Cormen Edition 3 Exercise 7.4 Question 4 (Page No. 184)

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Show that RANDOMIZED-QUICKSORT’s expected running time is $\Omega(n\ lg\ n)$.

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Cormen Edition 3 Exercise 7.4 Question 2 (Page No. 184)
Show that quicksort’s best-case running time is $\Omega(n\ lg\ n)$.

asked Jun 28 in Algorithms by akash.dinkar12 Boss (41.3k points) | 18 views

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Cormen Edition 3 Exercise 7.4 Question 3 (Page No. 184)
Show that the expression $q^2 +(n-q-1)^2$ achieves a maximum over $q=0,1,\dots ,n-1$ when $q=0$ or $q=n-1$.

asked Jun 28 in Algorithms by akash.dinkar12 Boss (41.3k points) | 11 views

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Cormen Edition 3 Exercise 7.2 Question 3 (Page No. 178)
Show that the running time of QUICKSORT is $\Theta(n^2)$ when the array $A$ contains distinct elements and is sorted in decreasing order.

asked Jun 27 in Algorithms by akash.dinkar12 Boss (41.3k points) | 13 views

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Cormen Edition 3 Exercise 7.2 Question 2 (Page No. 178)
What is the running time of QUICKSORT when all elements of the array $A$ have the same value?

asked Jun 27 in Algorithms by akash.dinkar12 Boss (41.3k points) | 30 views

cormen
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Cormen Edition 3 Exercise 7.4 Question 6 (Page No. 185)
Consider modifying the PARTITION procedure by randomly picking three elements from the array $A$ and partitioning about their median (the middle value of the three elements). Approximate the probability of getting at worst a $\alpha$-to-$(1-\alpha)$ split, as a function of $\alpha$ in the range $0<\alpha<1$.

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Cormen Edition 3 Exercise 7.4 Question 5 (Page No. 185)
We can improve the running time of quicksort in practice by taking advantage of the fast running time of insertion sort when its input is nearly sorted. Upon calling quicksort on a subarray with fewer than $k$ elements, let it simply return without ... $k$, both in theory and in practice?

asked Jun 28 in Algorithms by akash.dinkar12 Boss (41.3k points) | 11 views

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Cormen Edition 3 Exercise 7.1 Question 4 (Page No. 174)
QUICKSORT(A,p,r) 1 if p < r 2 q = PARTITION(A,p,r) 3 QUICKSORT(A, p , q-1) 4 QUICKSORT(A, q + 1, r) How would you modify QUICKSORT to sort into nonincreasing order?

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Cormen Edition 3 Exercise 7.4 Question 4 (Page No. 184)

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