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DAT600: Sorting Algorithms and Running Times - Find-Max-Subarray - Engineering Assignment Help
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Internal Code: 3IIA
Identify which algorithm has which big-Oh running time and explain your answer.
1.2) Calculate big-Oh running time, in terms of n, of the algorithm D shown below:
Algorithm D (n) {
s = 0; for i = 1 to n -1,
for j = n downto 1 in steps j = j / 2,
s = s + i*j; return s; }
Task: 2
Algorithm Design
Let E = {e1, e2, ..., en} be a sequence of integers. We say that an integer x forms a majority in E if x appears more than floor(n/2) times in E. For instance, the integer 3 is a majority in sequence E = {2, 3, 3, 2, 3, 3}, whereas the sequence E = {6, 3, 2, 7, 3, 1} has no majority.
Assume that for each i, we have 1 ? ei ? k, where k is an integer. Describe an algorithm, with O(n + k) running time, which decides if E has a majority.
Task: 3
Master Theorem
Using the Master theorem, find the running time (Big-O) of the following algorithms:
3.1) Merge sort is a classical recursive divide-and-conquer algorithm for sorting an array. The algorithm splits the array in half, recursively sorts the two halves, and then merges the two sorted sub-arrays into the final sorted array. Time taken for the algorithm can be denoted as:
3.2) Time taken for the Karatsuba’s multiplication algorithm is given by the following recurrence equation:
Task: 4
Understanding how “Find-Max-Subarray” and “Quicksort” works
4.1) Show step-by-step, how the procedure “find-max-subarray” determines the maximum subarray of the following row of numbers: A = [10 -2 8 -7 13 23 -18 14 24 8 -10 8]
4.2) Show step-by-step, how quicksort sorts the following row of numbers:
A = [10 2 8 7 13 23 18 14 24 8]
Engineering Assignment Help
Task: 1 Running Times For a given problem with input size n, algorithms A, B, C are executed. In terms of running time, one of the algorithms is O(n), another is O(n log n) and the third is O(n2). Some measured running times of these algorithms are given below:
Identify which algorithm has which big-Oh running time and explain your answer.
1.2) Calculate big-Oh running time, in terms of n, of the algorithm D shown below:
Algorithm D (n) {
s = 0; for i = 1 to n -1,
for j = n downto 1 in steps j = j / 2,
s = s + i*j; return s; }
Task: 2
Algorithm Design
Let E = {e1, e2, ..., en} be a sequence of integers. We say that an integer x forms a majority in E if x appears more than floor(n/2) times in E. For instance, the integer 3 is a majority in sequence E = {2, 3, 3, 2, 3, 3}, whereas the sequence E = {6, 3, 2, 7, 3, 1} has no majority.
Assume that for each i, we have 1 ? ei ? k, where k is an integer. Describe an algorithm, with O(n + k) running time, which decides if E has a majority.
Task: 3
Master Theorem
Using the Master theorem, find the running time (Big-O) of the following algorithms:
3.1) Merge sort is a classical recursive divide-and-conquer algorithm for sorting an array. The algorithm splits the array in half, recursively sorts the two halves, and then merges the two sorted sub-arrays into the final sorted array. Time taken for the algorithm can be denoted as:
3.2) Time taken for the Karatsuba’s multiplication algorithm is given by the following recurrence equation:
Task: 4
Understanding how “Find-Max-Subarray” and “Quicksort” works
4.1) Show step-by-step, how the procedure “find-max-subarray” determines the maximum subarray of the following row of numbers: A = [10 -2 8 -7 13 23 -18 14 24 8 -10 8]
4.2) Show step-by-step, how quicksort sorts the following row of numbers:
A = [10 2 8 7 13 23 18 14 24 8]
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