figure_solver.py

from collections import deque
grid = [3,3,1,3,2,2,0,0,2,1,2,0,0,0,0,0,1,1,3,0,3,3,1,0,3]
todo = deque([(grid, [])])
seen = set()
while True:
    grid, trail = todo.pop()
    if sum(grid) == -25:
        print(trail)
        exit(0)
    for x_col in range(5):
        target = grid[x_col + 20]
        if target != -1:
            temp = grid[:]
            flood = deque([(x_col, 4)])
            while len(flood):
                x, y = flood.pop()
                temp[x+y*5] = -1
                for xo, yo in [[-1, 0], [1, 0], [0, -1], [0, 1]]:
                    if 0 <= x+xo <= 4 and 0 <= y+yo <= 4 and temp[x+xo+(y+yo)*5] == target:
                        flood.append((x+xo,y+yo))
            for x in range(5):
                col = [temp[x+y*5] for y in range(4,-1,-1)]
                if sum(col) != -5:
                    col = [i for i in col if i >= 0]
                    col = col + [-1] * (5 - len(col))
                    for i, val in enumerate(col):
                        temp[x + (4 - i) * 5] = val
            if tuple(temp) not in seen:
                seen.add(tuple(temp))
                todo.appendleft((temp, trail + [x_col]))