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CS 502 Fundamental of Algorithms
Assignment # 01
Spring 2012
Total Marks = 10+10 = 20
Deadline
Your assignment must be uploaded / submitted before or on April 23, 2012
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Assignment Statements:
Question 1:
Consider sorting n numbers stored in array A by first finding the smallest element of A and exchanging it with the element in A[1]. Then find the second smallest element of A, and exchange it with A[2]. Continue in this manner for the first n - 1 elements of A. Write pseudo code for this algorithm, which is known as selection sort. What loop invariant does this algorithm maintain? Why does it need to run for only the first n - 1 element, rather than for all n elements? Give the best-case and worst-case running times of selection sort in Θ-notation.
Question 2:
We can extend our notation to the case of two parameters n and m that can go to infinity independently at different rates. For a given function g(n, m), we denote by O(g(n, m)) the set of functions
O(g(n, m)) = {f(n, m): there exist positive constants c, n0, and m0 such that 0 ≤ f(n, m) ≤ cg(n, m) for all n ≥ n0 and m ≥ m0}.
Give corresponding definitions for Ω(g(n, m)) and Θ(g(n, m)).
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2nd question solve karny k qabil hai kia? ya ye mazaq kia hai sir ne
yar mujy tu ye solution mila ha kahin se bt i dont know that it is right or wrong.......
i hav shared here so take idea and try to solve it because us book ki tu smaj hi nahi aa rahi yar.............ab bhi ni pta kesy kerna ha..hahahahahahahaha
Solution file is not opening
second question to thek bt first question ka pta nae
solution of cs502 assignment no1 # just and 70% idea.
good luck
CS502 FUNDAMENTAL OF ALGORITHMS
Umair sid
Question 1:
Consider sorting n numbers stored in array A by first finding the smallest element of A and exchanging it with the element in A[1]. Then find the second smallest element of A, and exchange it with A[2]. Continue in this manner for the first n - 1 elements of A. Write pseudo code for this algorithm, which is known as selection sort. What loop invariant does this algorithm maintain? Why does it need to run for only the first n - 1 element, rather than for all n elements? Give the best-case and worst-case running times of selection sort in Θ-notation.
Answer of no#1:
The Selection-sort (A)
For i ← 1 to length [A]
Do min-value ← A [i]
Min-index = i
For j = i +1to length [A]
Do if A[j] ≤ min-value
Min-value = A [j]
Min-index = j
A[i] ←→ A [min-index]
In this session the worst –case running time of SELECTION-Sort is Ө (n2)
Question 2:
We can extend our notation to the case of two parameters n and m that can go to infinity independently at different rates. For a given function g(n, m), we denote by O(g(n, m)) the set of functions
O(g(n, m)) = {f(n, m): there exist positive constants c, n0, and m0 such that 0 ≤ f(n, m) ≤ cg(n, m) for all n ≥ n_{0} and m ≥ m_{0}}.
Give corresponding definitions for Ω(g(n, m)) and Θ(g(n, m)).
Answer of no#2:
Ω(g(n,m)) = { f (n,m) : there exist positive constants c, n_{0} , and m_{0} such that 0 ≤ cg(n,m) ≤ f (n,m) for all n ≥ n_{0} and m ≥ m_{0} }.
Ө(g(n,m)) ={ ƒ(n,m) : there exist positive constants c1,c2 n, and m_{0} such that c1g(n,m) ≤ ƒ(n.m) ≤ c2g(n,m) for all n≥ n_{0} and m ≥ m_{0} }.
Solved by.
umair sid
umair sid gud keep it up
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