![1, Variation on 3.3#4] Give a big-O estimate in terms of n for the number of oper- ations used in this segment of an algorithm, where an operation is an addition or a multiplication, (ignoring comparisons used to test the conditions in the while loop). while i 〈 n j:= j + i [10 points]](http://img.homeworklib.com/questions/e86093b0-6296-11ec-9f3d-fbfc9aaddb66.png?x-oss-process=image/resize,w_560)
Homework Answers
We all know that Time Complexity of a loop is considered as O(Logn) if the loop variables is divided / multiplied by a constant amount.
Here the loop will stop when i >= n. If we let k be some arbitrary iteration of the loop, the value of i on iteration k will be 4k. The loop stops when 4k > n, which happens when k > log4 n. Therefore, the number of iterations is only O(log n), so the big O estimate in terms of n is O(log n).
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1, Variation on 3.3#4] Give a big-O estimate in terms of n for the number of...
Problem 7. Give a big-O estimate for the number of operations where an operation is an...
Problem 7. Give a big-O estimate for the number of operations where an operation is an addition or a multiplication, used in this segment of an algorithm (ignoring comparisons used to test the conditions in the vhile loop. while i Sn do end while
Give a big-O estimate for the number of additions ued in the segment of an algorithm...
Give a big-O estimate for the number of additions ued in the segment of an algorithm below. t:=0 for i := 1 to n for j := 1 to n t := t + i + j
consider this segment of an algorithm: for i := 1 ton n for j:=1 to n...
consider this segment of an algorithm: for i := 1 ton n for j:=1 to n top:=ij+j+10 a. find a function f(n) that counts the number of multiplication and additions performed in this segment. b. Give a big O estimate for the number of additions and multiplications used in the segment
1. Give the big-O characterization of the following loops, in terms of parameter n, and justify...
1. Give the big-O characterization of the following loops, in terms of parameter n, and justify your answer: a) for (int i=1; i<=n, i++) {for (int j=1; j<=n; j++) {a constant-time operation}} b) for (int i=1;i<=n, i++) {for (int i=1; j<=i; j++) {a constant-time operation}} c) for (int i=1;i<=n*n, i++) {for (int j=1; j<=n; j++) {a constant-time operation }} d) for (int i=1; i<=n*n, i++) {for (int j=1; j<=i; j++) {a constant-time operation }} e) for (int i=1; i<=n, i++)...
Need to find number of elementary expressions in terms of n, not looking for Big O...
Need to find number of elementary expressions in terms
of n, not looking for Big O complexity.
4. Work out the number of elementary operations in the worst possible case and the best possible case for the following algorithm (justify your answer): 0: function Nonsense (positive integer n) 1: it1 2: k + 2 while i<n do for j+ 1 to n do if j%5 = 0 then menin else while k <n do constant number C of elementary operations...
Discrete Math Give a big-Theta estimate for the number of additions in the following algorithm a)...
Discrete Math
Give a big-Theta estimate for the number of additions in the following algorithm a) procedure f (n: integer) bar = 0; for i = 1 to n^3 for j = 1 to n^2 bar = bar + i + j return bar b) Consider the procedure T given below. procedure T (n: positive integer) if n = 1 return 2 for i = 1 to n^3 x = x + x + x return T(/4) + T(/4) +...
Prove Big O in terms of nₒ and C? There are 5 examples: class Exercise {...
Prove Big O in terms of nₒ and C? There are 5 examples: class Exercise { public static int example1(int[] arr) { int n = arr.length, total = 0; for (int j=0; j < n; j++) // loop from 0 to n-1 total += arr[j]; return total; } public static int example2(int[] arr) { int n = arr.length, total = 0; for (int j=0; j < n; j += 2) // note the increment of 2 total += arr[j]; return...
Give a big-Oh characterization, in terms of n,of the running time for each of the following...
Give a big-Oh characterization, in terms of n,of the running time for each of the following code segments (use the drop-down): - public void func1(int n) { A. @(1). for (int i = n; i > 0; i--) { System.out.println(i); B. follogn). for (int j = 0; j <i; j++) System.out.println(j); c.e(n). System.out.println("Goodbye!"); D.@(nlogn). E.e(n). F.ein). public void func2 (int n) { for (int m=1; m <= n; m++) { system.out.println (m); i = n; while (i >0){ system.out.println(i); i...
Give the tightest bound in terms of Big O public type foo(n, a[]){ for (i=0, i<n;...
Give the tightest bound in terms of Big O public type foo(n, a[]){ for (i=0, i<n; i++){ if (a[i] == 0) return 0; } return 1; }
(1) Give a formula for SUM{i} [i changes from i=a to i=n], where a is an...
(1) Give a formula for SUM{i} [i changes from i=a to i=n], where a is an integer between 1 and n. (2) Suppose Algorithm-1 does f(n) = n**2 + 4n steps in the worst case, and Algorithm-2 does g(n) = 29n + 3 steps in the worst case, for inputs of size n. For what input sizes is Algorithm-1 faster than Algorithm-2 (in the worst case)? (3) Prove or disprove: SUM{i**2} [where i changes from i=1 to i=n] ϵ tetha(n**2)....
Problem 7. Give a big-O estimate for the number of operations where an operation is an addition or a multiplication, used in this segment of an algorithm (ignoring comparisons used to test the conditions in the vhile loop. while i Sn do end while
1. Give the big-O characterization of the following loops, in terms of parameter n, and justify your answer: a) for (int i=1; i<=n, i++) {for (int j=1; j<=n; j++) {a constant-time operation}} b) for (int i=1;i<=n, i++) {for (int i=1; j<=i; j++) {a constant-time operation}} c) for (int i=1;i<=n*n, i++) {for (int j=1; j<=n; j++) {a constant-time operation }} d) for (int i=1; i<=n*n, i++) {for (int j=1; j<=i; j++) {a constant-time operation }} e) for (int i=1; i<=n, i++)...
Need to find number of elementary expressions in terms
of n, not looking for Big O complexity.
4. Work out the number of elementary operations in the worst possible case and the best possible case for the following algorithm (justify your answer): 0: function Nonsense (positive integer n) 1: it1 2: k + 2 while i<n do for j+ 1 to n do if j%5 = 0 then menin else while k <n do constant number C of elementary operations...
Discrete Math
Give a big-Theta estimate for the number of additions in the following algorithm a) procedure f (n: integer) bar = 0; for i = 1 to n^3 for j = 1 to n^2 bar = bar + i + j return bar b) Consider the procedure T given below. procedure T (n: positive integer) if n = 1 return 2 for i = 1 to n^3 x = x + x + x return T(/4) + T(/4) +...
Give a big-Oh characterization, in terms of n,of the running time for each of the following code segments (use the drop-down): - public void func1(int n) { A. @(1). for (int i = n; i > 0; i--) { System.out.println(i); B. follogn). for (int j = 0; j <i; j++) System.out.println(j); c.e(n). System.out.println("Goodbye!"); D.@(nlogn). E.e(n). F.ein). public void func2 (int n) { for (int m=1; m <= n; m++) { system.out.println (m); i = n; while (i >0){ system.out.println(i); i...
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