p$\_$idxs $-$ a set of tuples representing pawn locations

$k_{-}$idx $-$ a tuple representing the starting position of a knight

Return a boolean denoting whether the passed in p$\_$idxs and k$\_$idx represent a solveable board

$\frac{?}{?}$#$3---k----$

$\frac{?}{?}$#$4--p----$

$\frac{?}{?}$#$5-----p--$

$\frac{?}{?}$#$6---p----$

$\frac{?}{?}$#$7--------$Row $7$: $(7,0),(7,1),(7,2),$dots$(7,7)$

$k_{-}$idx$=(3,3)\frac{?}{?}$# Initial knight index

$p_{i}dxs=\{(1,3),(2,1),(2,5),(4,2),(5,5),(6,3)\}\frac{?}{?}$# Set $of$ pawn indices

This board is solveable. Our knight can capture all $6$ pawns with $6$ consecutive moves:

$(2,5),(1,3),(2,1),(4,2),(6,3),(5,5)$

However, the following board is not solveable:

$\frac{?}{?}$# $01234567$

$\frac{?}{?}$#$O-....-$ Row $0$: $(0,0),(0,1),(0,2),$dots$(0,7)$

$\frac{?}{?}$#$1--------$

$\frac{?}{?}$#$2-p--p--$

$\frac{?}{?}$#$3---k----$

$\frac{?}{?}$#$4--p----$

$\frac{?}{?}$#$5-----p--$

$\frac{?}{?}$#$6---p---$

$\frac{?}{?}$#$7--------$Row $7$: $(7,0),(7,1),(7,2),$dots$(7,7)$

$k_{-}$idx$=(3,3)\frac{?}{?}$#Initial knight index

$p_{i}dxs=\{(2,1),(2,5),(4,2),(5,5),(6,3)\}\frac{?}{?}$# Set $of$ pawn indices

There is no way for our knight to capture all $5$ pawns in just $5$ moves.

Deliverables

Write Unittests

Use TDD on this assignment$-$ write a test, run it$,$ then implement functionality. You will be graded on your

tests. Starter code for

TestHw$5.$py includes some guidance on tests. Do not use the examples above as boards

in your tests.

Implment valid$\_$moves$($k$\_$idx$)$

valid$\_$moves$($k$\_$idx$)$ returns a set of tuples representing all valid moves for a knight at $k_{-}$idx.

Implement solveable$($p$\_$idxs, k$\_$idx$)$:

p$\_$idxs $-$ a set of tuples representing pawn locations

k$\_$idx $-$ a tuple representing the starting position of a knight

Return a boolean denoting whether the passed in p$\_$idxs and k$\_$idx represent a solveable board