Go: ///
// File:  0558.go
// Author: ymiyamoto
//
// Created on Sun Mar  4 20:58:45 2018
//
package main

import (
	"fmt"
	"strconv"
	"strings"
)

type pos struct {
	x, y int
}

var H, W, N int
var graph [][]string

func wfs(p pos, index int) (int, pos) {
	var q []pos
	dists := make([][]int, H)
	for i := range dists {
		dists[i] = make([]int, W)
	}

	q = append(q, p)
	for len(q) > 0 {
		p := q[0]
		dist := dists[p.x][p.y]
		q = q[1:]

		for _, d := range []pos{{-1, 0}, {1, 0}, {0, -1}, {0, 1}} {
			x := p.x + d.x
			y := p.y + d.y
			if 0 <= x && x < H && 0 <= y && y < W && graph[x][y] != "X" && dists[x][y] == 0 {
				dists[x][y] = dist + 1
				q = append(q, pos{x, y})
			}
		}
	}

	for i := range graph {
		for j := range graph[i] {
			if graph[i][j] == strconv.Itoa(index) {
				return dists[i][j], pos{i, j}
			}
		}
	}

	panic("not found")
}

func main() {
	fmt.Scan(&H, &W, &N)

	var start pos

	graph = make([][]string, H)
	for i := range graph {
		var s string
		fmt.Scan(&s)
		graph[i] = strings.Split(s, "")
		for j := range graph[i] {
			if graph[i][j] == "S" {
				start.x = i
				start.y = j
			}
		}
	}

	count := 0
	for i := 1; i <= N; i++ {
		c, s := wfs(start, i)
		start = s
		count += c
	}

	fmt.Println(count)
}

Python: # -*- coding: utf-8 -*-

import sys
sys.setrecursionlimit(10**6)

def calculate_distance(field,locations,current_HP):
	is_visit = [[False for _ in range(len(field[0]))] for __ in range(len(field))]
	frontier = set()
	frontier.add(locations[current_HP-1])
	for step in range(10**6):
		for cx,cy in frontier:
			if (cx,cy)==locations[current_HP]: return step
			is_visit[cx][cy]=True
		next_frontier = set()
		for cx,cy in list(frontier):
			for dx,dy in [[0,1],[0,-1],[1,0],[-1,0]]:
				nx = cx+dx
				ny = cy+dy
				if not (0<=nx<len(field)):		continue
				if not (0<=ny<len(field[nx])):	continue
				if field[nx][ny]=='X':			continue
				if is_visit[nx][ny]: 			continue
				next_frontier.add((nx,ny))
		if len(next_frontier)==0: return
		frontier = next_frontier
	return -10*3

def solve(field,locations):
	total_step=0
	for current_HP in range(1,len(locations)):
		total_step += calculate_distance(field,locations,current_HP)
	return total_step

def main():
	line=input().strip()
	H,W,N=list(map(int,line.split(' ')))
	field,locations=list(),dict()
	for i in range(H):
		field.append(list(input().strip()))
		for j,x in enumerate(field[-1]):
			if x=='S':
				locations[0] = (i,j,)
			if x.isdigit():
				x = int(x)
				field[-1][j] = x
				locations[x] = (i,j,)
	print(solve(field,locations))

if __name__=='__main__':
	main()

Python: 
def getStart(field):
    search_field = field[1:]     # cut the first [H,W,N] for min_path matrix
    for y in range(len(search_field)):
        for x in range(len(search_field[0])):
            if search_field[y][x] == "S":
                return x,y+1


def bfs(field,start_x,start_y,goal_N):
    direction = [[-1,0],[1,0],[0,-1],[0,1]]
    gotten_cheese = 1
    distance = 0
    que = []
    que.append([start_x,start_y])
    INF = 1000000
    min_path = [[INF] * field[0][1] for i in range(field[0][0])]
    min_path[start_y-1][start_x] = 0
    while len(que) != 0:
        current = que.pop(0)
        for d in direction:
            nx = current[0] + d[0]
            ny = current[1] + d[1]
            if 0 <= nx < field[0][1] and 1 <= ny < field[0][0]+1 and field[ny][nx] != "X" and min_path[ny-1][nx] == INF:
                min_path[ny-1][nx] = min_path[current[1]-1][current[0]] + 1
                if field[ny][nx] == gotten_cheese: # at the same cheese-power number
                    distance += min_path[ny-1][nx]
                    if field[ny][nx] == goal_N: # goal
                        print(distance)
                        return
                    else: # not goal, but could eat cheese
                        que = []
                        que.append([nx,ny])
                        gotten_cheese += 1
                        min_path = [[INF] * field[0][1] for i in range(field[0][0])]
                        min_path[ny-1][nx] = 0
                        break
                else:
                    que.append([nx,ny])


def main(field):
    sx,sy = getStart(field)
    bfs(field,sx,sy,field[0][2])

# field = [[10,10,9],
# [".","X",".",".",".","X",".","S",".","X"],
# [6,".",".",5,"X",".",".","X",1,"X"],
# [".",".",".","X","X","X","X",".",".","X"],
# ["X",".",".",9,"X",".",".",".","X","."],
# [8,".","X",2,"X",".",".","X",3,"X"],
# [".",".",".","X","X",".","X",4,".","."],
# ["X","X",".",".",".",".",7,"X",".","."],
# ["X",".",".","X",".",".","X","X",".","."],
# ["X",".",".",".","X",".","X","X",".","."],
# [".",".","X",".",".",".",".",".",".","."]]
#
# main(field)

matrix = []
while True:
    row = input().rstrip().split()
    if len(row) == 3:
        re_row = []
        for i in row:
            re_row.append(int(i))
        matrix.append(re_row)
    else:
        re_row = []
        for char in row[0]:
            if char.isdigit():
                re_row.append(int(char))
            else:
                re_row.append(char)
        matrix.append(re_row)
    if len(matrix) == int(matrix[0][0]) + 1:
        main(matrix)
        break

Python: import queue


# directions
x_dir = [0, 1, 0, -1]
y_dir = [1, 0, -1, 0]


# bfs algorithm
def bfs(h, w, cheese, maps, sx, sy, moves, visited):
    que = queue.Queue()
    que.put((moves, sx, sy))

    for i in range(h):
        for j in range(w):
            visited[i][j] = True

    visited[sy][sx] = False

    while que.qsize() > 0:
        c_moves, c_x, c_y = que.get()
        if maps[c_y][c_x] == cheese:
            return (c_moves, c_x, c_y)

        for i in range(4):
            n_x = c_x + x_dir[i]
            n_y = c_y + y_dir[i]

            if(0 <= n_x < w and 0 <= n_y < h and visited[n_y][n_x] and maps[n_y][n_x] != 'X'):
                que.put((c_moves+1, n_x, n_y))
                visited[n_y][n_x] = False

    return (-1, -1, -1)


# simulate mouse
def simulate(h, w, n, maps, sx, sy):
    moves = 0
    x, y = sx, sy

    visited = [[True for i in range(w)] for j in range(h)]

    for i in range(1, n+1, 1):
        moves, x, y = bfs(h, w, str(i), maps, x, y, moves, visited)

    return str(moves)


# main function
def main():
    str = (input()).split()

    H = int(str[0])
    W = int(str[1])
    N = int(str[2])

    maps = []
    sx, sy = 0, 0
    for i in range(H):
        maps.append(input())
        for j in range(W):
            if maps[i][j] == 'S':
                sx, sy = j, i

    print(simulate(H, W, N, maps, sx, sy))


if __name__ == '__main__':
    main()

Python: # -*- coding: utf-8 -*-

def get_shortest_distance(field,locations,current_HP):
	is_visit = [[False for _ in range(len(field[0]))] for __ in range(len(field))]
	frontier = set()
	frontier.add(locations[current_HP-1])
	for step in xrange(10**10):
		for cx,cy in frontier:
			if (cx,cy)==locations[current_HP]: return step
			is_visit[cx][cy]=True
		next_frontier = set()
		for cx,cy in list(frontier):
			for dx,dy in [[0,1],[0,-1],[1,0],[-1,0]]:
				nx = cx+dx
				ny = cy+dy
				if not (0<=nx<len(field)):		continue
				if not (0<=ny<len(field[nx])):	continue
				if field[nx][ny]=='X':			continue
				if is_visit[nx][ny]: 			continue
				next_frontier.add((nx,ny))
#		assert len(next_frontier)!=0,(current_HP,is_visit,frontier)
		frontier = next_frontier
#	assert True,('the goal is not reachable')

def solve(field,locations):
	total_step=0
	for current_HP in range(1,len(locations)):
		total_step += get_shortest_distance(field,locations,current_HP)
	return total_step

def main():
	line=input().strip()
	H,W,N=list(map(int,line.split(' ')))
	field,locations=list(),dict()
	for i in range(H):
		field.append(list(input().strip()))
		for j,x in enumerate(field[-1]):
			if x=='S':
				locations[0] = (i,j,)
			if x.isdigit():
				x = int(x)
				field[-1][j] = x
				locations[x] = (i,j,)
	print(solve(field,locations))

if __name__=='__main__':
	main()