Solve the Loop Invariant of Merge Sort using Induction. To show that initialization, maintenance, and termination...
Solve the Loop Invariant of Merge Sort using Induction. To show that initialization, maintenance, and termination holds true after each iteration.
Homework Answers
Induction are used for recursive algorithms like merge sort to prove the correctness using loop invariant
- induction-true before step 1
- maintenance -true before and after each step
- termination - gives correct result
The below opencourseware link from McGill has detailed explanation of these three steps.
https://www.cs.mcgill.ca/~jeromew/teaching/250/W2018/COMP250_Lecture11_W2018.pdf
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Solve the Loop Invariant of Merge Sort using Induction. To show
that initialization, maintenance, and termination...
Prove that the Merge() function of your own merge sort algorithm in the question 2 is...
Prove that the Merge() function of your own merge sort algorithm in the question 2 is correct using "induction on loop invariants" by following the guidelines below : (10 points) 3.1 Write down general description of loop invariant technique in your own words as proof of correctness. (2 points) 3.2 Identify the loop invariant of the loop in your merge() function (3 points) 3.3 Describe initialization step (0 points) 3.4 Describe maintenance step (4 points) 3.5 Describe Termination step (1...
C++ help please Sort the following list using MERGE sort as discussed in this chapter. Show...
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(a) Prove the following loop invariant by induction on the number of loop iterations: Loop Invariant:...
(a) Prove the following loop invariant by induction on the
number of loop iterations: Loop Invariant: After the kth iteration
of the for loop, total = a1 + a2 + · · · + ak and L contains
all elements from a1 , a2 , . . . ,
ak that are greater than the sum of all previous terms of the
sequence.
(b) Use the loop invariant to prove that the algorithm is
correct, i.e., that it returns a...
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2) Sorting (a) (5 pts) In a Merge Sort of 8 elements, the Merge function gets...
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For the while loop below, use the loop invariant given to show that if the pre-condition...
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(a) Prove the following loop invariant by induction on the
number of loop iterations: Loop Invariant: After the kth iteration
of the for loop, total = a1 + a2 + · · · + ak and L contains
all elements from a1 , a2 , . . . ,
ak that are greater than the sum of all previous terms of the
sequence.
(b) Use the loop invariant to prove that the algorithm is
correct, i.e., that it returns a...
2) Sorting (a) (5 pts) In a Merge Sort of 8 elements, the Merge function gets called 7 times. Consider a Merge Sort being executed on the array shown below. What does the array look like right AFTER the sixth call to the Merge function completes? نرا index value 0 40 2 12 4 11 5 99 6 31 7 16 27 18 0 1 2 زيا 4 5 6 7 Index Value (b) (5 pts) Consider sorting the array...
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For the while loop below, use the loop invariant given to show that if the pre-condition is the loop.In each step, clearly state true before the loop then the post-condition is true after what facts are assumed and what facts will be proven. (computes the sum of a list of numbers.) fa ,an While (<n) sum := sum + am j j+1 End-while ° Pre-condition: j- 1, sum a, n is a positive integer, a,,.. a, is a list of...
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