Use this to program a Futoshiki problem in Python using the backtracking strategy.

Futoshiki

Futoshiki $($inequality$)$ is another number puzzle game that has appeared in Puzzle

Communication Nikoli. Like Sudoku, the goal of Futoshiki is to complete an $\backslash$times $$

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$$output$2024/1/2918$:$35$ page $18$ #$24$

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$18$ Project: Logic Puzzles

Latin square with the digits $1$ to $.$ Rather than using the $3\backslash$times $3$ subsquares of Sudoku,

the puzzle contains inequality constraints specifying that some cells must be greater

than or less than their neighbors.

Try it yourself

Try to solve the following puzzle. Tip: start with the four squares in the lower

left.

$<$

$>$

$$

$$

$<$

$>$

$>$

Solution

The four squares in the lower left must contain $4-3-2-1$ in a cycle. Checking

will show that the top$-$middle squares must then contain $4$ and $1.$

$1234$

$4321$

$3142$

$2413$

$<$

$>$

$$

$$

$<$

$>$

$>$

Modify your Sudoku solving program to solve Futoshiki puzzles. Again, the key is

encoding the constraints. The simplest approach is to make a valid method with one

check per inequality. Remember that you$$ll need to distinguish between constraints

where both variables have been assigned and constraints where one or both variables

are still undetermined

The solution should look like:

$[2,4,1,3]$

$[3,1,4,2]$

$[4,3,2,1]$

$[1,2,3,4]$