Solve grid shortest-path and tree DP

Problem A — Shortest path in a maze (BFS)

You are given a 2D grid representing a maze:

• grid[r][c] is either '.' (open cell) or '#' (wall).
• You are also given a start coordinate S = (sr, sc) and an end coordinate E = (er, ec) .
• From an open cell, you may move up/down/left/right by 1 cell (no diagonals).
• You cannot move outside the grid or into walls.

Task: Return the minimum number of steps from S to E. If E is unreachable, return -1.

Input (conceptual): grid, S, E

Output: minimum steps as an integer

Constraints (typical):

• 1 <= rows, cols <= 2000 (assume potentially large)
• Start/end are within bounds and on open cells.

Problem B — Max sum of non-adjacent nodes in a binary tree

You are given the root of a binary tree where each node has an integer value (can be 0 or positive).

You want to select a set of nodes to maximize the sum of their values subject to the constraint:

• If you select a node, you cannot select its direct children.

Task: Return the maximum achievable sum.

Input (conceptual): root of a binary tree

Output: maximum sum as an integer

Constraints (typical):

• Number of nodes up to 10^5
• Values up to 10^4