#Dynamic Programming

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?

Determine the minimum cost path in a given grid where each cell has a cost. Provide the algorithm to find the path with the least cost from the top left to the bottom right of the grid.

Solve the Coin Change 2 problem. Your solution should involve returning the number of combinations of coins that can make up a given amount. For example, an input of amount 5 with coins [1, 2, 5] would yield a certain number of combinations.

Solve optimization problems that focus on dynamic programming and mathematical techniques.