Solve matrix add, frequency count, longest consecutive

You are asked to solve the following 3 coding tasks (in any language). Implement each as a function.

1) Add two matrices

Input: Two 2D integer arrays A and B, each of shape m x n.

Task: Return a new matrix C of shape m x n where C[i][j] = A[i][j] + B[i][j].

Assumptions:

• A and B have the same dimensions.

Example:

• A = [[1,2],[3,4]] , B = [[5,6],[7,8]] → [[6,8],[10,12]]

2) Count occurrences of names

Input: A list/array of strings names.

Task: Return a dictionary / hash map from name → frequency (count of how many times it appears).

Example:

• names = ["Amy","Bob","Amy"] → { "Amy": 2, "Bob": 1 }

3) Longest consecutive sequence

Input: An integer array nums (can contain duplicates and negative numbers).

Task: Return the length of the longest sequence of consecutive integers that can be formed from the elements of nums (order in the array does not matter).

Complexity requirement: Aim for O(n) time using a hash set (typical “Longest Consecutive Sequence” problem).

Examples:

• nums = [100,4,200,1,3,2] → 4 (sequence 1,2,3,4 )
• nums = [0,3,7,2,5,8,4,6,0,1] → 9 (sequence 0..8 )

Clarifications:

• Duplicates should not inflate the sequence length.
• If nums is empty, return 0 .