added puzzle solution

solve.py

@@ -0,0 +1,129 @@
+import pprint
+import operator
+import numpy as np
+import math
+from copy import copy, deepcopy
+
+piece=[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0]]
+sizeofcube=5
+
+def init_cube(size=sizeofcube):
+    return [[[0 for x in range(0,size)] for y in range(0,size)] for z in range(0,size)]
+
+def move_start_position(piece,index):
+    return [np.subtract(x, piece[index]) for x in piece]
+
+def draw_cube(cube):
+    from mpl_toolkits.mplot3d import Axes3D
+    import matplotlib.pyplot as plt
+    fig = plt.figure()
+    ax = fig.gca(projection='3d')
+    ax.set_aspect('equal')
+    ax.set_xlabel('x', fontsize=10)
+    ax.set_ylabel('y', fontsize=10)
+    ax.set_zlabel('z', fontsize=10)
+
+    ma=np.array(cube)
+    ax.voxels(ma, edgecolor="k")
+    plt.show()
+
+def put_piece_in_cube(piece,cube,position,index):
+    cursors = [np.add(position,p) for p in piece]
+    in_cube = [ max(c) < len(cube) and min(c) >= 0 for c in cursors]
+    if all(in_cube):
+        for cursor in cursors:
+            try:
+                if cube[cursor[0]][cursor[1]][cursor[2]]!=0:
+                    return False
+            except:
+                return False
+        for cursor in cursors:
+            cube[cursor[0]][cursor[1]][cursor[2]]=index
+        return True
+    else:
+        return False
+
+def rotate_vector(vector,axis,angle):
+    x,y,z=vector
+    angle=math.radians(angle)
+    if axis == "z":
+        return (int(round((x*math.cos(angle)) - (y*math.sin(angle)))),int(round((x*math.sin(angle)) + (y*math.cos(angle)))),z)
+    if axis == "y":
+        return (int(round(x*math.cos(angle) + z*math.sin(angle))),y,int(round(-x*math.sin(angle) + z*math.cos(angle))))
+    if axis == "x":
+        return (x,int(round(y*math.cos(angle) - z*math.sin(angle))),int(round(y*math.sin(angle) + z*math.cos(angle))))
+
+def rotate_piece(piece,axis,angle):
+    return [rotate_vector(x, axis, angle) for x in piece]
+
+def shift_piece(piece,anchor_index):
+    anchor=piece[anchor_index]
+    return [np.subtract(p,anchor) for p in piece]
+
+def generate_rotations(piece):
+    all_rotations=set()
+    for i in range(0,4):
+        for j in range(0,4):
+            for k in range(0,4):
+                for p in range(0,5):
+                    rotated_piece=rotate_piece(rotate_piece(rotate_piece(shift_piece(piece,p),"x",k*90),"y",j*90),"z",i*90)
+                    all_rotations.add(tuple(rotated_piece))
+    return frozenset(all_rotations)
+
+def find_empty_spot(cube):
+    for z in range(0,sizeofcube):
+        for y in range(0,sizeofcube):
+            for x in range(0,sizeofcube):
+                if cube[x][y][z]==0:
+                    return (x,y,z)
+    return None
+
+def solve(cube,index):
+    #make copy of cube
+    global maxindex
+    if index > maxindex:
+        print(index)
+        maxindex=index
+
+    backup=deepcopy(cube)
+    # draw_cube(backup)
+    #make copy of available pieces
+    global all_rotations
+    pieces=set(all_rotations.copy())
+
+    # print("{}:find empty spot#########################".format(index))
+    empty_pos=find_empty_spot(backup)
+
+    if empty_pos==None:
+        pprint.pprint(cube)
+        draw_cube(cube)
+        return True
+    else:
+        (x,y,z)=empty_pos
+        # print("{}:empty_spot at ({},{},{})".format(index,x,y,z))
+        #found empty space > trying to fill it
+        while len(pieces)>0:
+            #use copy of cube without my parts
+            local_cube=deepcopy(backup)
+            piece=pieces.pop()
+            if put_piece_in_cube(piece, local_cube, (x,y,z), index):
+                # print("{}:found fitting piece {} ({} left)".format(index,piece,len(pieces)))
+                if solve(local_cube, index+1):
+                    return True
+                else:
+                    # print("{}:removing ({},{},{}):{}".format(index,x,y,z,len(pieces)))
+                    pass
+        #nothing fits return fail
+        return False
+
+
+maxindex=0
+
+
+def main():
+    global all_rotations
+    all_rotations=generate_rotations(piece)
+    solve(init_cube(),1)
+
+if __name__ == '__main__':
+    main()