help as Im confused. Thank You! def method3(n): for i in range(n): for j in range(100): for k in range(n): print(i+j+k) What is the runtime (tightest/closest bound in terms of O) for the above python function (method 3)? Please briefly explain. Enter your answer here def method4(n): for i in range(n): for j in range(n, o, -2):...
4. Big-Oh and Rune time Analysis: describe the worst case running time of the following pseudocode functions in Big-Oh notation in terms of the variable n. howing your work is not required (although showing work may allow some partial t in the case your answer is wrong-don't spend a lot of time showing your work.). You MUST choose your answer from the following (not given in any particular order), each of which could be re-used (could be the answer for...