Optimize dict ints tuple set with Numba?

Question

I am learning how to use Numba (although I am already pretty familiar with Cython). How do I speed up this code? Note that the function returns dict sets of two int tuples. I am using an IPython laptop. I would prefer Numba over Keaton.

@autojit
def generateadj(width,height):
    adj = {}
    for y in range(height):
        for x in range(width):
            s = set()
            if x>0:
                s.add((x-1,y))
            if x<width-1:
                s.add((x+1,y))
            if y>0:
                s.add((x,y-1))
            if y<height-1:
                s.add((x,y+1))
            adj[x,y] = s
    return adj

I managed to write this in Cython, but I had to abandon the way of structuring data. I do not like it. I read somewhere in the Numba documentation that it can work with basic things like lists, tuples, etc.

%%cython
import numpy as np

def generateadj(int width, int height):
    cdef int[:,:,:,:] adj = np.zeros((width,height,4,2), np.int32)
    cdef int count

    for y in range(height):
        for x in range(width):
            count = 0
            if x>0:
                adj[x,y,count,0] = x-1
                adj[x,y,count,1] = y
                count += 1
            if x<width-1:
                adj[x,y,count,0] = x+1
                adj[x,y,count,1] = y
                count += 1
            if y>0:
                adj[x,y,count,0] = x
                adj[x,y,count,1] = y-1
                count += 1
            if y<height-1:
                adj[x,y,count,0] = x
                adj[x,y,count,1] = y+1
                count += 1
            for i in range(count,4):
                adj[x,y,i] = adj[x,y,0]
    return adj

Answer 1

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@jit
def gen_adj_loop(width, height, adj):
    i = 0
    for x in range(width):
        for y in range(height):
            if x > 0:
                adj[i,0] = x
                adj[i,1] = y
                adj[i,2] = x - 1
                adj[i,3] = y
                i += 1

            if x < width - 1:
                adj[i,0] = x
                adj[i,1] = y
                adj[i,2] = x + 1
                adj[i,3] = y
                i += 1

            if y > 0:
                adj[i,0] = x
                adj[i,1] = y
                adj[i,2] = x
                adj[i,3] = y - 1
                i += 1

            if y < height - 1:
                adj[i,0] = x
                adj[i,1] = y
                adj[i,2] = x
                adj[i,3] = y + 1
                i += 1
    return

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3 4 4 4
3 4 3 3
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:

@jit
def gen_adj(width, height):
    # each pixel has four neighbors, but some of these neighbors are
    # off the grid -- 2*width + 2*height of them to be exact
    n_entries = width*height*4 - 2*width - 2*height
    adj = np.zeros((n_entries, 4), dtype=int)
    gen_adj_loop(width, height, adj)

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