# Mathematics and statistics problems

Assignment
1. Suppose that a client performs an intermixed sequence of (stack) push and pop operations. The push operations put the integers 0 through 9 in order onto the stack; the pop operations print out the return value. Which of the following sequence(s) could not occur? ( May be more than one sequence.)

a) 4 3 2 1 0 9 8 7 6 5
b) 2 5 6 7 4 8 9 3 1 0
c) 4 6 8 7 5 3 2 9 0 1
d) 4 3 2 1 0 5 6 7 8 9
e) 1 2 3 4 5 6 7 8 9 0
f) 0 4 6 5 3 8 1 7 2 9
2. Let A be a given array of n integers.Characterize, using the big-Oh notation, the worst-case running time of
The Best characterization is :
3. For a binary tree (not necessary a BST), we are given the following information
preorder traversal sequence : D F I G T A L M X
postorder traversal sequence : I T G F L X M A D
Can you construct and draw the tree from the given ? If so, draw the tree. Is the tree unique? If the tree is not unique, how many possible binary tree with the given pair of traversal sequences?
4. Characterize, using the big-Oh notation, the worst-case running time of
4. 1. Alg Ex1(A):
Input: array A storing n > 0 integers.
Output : The sum of the elements in A.

s <– A[0]

for i <– 1 to n-1 do

s <– s + A[i]

return s
4.2 Alg Ex2(A):
Input: array A storing n > 0 integers.
Output : The sum of the elements at even cells in A.

s <– A[0]

for i <– 2 to n-1 by increments of 2 do

s <– s + A[i]

return s
4.3Alg Ex3(A) :
Input: array A storing n > 0 integers.
Output : The sum of the prefix sums in A.

s <– 0

for i <– 0 to n-1 do

s <– s + A[0]

for j <– 1 to i do

s <– s + A[j]

return s
4.4AlgEx4(A) :
Input: array A storing n > 0 integers.
Output : The sum of the prefix sums in A.

s <– A[0]

t <– s

for i <– 1 to n-1 do

s <– s + A[i]

t <– t + s

return s
4.5AlgEx5(A,B) :
Input: Arrays A and B each storing n > 0 integers.
Output : The number of elements in B equal to the sum of prefix sums in A.

c <– 0

for i <– 0 to n-1 do

s <– 0

for j <– 0 to n-1 do

s <– s + A[0]

for k <– 1 to j do

s <– s + A[k]

if B[i] = s then

c <– c + 1
return c

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