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The shape definitions are handed to you so that part isn't the puzzle.
Clarify the five predefined shapes and their orientations, then simulate the placement process by iterating through each figure and scanning the grid in row-major order to find the first valid top-left position. For each candidate position, check if the shape fits within bounds and does not overlap existing cells; if valid, place the figure and update the grid, otherwise skip it.
Pro tip: Discuss how to optimize the placement search by precomputing the shape's bounding box and using a sliding window or early termination to avoid redundant checks, especially for large grids.
Confirm the exact definitions of the five shapes (e.g., their coordinates relative to top-left) and any orientation rules. Ensure you understand the grid dimensions and that placement must be within bounds and non-overlapping.
For each figure in order, iterate through all possible top-left positions in row-major order. For each position, check if the shape fits within the grid and does not overlap any already-filled cells.
Write a helper function to validate a placement at a given position. If valid, fill the corresponding cells with the figure's 1-based index and break to the next figure; if no valid position is found, skip the figure.
Discuss time and space complexity: O(n*m*k) per figure in the worst case, where k is the number of cells in the shape. Consider optimizations like precomputing shape offsets or using a more efficient search if needed.
Walk through examples including empty grid, shapes that exactly fit, shapes that cannot be placed, and multiple figures. Verify the row-major order and 1-based indexing.
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