Homework Answers
Algorithm 1 gives the best visual representation of the code.
The given code has 3 nested loops, each running for 'n' iterations . Hence total iterations of the nested loops would be n*n*n.
The code then exits the nested sturcutre and begins another loop which iterates for only n/2 steps.
Hence we can visualize it as another block with iterations=n/2
Hence, algorithm 1 suits the code the best.
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II. ALGORITHM COMPLEXITY AND ASYMPTOTIC ANALYSIS The below visual representations of iterative looping structures are provided...
1(5 pts): For each code fragment below, give the complexity of the algorithm (O or Θ)....
1(5 pts): For each code fragment below, give the complexity of the algorithm (O or Θ). Give the tightest possible upper bound as the input size variable increases. The input size variable in these questions is exclusively n. Complexity Code public static int recursiveFunction (int n)f f( n <= 0 ) return 0; return recursiveFunction (n - 1) 1; for(int i 0i <n; i+) j=0; for ( int j k=0; i; k < < j++) for (int j; m <...
discrete math (1) (15 pts) Time Complexity Analysis 1) (5 pts) What is the time complexity...
discrete math
(1) (15 pts) Time Complexity Analysis 1) (5 pts) What is the time complexity of the following code segment? Explain your answer; otherwise, you can't get full mark from this question. for(int i=1; i<n; i*=2) { sum-0; sum++; Answer: 2) (5 pts) What is the time complexity of the following code segment? Explain your answer; otherwise, you can't get full mark from this question. for(int j=0; j<n; j++){ for (int k=0; k<n; k++) { for (int =0; i<n;...
Exercise 7.3.5: Worst-case time complexity - mystery algorithm. The algorithm below makes some changes to an...
Exercise 7.3.5: Worst-case time complexity - mystery algorithm. The algorithm below makes some changes to an input sequence of numbers. MysteryAlgorithm Input: a1, a2....,an n, the length of the sequence. p, a number Output: ?? i != 1 j:=n While (i < j) While (i <j and a < p) i:= i + 1 End-while While (i <j and a 2 p) j:=j-1 End-while If (i < j), swap a, and a End-while Return( aj, a2,...,an) (a) Describe in English...
For each C++ function below, give the tightest can asymptotic upper bound that you can determine....
For each C++ function below, give the tightest can asymptotic upper bound that you can determine. (a) void mochalatte(int n) { for (int i = 0: i < n: i++) { count < < "iteration;" < < i < < end1: } } (b) void nanaimobar (int n) { for (int i = 1: i < 2*n: i = 2*i) { count < < "iteration;" < < i < < end1: } } void appletart (int n) { for (int...
Question One (2 marks): What is the complexity of the given code as a function of the problem size n? Show the (complete) details of your analysis. Note: a [ i] s an array with n elements. for (int i...
Question One (2 marks): What is the complexity of the given code as a function of the problem size n? Show the (complete) details of your analysis. Note: a [ i] s an array with n elements. for (int i- 0; i < n; i++) if (Math.random) > 0.5) if (i%2-0) Insertionsort (a[i]); else Quicksort (a[i]) else for (int j = 0; j < i; j++) for (int k 0: k 〈 i; k++) o (logn)
Question One (2 marks):...
Question No.1 [CLO 1][7 marks] 1. Consider the following pseudocode: Algorithm IterativeFunction (a, b) // a...
Question No.1 [CLO 1][7 marks] 1. Consider the following pseudocode: Algorithm IterativeFunction (a, b) // a and b are integers while (a>0) B- a/2 A a-2 end while return b; i. What is the time complexity of the IterativeFunction pseudocode shown above? ii. What is the space complexity of the IterativeFunction pseudocode shown above? 2. What is the time complexity of the following algorithm (Note that n(n+1) 2,2 n(n+1)(2n+1) 2 and ): Provide both T(n) and order, e(f(n)). int A=0;...
When asked to describe an algorithm you are expected to give a clear pseudo-code description of...
When asked to describe an algorithm you are expected to give a
clear pseudo-code description of the algorithm
1. (10 pts) Here is a new sorting algorithm NewSort Suppose the original call made is NewSort(A,0,n-1) where A is an array integers. == void NewSort(int A[], int i, int j){ \\ sorts the subarray Aſi..j] if (j i+1) \\when there are only 2 elements if (A[i] > A[j]) swap(A,i,j) \\swaps A[i] and A[j] else { int k = (j-i+1)/3; NewSort(A,i,j-k); \\...
8. R-4.8 Order the following functions by asymptotic growth rate. 4nlogn + 2n 2^10 2^logn 3n...
8. R-4.8 Order the following functions by asymptotic growth rate. 4nlogn + 2n 2^10 2^logn 3n + 100logn 4n 2^n n^2 + 10n n^3 nlogn 9. R-4.9 Give a big-Oh characterization, in terms of n, of the running time of the example 1 method shown in Code Fragment 4.12. 10. R-4.10 Give a big-Oh characterization, in terms of n, of the running time of the example 2 method shown in Code Fragment 4.12. 11. R-4.11 Give a big-Oh characterization, in...
Below is a linear time complexity algorithm Max-Min-VER1 to find the biggest and smallest element a...
Below is a linear time complexity algorithm Max-Min-VER1 to find the biggest and smallest element a given list. Input: A is a given list Output: two integers Example: Given A = {1, 5, 9, -3}. It returns -3 (the smallest element), and 9 (the biggest element) Max-Min-VER1(A, n) Line 1: large ← A[0] Line 2: for I from 1 to n - 1 do Line 3: large ← Math.max(large, A[I]) Line 4: small ← A[0] Line 5: for I from...
1(5 pts): For each code fragment below, give the complexity of the algorithm (O or Θ). Give the tightest possible upper bound as the input size variable increases. The input size variable in these questions is exclusively n. Complexity Code public static int recursiveFunction (int n)f f( n <= 0 ) return 0; return recursiveFunction (n - 1) 1; for(int i 0i <n; i+) j=0; for ( int j k=0; i; k < < j++) for (int j; m <...
discrete math
(1) (15 pts) Time Complexity Analysis 1) (5 pts) What is the time complexity of the following code segment? Explain your answer; otherwise, you can't get full mark from this question. for(int i=1; i<n; i*=2) { sum-0; sum++; Answer: 2) (5 pts) What is the time complexity of the following code segment? Explain your answer; otherwise, you can't get full mark from this question. for(int j=0; j<n; j++){ for (int k=0; k<n; k++) { for (int =0; i<n;...
Exercise 7.3.5: Worst-case time complexity - mystery algorithm. The algorithm below makes some changes to an input sequence of numbers. MysteryAlgorithm Input: a1, a2....,an n, the length of the sequence. p, a number Output: ?? i != 1 j:=n While (i < j) While (i <j and a < p) i:= i + 1 End-while While (i <j and a 2 p) j:=j-1 End-while If (i < j), swap a, and a End-while Return( aj, a2,...,an) (a) Describe in English...
For each C++ function below, give the tightest can asymptotic upper bound that you can determine. (a) void mochalatte(int n) { for (int i = 0: i < n: i++) { count < < "iteration;" < < i < < end1: } } (b) void nanaimobar (int n) { for (int i = 1: i < 2*n: i = 2*i) { count < < "iteration;" < < i < < end1: } } void appletart (int n) { for (int...
Question One (2 marks): What is the complexity of the given code as a function of the problem size n? Show the (complete) details of your analysis. Note: a [ i] s an array with n elements. for (int i- 0; i < n; i++) if (Math.random) > 0.5) if (i%2-0) Insertionsort (a[i]); else Quicksort (a[i]) else for (int j = 0; j < i; j++) for (int k 0: k 〈 i; k++) o (logn)
Question One (2 marks):...
Question No.1 [CLO 1][7 marks] 1. Consider the following pseudocode: Algorithm IterativeFunction (a, b) // a and b are integers while (a>0) B- a/2 A a-2 end while return b; i. What is the time complexity of the IterativeFunction pseudocode shown above? ii. What is the space complexity of the IterativeFunction pseudocode shown above? 2. What is the time complexity of the following algorithm (Note that n(n+1) 2,2 n(n+1)(2n+1) 2 and ): Provide both T(n) and order, e(f(n)). int A=0;...
When asked to describe an algorithm you are expected to give a
clear pseudo-code description of the algorithm
1. (10 pts) Here is a new sorting algorithm NewSort Suppose the original call made is NewSort(A,0,n-1) where A is an array integers. == void NewSort(int A[], int i, int j){ \\ sorts the subarray Aſi..j] if (j i+1) \\when there are only 2 elements if (A[i] > A[j]) swap(A,i,j) \\swaps A[i] and A[j] else { int k = (j-i+1)/3; NewSort(A,i,j-k); \\...
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