# Magnet Puzzle | Backtracking-9

The puzzle game Magnets involves placing a set of domino-shaped magnets (or electrets or other polarized objects) in a subset of slots on a board so as to satisfy a set of constraints. For example, the puzzle on the left has the solution shown on the right:

Each slot contains either a blank entry (indicated by ‘x’s), or a “magnet” with a positive and negative end. The numbers along the left and top sides show the numbers of ‘+’ squares in particular rows or columns. Those along the right and bottom show the number of ‘-’ signs in particular rows or columns. Rows and columns without a number at one or both ends are unconstrained as to the number of ‘+’ or ‘-’ signs, depending on which number is not present. In addition to fulfilling these numerical constraints, a puzzle solution must also satisfy the constraint that no two orthogonally touching squares may have the same sign (diagonally joined squares are not constrained).

You are given top[], bottom[], left[], right[] arrays indicates the count of + or – along the top(+), bottom(-), left(+) and right(-) edges respectively. Values of -1 indicate any number of + and – signs. Also given matrix rules[][] contain any one T, B, L or R characters. For a vertical slot in the board, T indicates its top end and B indicates the bottom end. For a horizontal slot in the board, L indicates left end and R indicates the right end.

Examples:

Input : M = 5, N = 6 top[] = { 1, -1, -1, 2, 1, -1 } bottom[] = { 2, -1, -1, 2, -1, 3 } left[] = { 2, 3, -1, -1, -1 } right[] = { -1, -1, -1, 1, -1 } rules[][] = { { L, R, L, R, T, T }, { L, R, L, R, B, B }, { T, T, T, T, L, R }, { B, B, B, B, T, T }, { L, R, L, R, B, B }}; Output : + - + - X - - + - + X + X X + - + - X X - + X + - + X X X - Input : M = 4, N = 3 top[] = { 2, -1, -1 } bottom[] = { -1, -1, 2 } left[] = { -1, -1, 2, -1 } right[] = { 0, -1, -1, -1 } rules[][] = { { T, T, T }, { B, B, B }, { T, L, R }, { B, L, R } }; Output : + X + – X – + – + – + –

We can solve this problem using Backtracking.

**Source :**https://people.eecs.berkeley.edu/~hilfingr/programming-contest/f2012-contest.pdf

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