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 <bits/stdc++.h>
using namespace std ;

#define pb(n) push_back(n)
#define fi first
#define se second
#define X real()
#define Y imag()
#define value(x,y,w,h) (x >= 0 && x < w && y >= 0 && y < h)
#define all(r) (r).begin(),(r).end()
#define gsort(st,en) sort((st),(en),greater<int>())
#define vmax(ary) *max_element(all(ary))
#define vmin(ary) *min_element(all(ary))
#define debug(x) cout<<#x<<": "<<x<<endl
#define fcout(n) cout<<fixed<<setprecision((n))
#define scout(n) cout<<setw(n)
#define vary(type,name,size,init) vector< type> name(size,init)

#define rep(i,n) for(int i = 0; i < (int)(n);++i)
#define REP(i,a,b) for(int i = (a);i < (int)(b);++i)
#define repi(it,array) for(auto it = array.begin(),end = array.end(); it != end;++it)
#define repa(n,array) for(auto &n :(array))

using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using dict = map<string,int>;
using comd = complex<double>;
using pii = pair<int,int> ;

constexpr int imax = ((1<<30)-1)*2+1 ;
constexpr int inf = 10000000;
constexpr double PI = acos(-1.0) ;
double eps = 1e-10 ;
const int dy[] = {-1,0,1,0};
const int dx[] = {0,-1,0,1};

int N,W,H,S;
vector<vector<int>> maps;
int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  char c;
  int n = 0;
  cin >> W >> H >> N;
  char area[H][W];
  maps = vector<vector<int>>(H,vector<int>(W,-1));
  pii pos;
  rep(i,W){
    rep(j,H){
      cin >> c ;
      area[j][i] = c;
      if(c == 'S'){
        pos = make_pair(j,i);
        ++n;
      }
    }
  }
  queue<pii> q;
  q.push(pos);
  maps[pos.fi][pos.se] = 0;
  n = 1;
  int ans = 0;
  for(n = 1; n < N+1;++n){
    maps = vector<vector<int>>(H,vector<int>(W,-1));
    q = queue<pii>();
    q.push(pos);
    maps[pos.fi][pos.se] = 0;
    while(!q.empty()){
      pii p = q.front();q.pop();
      rep(i,4){
        int x = p.fi + dx[i],y = p.se+dy[i];
        if(value(x,y,H,W)){
          if(area[x][y] - '0' == n){
            ans += maps[p.fi][p.se] + 1;
            pos = make_pair(x,y);
            q = queue<pii>();
            break;
          }
          else if(area[x][y] != 'X' && ( maps[x][y] == -1)){
            q.push(make_pair(x,y));
            maps[x][y] = maps[p.fi][p.se] +1 ;
          }
        }
      }
    }
  }
  cout << ans << endl;
  return 0;
}

C++: #include <iostream>
#include <queue>

using namespace std;

typedef pair<int, int> p;

int w, h, n, result, steps;
char map[1000][1000], parent[1000][1000];
bool visited[1000][1000];
p start, last_start, goal, cur;
queue<p> myqueue;

void init(int in){
    start = last_start;

    while(!myqueue.empty()) myqueue.pop();

    for(int i=0; i<w; ++i){
        for(int j=0; j<h; ++j){
            parent[i][j] = '0';
            if(map[i][j] == 'X'){
                visited[i][j] = true;
            }else if(map[i][j] == '0'+in){
                goal = make_pair(i, j);
                visited[i][j] = false;
            }else{
                visited[i][j] = false;
            }
        }
    }
    //ripple[start.first][start.second] = 0;
    return ;
}

int main(){
    cin >> w >> h >> n;

    for(int i=0; i<w; ++i){
        for(int j=0; j<h; ++j){
            cin >> map[i][j];
            if(map[i][j] == 'S')
                last_start = make_pair(i, j);
        }
    }

    result = 0;
    for(int i=1; i<=n; ++i){
        init(i);
        myqueue.push(start);

        while(!myqueue.empty()){
            cur = myqueue.front();
            myqueue.pop();

            if(cur == goal){
                break;
            }

            visited[cur.first][cur.second] = true;

            int x = cur.first, y = cur.second;
            if(x-1 >= 0 && !visited[x-1][y]){
                myqueue.push(make_pair(x-1, y));
                parent[x-1][y] = '1';
            }
            if(y-1 >= 0 && !visited[x][y-1]){
                myqueue.push(make_pair(x, y-1));
                parent[x][y-1] = '2';
            }
            if(x+1 < w && !visited[x+1][y]){
                myqueue.push(make_pair(x+1, y));
                parent[x+1][y] = '3';
            }
            if(y+1 < h && !visited[x][y+1]){
                myqueue.push(make_pair(x, y+1));
                parent[x][y+1] = '4';
            }
        }
        int counter = 0;
        p bcur = goal;
        while(bcur != start){
            counter++;
            if(parent[bcur.first][bcur.second]=='1')
                bcur.first++;
            else if(parent[bcur.first][bcur.second]=='2')
                bcur.second++;
            else if(parent[bcur.first][bcur.second]=='3')
                bcur.first--;
            else if(parent[bcur.first][bcur.second]=='4')
                bcur.second--;
        }
        result += counter;
        last_start = goal;
    }
    cout << result << endl;
    return 0;
}