Implement core puzzle/array/grid routines

You may be asked to solve one or more of the following coding exercises (write clean, testable code; discuss time/space complexity): 1) **Jigsaw assembly (small backtracking)** - You are given `N` square tiles. Each tile has 4 edge labels: `top`, `right`, `bottom`, `left` (strings). Two adjacent tiles are compatible if the touching edges have the same label. - A tile may be rotated (0/90/180/270 degrees), which permutes its edge labels. - Given integers `R` and `C` such that `R*C == N`, determine whether the tiles can be arranged into an `R x C` grid so that **all internal adjacent edges match**. (Optionally: also return one valid arrangement of tile IDs and rotations.) - Assume `N` is small enough for backtracking (e.g., `N <= 12`). 2) **ASCII canvas printer** - Implement an ASCII drawing engine with a blank canvas of size `H x W` initialized with spaces. - You will receive a list of drawing commands such as: - `RECT x y width height ch` (fill the rectangle with character `ch`) - `HLINE x1 x2 y ch` (draw a horizontal line) - `VLINE x y1 y2 ch` (draw a vertical line) - Later commands overwrite earlier ones. - Output the final canvas as `H` lines of `W` characters. 3) **Product of array except self** - Given an integer array `nums` of length `n`, return an array `out` where `out[i]` equals the product of all `nums[j]` for `j != i`. - Do not use division. - Target `O(n)` time; extra space should be `O(1)` besides the output array. 4) **2048 move simulation** - Given a `4 x 4` grid of non-negative integers (powers of two or zero) and a direction in `{left, right, up, down}`: - Slide all tiles as far as possible in that direction. - Merge equal adjacent tiles once per move (e.g., `2 2 2 0` moving left becomes `4 2 0 0`, not `8 0 0 0`). - Return the updated grid (optionally also return the score gained from merges).