Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

The Goal

You are given a board where you must place magnets and wooden blocks so that all rules are satisfied and the final configuration is stable.

Rules

Each magnet consists of two parts: a blue negative pole (-) and a red positive pole (+). You have an unlimited supply of such magnets. Your task is to place the magnets on the board so that the following conditions are met:

Magnets may only be placed in predefined two-cell regions, which can be oriented horizontally or vertically.
Identical poles (cells with +, -) can't touch each other making the board unstable.
The numbers on the left side of the board (leftHint) indicate the exact number of + poles that must appear in each row.
The numbers above the board (topHint) indicate the exact number of + poles that must appear in each column.
The numbers on the right side of the board (rightHint) indicate the exact number of - poles that must appear in each row.
The numbers below the board (bottomHint) indicate the exact number of - poles that must appear in each column.
The board must be fully covered by magnets and wooden blocks. Each wooden block, like a magnet, occupies a predefined two-cell region, and is marked with x.

For a clearer understanding, see the example below:

Example of a valid solution

Additional Info

- Press the gear icon in the viewer to access extra display options
- This puzzle is based on the logic game Magnets by Simon Tatham
- Source code available on GitHub
- Design available on Figma

Game Input

Initial input

Line 1: single integer width, the width of the board.

Line 2: single integer height, the height of the board.

Line 3: height space-separated integers leftHint (number of + poles in each row, from top to bottom).

Line 4: width space-separated integers topHint (number of + poles in each column, from left to right).

Line 5: height space-separated integers rightHint (number of - poles in each row, from top to bottom).

Line 6: width space-separated integers bottomHint (number of - poles in each column, from left to right).

Note: You will receive -1 if there is no hint specified for given row or column.

Turn input

height lines: each line contains a string of width characters:

+ → cell occupied by the positive pole of a magnet.
- → cell occupied by the negative pole of a magnet.
x → cell occupied by wooden block.
Letter (A–Z, a–z , excluding x) marking predefined two-cell regions which are unoccupied. Identical letters mark two adjacent cells that belong to the same region.

Turn output

Single line: three space-separated values - integers x and y and character symbol (one of +, -, x).
This output will place symbol at [x, y], the coordinates of a cell (the matching cell is placed automatically).

Note: The board's top-left position is [0, 0].

Constraints

5 ≤ width, height ≤ 10

Allotted response time to output in first turn is ≤ 3s
Allotted response time to output in other turns is ≤ 50ms

Solve it

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