Q1. Given a sequence of integers, find the longest increasing subsequence. Example:
arr = [1, 2, 5, 3, 7]
ans : [1, 2, 5, 7] or [1, 2, 3, 7]
arr = [4, 3, 1, 2]
ans: [1, 2].
Solution:
[1, 2, 3, 3, 4]
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Q2. Given a vectors of numbers of fixed length, for example:
v1 = [4, 3, 1, 2] v2 = [2, 4, 3, 5]
The relationship nested between two vectors is defined as follows:
if the corresponding entries of a vector are all smaller than the other vector, after rearranging entries of vector if needed, then first vector
is said to be nested in the other. Example
Not nested
v1 - [4, 3, 1, 2] v2 - [2, 4, 3, 5]
v2 - [2, 4, 3, 5] v1 - [4, 3, 1, 2]
After re-arranging:
Nested
v1 - [4, 3, 1, 2]
v2 - [5, 4, 2, 3]
Hence v1 is nested in v2.
Given a pair of such vectors , write a function as follows:
function isNested(Vec a, Vec b);
Result:
-1 if a is nested in b
1 if b is nested in a
0 if nesting is not possible.
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Q3. Given a list of numbers in random order. Is it possible to pair all elements in the list in such a way that no two pairs share an element
and the sum of elements in a pair is divisible by 101. Example:
v1 [ 1, 100, 1]
Ans: No
v2 [1, 100, 100, 1] [2, 98, 101, 1]
Ans: Yes
v3 [1, 200, 100, 100, 2, 1]
Ans: yes
