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: 
def bfs(field,H,W,start_x,start_y,tmp_N):
    direction = [[-1,0],[1,0],[0,-1],[0,1]]
    que = []
    que.append([start_x,start_y])
    INF = 1000000
    min_path = [[INF] * W for i in range(H)]
    min_path[start_y][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 < W and 0 <= ny < H and field[ny][nx] != "X" and min_path[ny][nx] == INF:
                min_path[ny][nx] = min_path[current[1]][current[0]] + 1
                if field[ny][nx] == tmp_N: # at the same cheese-power number
                    return nx,ny,min_path[ny][nx]
                else:
                    que.append([nx,ny])

def getField():
    matrix = []
    first = input().strip()
    H,W,N = map(int,first.split())
    for i in range(H):
        row = list(input().strip())
        for j in range(W):
            if row[j].isdigit():
                row[j] = int(row[j])
        matrix.append(row)
    return matrix,H,W,N

def getStart(field):
    for y in range(len(field)):
        for x in range(len(field[0])):
            if field[y][x] == "S":
                return x,y

def main():
    matrix,H,W,N = getField()
    sx,sy = getStart(matrix)
    distance = 0
    for k in range(N):
        if k != 0:
            tmp_x,tmp_y,tmp_dist = bfs(matrix,H,W,tmps[0],tmps[1],k+1)
            distance += tmp_dist
            tmps = [tmp_x,tmp_y]
        else:
            tmp_x,tmp_y,tmp_dist = bfs(matrix,H,W,sx,sy,k+1)
            distance += tmp_dist
            tmps = [tmp_x,tmp_y]
    print(distance)


if __name__=='__main__':
    main()

Python: def bfs(field,H,W,start_x,start_y,tmp_N):
    direction = [[-1,0],[1,0],[0,-1],[0,1]]
    que = []
    que.append([start_x,start_y])
    INF = 1000000
    min_path = [[INF] * W for i in range(H)]
    min_path[start_y][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 < W and 0 <= ny < H and field[ny][nx] != "X" and min_path[ny][nx] == INF:
                min_path[ny][nx] = min_path[current[1]][current[0]] + 1
                if field[ny][nx] == tmp_N:
                    return nx,ny,min_path[ny][nx]
                else:
                    que.append([nx,ny])

def getField():
    matrix = []
    first = input().strip()
    H,W,N = map(int,first.split())
    for i in range(H):
        row = list(input().strip())
        for j in range(W):
            if row[j].isdigit():
                row[j] = int(row[j])
        matrix.append(row)
    return matrix,H,W,N

def getStart(field):
    for y in range(len(field)):
        for x in range(len(field[0])):
            if field[y][x] == "S":
                return x,y

def main():
    matrix,H,W,N = getField()
    sx,sy = getStart(matrix)
    distance = 0
    tmp_x,tmp_y,tmp_dist = bfs(matrix,H,W,sx,sy,1)
    distance += tmp_dist
    tmps = [tmp_x,tmp_y]
    for k in range(N-1):
        tmp_x,tmp_y,tmp_dist = bfs(matrix,H,W,tmps[0],tmps[1],k+2)
        distance += tmp_dist
        tmps = [tmp_x,tmp_y]
    print(distance)

if __name__=='__main__':
    main()

Python: from collections import deque

H, W, N = map(int, input().split())
field = [list(input()) for i in range(H)]
node_posi = {}
Q = deque()

def search(start, goal):
	Q.append(start)
	while Q:
		x, y, c = Q.popleft()
		searched[y][x] = 1
		
		if ([x, y, 0] == goal):
			return c
		
		for q in range(4):
			nx = x + [1,0,-1,0][q]
			ny = y + [0,1,0,-1][q]
			if (nx >= 0 and nx <= W-1) and (ny >= 0 and ny <= H-1) and (searched[ny][nx] == 0) and (field[ny][nx] != 'X') and (field[ny][nx] != 'S'):
				Q.append([nx, ny, c+1])

for i in range(H):
	for j in range(W):
		if field[i][j] in 'S123456789':
			node_posi[field[i][j]] = [j, i, 0]

s =	'S123456789'
cost = 0
for i in range(len(node_posi)-1):
	Q.clear()
	searched = [[0]*W for i in range(H)]
	cost += search(node_posi[s[i]], node_posi[s[i+1]])
print(cost)

Python: def v():
 from collections import deque
 H,W,N=map(int,input().split())
 e='X'*(W+2)
 M=e+''.join('X'+input()+'X'for _ in[0]*H)+e
 m=(1,-1,W+2,-W-2)
 def f(s,g):
  p,t=s,0
  q=deque()
  b=[1]*len(M);b[s]=0
  while 1:
   for d in m:
    n=p+d
    if'X'!=M[n]and b[n]:
     if M[n]==g:return(n,t+1)
     b[n]=0;q.append([n,t+1])
   p,t=q.popleft()
 s=M.find('S')
 a=0
 for i in range(1,N+1):
  s,t=f(s,str(i))
  a+=t
 print(a)
v()

Python: from collections import deque
import sys
sys.setrecursionlimit(10000)

H, W, N = map(int, input().split())
field = [list(input()) for i in range(H)]
us = [str(i) for i in range(N, 0, -1)]
queue = deque([])
dx = [1,0,-1,0]
dy = [0,1,0,-1]

def search():
	global flag
	global us
	global count
	global queue

	x, y, c = queue.popleft()
	
	if (field[y][x] == us[-1]):
		flag = True
		if (us[-1] == str(N)):
			print(c)
			exit()
		us.pop()
		queue.clear()
		queue.append([x, y, c])
		return

	for q in range(4):
		nx = x + dx[q]
		ny = y + dy[q]
		if (nx >= 0 and nx <= W-1) and (ny >= 0 and ny <= H-1) and ([nx,ny] not in queue) and (field[ny][nx] != 'X') and (field[ny][nx] != 'S'):
			queue.append([nx, ny, c+1])


bf = False
for i in range(H):
	for j in range(W):
		if field[i][j] == 'S':
			c = 0
			queue.append([j, i, c])
			bf = True
			break
	if (bf):
		break

while 1:
	flag = False
	search()