#Dynamic Programming

Implement an algorithm to find the longest increasing subsequence in a given array of integers. You can use dynamic programming with a time complexity of O(n²) or optimize your solution with binary search to achieve a time complexity of O(n log n).

Given a matrix, find the maximum sum path from top-left to bottom-right. You can only move right or down at any point in time. For example, given the matrix [[1, 2, 3], [4, 5, 6]], the maximum sum path is 1 → 2 → 5 → 6 = 14.

Solve a dynamic programming problem that is categorized as medium to hard. Ensure you understand the problem constraints and provide a robust solution.

You are climbing a staircase. It takes n steps to reach the top, and you can take either 1 or 2 steps at a time. In how many distinct ways can you climb to the top?

Given a binary matrix, find the maximum size square sub-matrix that contains all 1s. For example, given the binary matrix: 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 what would be the output?