Spirals

In the file "Spirals$/$main$.$cpp$",$ write a function Counting$\_$Spiral$()$ which generated a $2$D vector of characters representing a spiral of numbers as show below.

$432$

$501$

$678$

The numbers will start at the center of the spiral and spiral outwards in the manner shown above.

The parameter length is the side length of the square and will always be an odd number, therefore there is always center.

The numbers will be modded $(\%)$ by $10$ to ensure they are single digits.

Here is an example with length $=5$ without the mod $10($Not what your function should output$)$

$1615141312$

$1743211$

$1850110$

$196789$

$2021222324$

And here is the same example with the mod $10($Desired Output$)$

$65432$

$74321$

$85010$

$96789$

$01234$

Here is what your vector indexes should look like for length $=3$

$[0][0]=\text{'}4\text{'}[0][1]=\text{'}3\text{'}[0][2]=\text{'}2\text{'}$

$[1][0]=\text{'}5\text{'}[1][1]=\text{'}0\text{'}[1][2]=\text{'}1\text{'}$

$[2][0]=\text{'}6\text{'}[2][1]=\text{'}7\text{'}[2][2]=\text{'}8\text{'}$

Algorithms

The starting point of every spiral is the $0$ in the center

Always initialize vectors to the final size of the spiral

You should assume you$$re done when you hit the bounds of the vectors

Use a $($x$,$y$)$ plane to visualize the algorithms first

Focus on creating some small spirals $(3$x$3$ & $5$x$5)$ first

There are two algorithms to generate the spiral:

Imagine line segments spiraling out from the center. Each line segment bellow is identified by a different letter, and their direction rotates through the cardinal directions $($up$,$ down, left right$).$ Every $2$ segments the length increases by $1.$

h h h h g

i d d c g

i e a b g

i e f f f

i j j j j j

b $=1$ right f $=3$ right

c $=1$ up g $=3$ up

d $=2$ left h $=4$ left

e $=2$ down i $=4$ down

j $=5$ right

Define bounds within the x$,$y plane to create a small portion of the spiral fill it in$,$ and then increase the bounds by one in each direction and repeat. When filling in$,$ add numbers in a direction until you hit a bound, then change direction.

$1$x$13$x$35$x$5$

x x x x x x x x x x $65432$

x x x x x x $432$ x $74321$

x x $0$ x x $-->$ x $501$ x $-->85010-->$ NxN

x x x x x x $678$ x $96789$

x x x x x x x x x x $01234$

Test locally and visually inspect your output with Two$\_$D$\_$Vector$\_$To$\_$String$().$ Visualizing whats going on is key to developing the algorithm.