a) Find all the solutions of the equation (mod 114).
To solve the congruence equation numerically: \[ 6X \equiv 4 \pmod{114} \] ### Step 1: Check for Invertibility ________ _____ _______ __________ ______ ______ _______ ___ __________.
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a) For the set of keys {3, 7, 9, 4, 6, 8, 12} draw binary search trees of height 2, 3, 4, 5 and 6.
b) Using Fig. 6.3 in page 134 of the book as a model, illustrate the operation of Build-Max-Heap on the array
For the following set of points, describe how the closest-pair algorithm finds a closest pair of
points:
(3, 2), (2, 1), (2, 3), (1, 2), (3, 1), (2, 2), (1, 3), (3, −1), (5, −2)
Compute the DFT of the vector (−1, 3, 1, −1).
a) The maximum subsequence sum problem is defined as follows: If are in Z, find the maximum value
for all
We assume that the answer is 0 if all the
are negative or if the sum is empty. The following algorithm finds a solution to the problem. Here, we assume that
s are stored in the array A.
Maximum-Subsequence
1
2
3
4
5
6
7
8
State precisely a loop invariant for the for loop in line 2–8. Prove that your loop invariant holds and hence conclude that the algorithm works.
b) Analyse the algorithm and find an upper bound for the run time of the above algorithm.
b) Using Fig. 7.1 in page 147 of the book as the model, illustrate the operation of Partition on the array
b) When working modulo how many spurious hits does the Rabin-Karp matcher encounter in the text
when looking for the pattern
when looking for the pattern
) Find an optimal parenthesisation of a matrix chain product whose sequence of dimensions is (3, 5, 7, 3, 4).