Merge Quad Regions Algorithm

2024-04-04 11:04 UTC gpt-4 Open in ChatGPT ↗

I have this python fucntion that merges single excel cells into regions, if they can be merged.

I want to make a similar function, that operates on bigger quad regions, and merges them further if they can be merged (if their width or height is the same, and they are next to each other or above/below eaach other)

def merge_cells(cells): # Converts a list of cell references into a minimal set of rectangular ranges. # First, convert all cell references to numeric coordinates. coords = [cell_to_coords(cell) for cell in cells]

# Sort coordinates to prepare for grouping.
coords.sort()

# Group cells by rows to identify potential blocks for merging.
rows = {}
for r, c in coords:
    if r in rows:
        rows[r].append(c)
    else:
        rows[r] = [c]

# Attempt to merge contiguous columns within each row.
merged = []

for r in rows:
    rows[r].sort()
    start_col = rows[r][0]
    last_col = start_col

    for c in rows[r][1:]:
        if c == last_col + 1:
            # If the current column is adjacent to the last, extend the range.
            last_col = c
        else:
            # If not contiguous, finalize the current range and start a new one.
            merged.append(((r, start_col), (r, last_col)))
            start_col = last_col = c

    # Ensure the last range in the row is added.
    merged.append(((r, start_col), (r, last_col)))

# Now, attempt to merge these horizontal ranges vertically.
final_merged = []
while merged:
    base = merged.pop(0)
    i = 0
    while i < len(merged):
        # Check if the current range is vertically adjacent to the base range and has matching column boundaries.
        if merged[i][0][1] == base[0][1] and merged[i][1][1] == base[1][1] and (merged[i][0][0] == base[1][0] + 1 or merged[i][1][0] == base[0][0] - 1):
            # Merge vertically by expanding the base range.
            base = ((min(base[0][0], merged[i][0][0]), base[0][1]), (max(base[1][0], merged[i][1][0]), base[1][1]))
            merged.pop(i)
        else:
            i += 1
    final_merged.append(base)

# Convert numeric ranges back to Excel range references.
range_strs = []
for start, end in final_merged:
    start_cell = coords_to_cell(start[0], start[1])
    end_cell = coords_to_cell(end[0], end[1])

    if start_cell == end_cell:
        # For a single cell, just return its reference.
        range_strs.append(start_cell)
    else:
        # For a range, return the starting and ending references.
        range_strs.append(f"{start_cell}:{end_cell}")

return range_strs

To create a similar function that operates on larger quad regions (essentially groups of already merged cells or regions) and merges them further based on their width or height, we need to approach this by treating each initially merged region as a ‘cell’ in the broader context. Here’s a conceptual breakdown on how to approach this:

Input Format Adjustment: Assume the input is a list of tuples representing merged regions. Each tuple has the format ((start_row, start_col), (end_row, end_col)), where start_row and start_col define the upper-left corner of the region, and end_row and end_col define the lower-right corner.
Merging Logic Extension: The merging logic must now consider both horizontal and vertical possibilities for merging these larger regions. This involves checking if the regions are adjacent (either directly above/below or next to each other) and if their corresponding widths or heights match.
Implementation:
- Horizontal Merging: Check if regions are on the same row (start_row of one region is equal to start_row of another) and if the width (calculated by end_col - start_col + 1) is the same. If they’re adjacent (the end_col of one region is immediately next to the start_col of the other), they can be merged horizontally.
- Vertical Merging: Check if regions are in the same column (start_col of one region is equal to start_col of another) and if the height (calculated by end_row - start_row + 1) is the same. If they’re adjacent (the end_row of one region is immediately above the start_col of the other), they can be merged vertically.
Output Format: The output remains a list of tuples with the format ((start_row, start_col), (end_row, end_col)), representing the new, larger merged regions.

Let’s draft a Python function to implement this logic:

def merge_quad_regions(regions):
    # Sort regions by start row and start column to prepare for merging.
    regions.sort(key=lambda x: (x[0][0], x[0][1]))

    # Attempt to merge horizontally first.
    horizontal_merged = []
    while regions:
        base = regions.pop(0)
        i = 0
        while i < len(regions):
            # Check if the regions are adjacent and have the same height.
            if (regions[i][0][0] == base[0][0] and regions[i][1][0] == base[1][0]) and \
               (regions[i][0][1] == base[1][1] + 1 or regions[i][1][1] == base[0][1] - 1):
                # Merge horizontally.
                base = ((base[0][0], min(base[0][1], regions[i][0][1])), (base[1][0], max(base[1][1], regions[i][1][1])))
                regions.pop(i)
            else:
                i += 1
        horizontal_merged.append(base)

    # Attempt to merge the horizontally merged regions vertically.
    vertical_merged = []
    while horizontal_merged:
        base = horizontal_merged.pop(0)
        i = 0
        while i < len(horizontal_merged):
            # Check if the regions are adjacent and have the same width.
            if (horizontal_merged[i][0][1] == base[0][1] and horizontal_merged[i][1][1] == base[1][1]) and \
               (horizontal_merged[i][0][0] == base[1][0] + 1 or horizontal_merged[i][1][0] == base[0][0] - 1):
                # Merge vertically.
                base = ((min(base[0][0], horizontal_merged[i][0][0]), base[0][1]), (max(base[1][0], horizontal_merged[i][1][0]), base[1][1]))
                horizontal_merged.pop(i)
            else:
                i += 1
        vertical_merged.append(base)

    return vertical_merged

This function starts by trying to merge adjacent regions horizontally and then attempts to merge the resulting regions vertically, ensuring that both width and height criteria are respected. Remember, the implementation assumes that each input region is already a minimal merged block from the previous process.

Given that your regions are represented in Excel notation (like “A1:B2”), we’ll adjust the function to first convert these notations into numerical coordinates before proceeding with the merging logic. The steps include:

Parsing Excel Notation: Convert the region notation from Excel’s alphanumeric format to numerical coordinates. This involves splitting the notation into start and end parts, then converting the column letters to numbers.
Merging Logic: Utilize the same logic as described earlier, but with the regions now in a numeric format.
Output Conversion: Convert the merged numeric regions back to Excel notation for the output.

Here’s a comprehensive function including these steps:

def excel_to_coords(excel_ref):
    """Convert Excel cell reference to numeric coordinates (row, col)."""
    col_part, row_part = '', ''
    for char in excel_ref:
        if char.isdigit():
            row_part += char
        else:
            col_part += char
    col = sum((ord(char) - ord('A') + 1) * (26 ** i) for i, char in enumerate(reversed(col_part.upper())))
    row = int(row_part)
    return row, col

def coords_to_excel(row, col):
    """Convert numeric coordinates to Excel cell reference."""
    col_part = ''
    while col:
        col, remainder = divmod(col - 1, 26)
        col_part = chr(remainder + ord('A')) + col_part
    row_part = str(row)
    return f"{col_part}{row_part}"

def merge_quad_regions_excel(regions):
    # Convert region notations to numeric coordinates.
    numeric_regions = []
    for region in regions:
        start_ref, end_ref = region.split(':')
        start_coords = excel_to_coords(start_ref)
        end_coords = excel_to_coords(end_ref)
        numeric_regions.append((start_coords, end_coords))

    # Merge regions (numeric logic from the previous example).
    # This step would be identical to the merging logic provided earlier,
    # so it's omitted here for brevity. Let's assume the function returns
    # merged numeric regions.
    merged_numeric_regions = merge_quad_regions(numeric_regions)  # Assuming this function exists and operates on numeric regions.

    # Convert merged numeric regions back to Excel notation.
    merged_excel_regions = [f"{coords_to_excel(*start)}:{coords_to_excel(*end)}" for start, end in merged_numeric_regions]

    return merged_excel_regions

# Example usage:
regions = ["A1:B2", "A3:B4", "C1:D2", "C3:D4"]  # Example input regions in Excel notation.
merged_regions = merge_quad_regions_excel(regions)
print(merged_regions)

This code snippet assumes the presence of a merge_quad_regions function that takes numeric regions as input and returns merged numeric regions. Since we’ve previously discussed the conceptual approach for merging, you should integrate that logic into the merge_quad_regions function or adjust the merging part of merge_quad_regions_excel directly.

Remember, excel_to_coords and coords_to_excel are utility functions for converting between Excel’s alphanumeric cell references and numeric coordinates, facilitating the process of merging based on numeric calculations and then converting back to the Excel notation for the output.

To process both single cells and larger regions from the same function, we need to adjust our approach to accommodate both types of input. Here’s how you can achieve this:

Input Processing: Modify the function to accept a list of cell references and regions. Single cells will be treated as regions with the same start and end points.
Normalization: Convert all inputs, whether single cells or regions, into a uniform format of numeric coordinates representing the top-left and bottom-right corners of each region.
Merging: Apply the same merging logic as before to these numeric regions.
Output Conversion: Convert the numeric coordinates of merged regions back into Excel notation.

Let’s integrate these steps into a single function:

def cell_or_region_to_coords(input_ref):
    """Convert Excel cell or region reference to numeric coordinates."""
    if ':' in input_ref:
        start_ref, end_ref = input_ref.split(':')
    else:
        start_ref = end_ref = input_ref
    start_coords = excel_to_coords(start_ref)
    end_coords = excel_to_coords(end_ref)
    return start_coords, end_coords

def merge_cells_and_regions(inputs):
    # Convert all inputs to numeric coordinates.
    numeric_regions = [cell_or_region_to_coords(input_ref) for input_ref in inputs]

    # Sort and prepare for merging. This example will not reimplement the merging logic,
    # but it should follow the principles outlined previously.
    numeric_regions.sort(key=lambda x: (x[0][0], x[0][1]))
    # Implement merging logic here, similar to merge_quad_regions, adapted as necessary.
    merged_numeric_regions = merge_quad_regions(numeric_regions)  # Placeholder for actual merging logic.

    # Convert merged numeric regions back to Excel notation.
    merged_excel_regions = [f"{coords_to_excel(*start)}:{coords_to_excel(*end)}" if start != end else coords_to_excel(*start) for start, end in merged_numeric_regions]

    return merged_excel_regions

# This utility function assumes the existence of excel_to_coords and coords_to_excel,
# which you need to define or reuse from earlier examples.

# Example usage:
inputs = ["A1", "B1:C2", "D3", "A4:B5"]  # Mixed single cells and regions in Excel notation.
merged_regions = merge_cells_and_regions(inputs)
print(merged_regions)

In this integrated approach, the key is the cell_or_region_to_coords function, which interprets both single cells and regions uniformly as coordinate pairs. This allows the merging logic (which you should adapt based on the specifics of how you want regions to be merged) to operate on a consistent data format.

Note: The placeholder merge_quad_regions should be replaced with the actual implementation of your merging logic, which might involve both horizontal and vertical checks and potentially additional steps to handle single cells effectively. This approach ensures that all types of input are normalized to a format that facilitates merging, after which they are converted back into the appropriate Excel notation.