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)
}

C++: #include<cstdio>
#include<iostream>
#include<algorithm>
#include<queue>
using namespace std;
struct k{
    int nx;
    int ny;
    int power;
    int nowans;
};
int fiemin[15][1002][1002];
int main(){
    int h,w,n;
    char fie[1002][1002];
    for(int i=0;i<15;i++){
        for(int j=0;j<1002;j++){
            for(int k=0;k<1002;k++){
                fiemin[i][j][k]=2100000000;
            }
        }
    }
    int nx,ny,po,judge;
    struct k now;
    queue<k> que;
    scanf("%d %d %d",&h,&w,&n);
    for(int i=0;i<h;i++)
        scanf("%s",&fie[i]);
    for(int i=0;i<h;i++){
        for(int j=0;j<w;j++){
            if(fie[i][j]=='S'){
                now.ny=i,now.nx=j,now.power=0,now.nowans=0;
                fie[i][j]='.';
                goto a;
            }
        }
    }
a:
    que.push(now);
    for(int i=0;;i++){
        now=que.front(),que.pop();

        //printf("[%d][%d][%d][%d]\n",now.nx,now.ny,now.nowans,now.power);

        if(now.power==n){
            printf("%d\n",now.nowans);
            break;
        }
        judge=1;
        if(0<=now.ny-1){
            if(fie[now.ny-1][now.nx]==now.power+1+'0'){
                if(now.nowans+1<fiemin[now.power+1][now.ny-1][now.nx]){
                        while (!que.empty())
                            que.pop();
                        now.ny--,now.power++,now.nowans++;
                        que.push(now);
                        fiemin[now.power+1][now.ny][now.nx]=now.nowans;
                        now.ny++,now.power--,now.nowans--;
                }
            }
            else if(fie[now.ny-1][now.nx]!='X'){
                if(now.nowans+1<fiemin[now.power][now.ny-1][now.nx]){
                        now.ny--,now.nowans++;
                        que.push(now);
                        fiemin[now.power][now.ny][now.nx]=now.nowans;
                        now.ny++,now.nowans--;
                }
            }
        }
        judge=1;
        if(now.nx+1<w){
            if(fie[now.ny][now.nx+1]==now.power+1+'0'){
                if(now.nowans+1<fiemin[now.power+1][now.ny][now.nx+1]){
                        while (!que.empty())
                            que.pop();
                        now.nx++,now.power++,now.nowans++;
                        que.push(now);
                        fiemin[now.power+1][now.ny][now.nx]=now.nowans;
                        now.nx--,now.power--,now.nowans--;
                }
            }
            else if(fie[now.ny][now.nx+1]!='X'){
                if(now.nowans+1<fiemin[now.power][now.ny][now.nx+1]){
                        now.nx++,now.nowans++;
                        que.push(now);
                        fiemin[now.power][now.ny][now.nx]=now.nowans;
                        now.nx--,now.nowans--;
                }
            }
        }
        judge=1;
        if(now.ny+1<h){
            if(fie[now.ny+1][now.nx]==now.power+1+'0'){
                if(now.nowans+1<fiemin[now.power+1][now.ny+1][now.nx]){
                        while (!que.empty())
                            que.pop();
                        now.ny++,now.power++,now.nowans++;
                        que.push(now);
                        fiemin[now.power+1][now.ny][now.nx]=now.nowans;
                        now.ny--,now.power--,now.nowans--;
                }
            }
            else if(fie[now.ny+1][now.nx]!='X'){
                if(now.nowans+1<fiemin[now.power][now.ny+1][now.nx]){
                        now.ny++,now.nowans++;
                        que.push(now);
                        fiemin[now.power][now.ny][now.nx]=now.nowans;
                        now.ny--,now.nowans--;
                }
            }
        }
        judge=1;
        if(0<=now.nx-1){
            if(fie[now.ny][now.nx-1]==now.power+1+'0'){
                if(now.nowans+1<fiemin[now.power+1][now.ny][now.nx-1]){
                        while (!que.empty())
                            que.pop();
                        now.nx--,now.power++,now.nowans++;
                        que.push(now);
                        fiemin[now.power+1][now.ny][now.nx]=now.nowans;
                        now.nx++,now.power--,now.nowans--;
                }
            }
            else if(fie[now.ny][now.nx-1]!='X'){
                if(now.nowans+1<fiemin[now.power][now.ny][now.nx-1]){
                        now.nx--,now.nowans++;
                        que.push(now);
                        fiemin[now.power][now.ny][now.nx]=now.nowans;
                        now.nx++,now.nowans--;
                }
            }
        }
    }
    return 0;
}

C++: #include <algorithm>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <map>
#include <math.h>
#include <set>
#include <stdio.h>
#include <string>
#include <utility>
#include <vector>

using namespace std;

struct N {
  int x, y, cost;
};

bool operator<(const N &lhs, const N &rhs) { return lhs.cost < rhs.cost; }

int main() {
  int h, w, n;
  cin >> h >> w >> n;
  vector<pair<int, int>> gp(n + 1);
  vector<string> mp(h);
  for (int i = 0; i < h; i++) {
    cin >> mp[i];
  }
  for (int i = 0; i < h; i++)
    for (int j = 0; j < w; j++) {
      if (mp[i][j] == 'S') {
        gp[0].first = j;
        gp[0].second = i;
      } else if (mp[i][j] >= '1' && mp[i][j] <= '9') {
        gp[mp[i][j] - '0'].first = j;
        gp[mp[i][j] - '0'].second = i;
      }
    }

  int hx[4] = {0, 0, 1, -1};
  int hy[4] = {1, -1, 0, 0};

  int ans = 0;
  for (int i = 0; i < n; i++) {
    multiset<N> q;
    N start{gp[i].first, gp[i].second, 0};
    q.insert(start);
    vector<vector<bool>> ch(h);
    for (int j = 0; j < h; j++)
      ch[j].resize(w);
    while (q.size() > 0) {
      N now = *q.begin();
      q.erase(q.begin());
      if (ch[now.y][now.x])
        continue;
      ch[now.y][now.x] = true;
      if (now.y == gp[i + 1].second && now.x == gp[i + 1].first) {
        ans += now.cost;
        break;
      }
      for (int j = 0; j < 4; j++) {
        int nx = now.x + hx[j], ny = now.y + hy[j];
        if (nx < 0 || nx >= w || ny < 0 || ny >= h)
          continue;
        if (mp[ny][nx] == 'X')
          continue;
        N next{nx, ny, now.cost + 1};
        q.insert(next);
      }
    }
  }
  cout << ans << endl;
  return 0;
}