Software Engineer

Given two strings, 'S' and 'T' with lengths 'M' and 'N', find the length of the 'Longest Common Subsequence'.

For a string 'str'(per se) of length K, the subsequences are the strings containing characters in the same relative order as they are present in 'str,' but not necessarily contiguous. Subsequences contain all the strings of length varying from 0 to K.

Example :

Subsequences of string "abc" are:  ""(empty string), a, b, c, ab, bc, ac, abc.

We need to count the chracters based on frquency

Rain water trapping

Given a connected directed acyclic graph having ‘N’ nodes and ‘M’ edges. A matrix ‘edges’ of size M x 2 is given, which represents the ‘M’ edges such that there is an edge directed from node edges[i][0] to node edges[i][1].

You are supposed to find all possible paths from node 0 to node n - 1.

Note

Nodes are numbered from 0 to N - 1.

The graph given is connected.

Print the path[][] in sorted order i.e path[i] is an array containing the path from 0 to n-1, and path[i] is lexicographically smaller than path[i + 1] then path[i] should appear before path[i + 1].

Assume we have two solutions
S1: A1 B1 C1 D1  
S2: A2 B2 C2 D2

S1 is lexicographically smaller than S2 iff,
A1 < A2 OR
A1 = A2 AND B1 < B2 OR
A1 = A2 AND B1 = B2 AND C1 < C2 OR 
A1 = A2 AND B1 = B2 AND C1 = C2 AND D1 < D2

For Example :

The following is an example of DAG i.e a directed graph with no cycles in it. 

For a given array with N elements, you need to find the length of the longest subsequence from the array such that all the elements of the subsequence are sorted in strictly increasing order.

Strictly Increasing Sequence is when each term in the sequence is larger than the preceding term.

For example:

[1, 2, 3, 4] is a strictly increasing array, while [2, 1, 4, 3] is not.

We have two water jugs, one measures 4 Gallons (4G) while the other measure 9 Gallons (9G). But there is no measuring label mentioned on either of these two jugs i.e. we cannot know the exact amount filled in the jug. Now, assuming there is an infinite amount of water supply, can we measure all 1G, 2G, 3G…….. upto 9G using these unmarked jugs.

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