D-BFS 双向广度优先搜索
从起点和终点同时开始搜索，直到两个搜索的点相交，得到最短路径
Code:

// D-BFS
//by:MuQY
#include <iostream>
#include <algorithm>
#include <string.h>
#include <queue>
#include <string>
using namespace std;
int stmap[10005]; // 标记每一个情况下走了几步
int vis[10005];   // 标记每个情况下有没有被访问过，是正向还是逆向
string s, e;
struct Node
{
    int num[4];
    int step;
};
queue<Node> q, p; // q从s开始，p从e开始
int get_Num(int c[])
{
    int tmp = 0;
    for (int i = 0; i < 4; i++)
    {
        tmp *= 10;
        tmp += c[i];
    }
    return tmp;
}
void bfs()
{
    memset(vis, 0, sizeof(vis));
    memset(stmap, 0, sizeof(stmap));
    Node a, b;
    int tmp;
    while (!q.empty() || !p.empty())
    {
        if (!q.empty()){
            a = q.front();
            q.pop();
            for (int i = 0; i < 4; i++){
                b = a;
                b.num[i] = a.num[i] + 1;//+1
                if(b.num[i] == 10){
                    b.num[i] = 1;
                }
                tmp = get_Num(b.num);
                if(vis[tmp] == 0){//没有出现过
                    b.step = a.step + 1;
                    stmap[tmp] = b.step;
                    vis[tmp] = 1;
                    q.push(b);
                }
                else if(vis[tmp] == 2){//有交点
                    cout << a.step + stmap[tmp] + 1;
                    return;
                }
                b.num[i] = a.num[i] - 1; //-1
                if(b.num[i] == 0){
                    b.num[i] = 9;
                }
                tmp = get_Num(b.num);
                if (vis[tmp] == 0)
                { // 没有出现过
                    b.step = a.step + 1;
                    stmap[tmp] = b.step;
                    vis[tmp] = 1;
                    q.push(b);
                }
                else if (vis[tmp] == 2)
                { // 有交点
                    cout << a.step + stmap[tmp] + 1 << endl;
                    return;
                }
            }
            for (int i = 0; i < 3; i++){//交换相邻数字
                b = a;
                swap(b.num[i], b.num[i + 1]);
                tmp = get_Num(b.num);
                if(vis[tmp] == 0){
                    b.step = a.step + 1;
                    stmap[tmp] = b.step;
                    vis[tmp] = 1;
                    q.push(b);
                }
                else if(vis[tmp] == 2){
                    cout << a.step + stmap[tmp] + 1 << endl;
                    return;
                }
            }
        }
        if(!p.empty()){
            a = p.front();
            p.pop();
            for (int i = 0; i < 4; i++)
            {
                b = a;
                b.num[i] = a.num[i] + 1; //+1
                if (b.num[i] == 10)
                {
                    b.num[i] = 1;
                }
                tmp = get_Num(b.num);
                if (vis[tmp] == 0)
                { // 没有出现过
                    b.step = a.step + 1;
                    stmap[tmp] = b.step;
                    vis[tmp] = 2;
                    p.push(b);
                }
                else if (vis[tmp] == 1)
                { // 有交点
                    cout << a.step + stmap[tmp] + 1 << endl;
                    return;
                }
                b.num[i] = a.num[i] - 1; //-1
                if (b.num[i] == 0)
                {
                    b.num[i] = 9;
                }
                tmp = get_Num(b.num);
                if (vis[tmp] == 0)
                { // 没有出现过
                    b.step = a.step + 1;
                    stmap[tmp] = b.step;
                    vis[tmp] = 2;
                    p.push(b);
                }
                else if (vis[tmp] == 1)
                { // 有交点
                    cout << a.step + stmap[tmp] + 1 << endl;
                    return;
                }
            }
            for (int i = 0; i < 3; i++)
            { // 交换相邻数字
                b = a;
                swap(b.num[i], b.num[i + 1]);
                tmp = get_Num(b.num);
                if (vis[tmp] == 0)
                {
                    b.step = a.step + 1;
                    stmap[tmp] = b.step;
                    vis[tmp] = 2;
                    p.push(b);
                }
                else if (vis[tmp] == 1)
                {
                    cout << a.step + stmap[tmp] + 1 << endl;
                    return;
                }
            }
        }
    }
}

int main()
{
    int tcase;
    cin >> tcase;
    while (tcase--)
    {
        while(!q.empty()){
            q.pop();
        }
        while(!p.empty()){
            p.pop();
        }
        Node ss, ee;
        int s_num, e_num;
        memset(stmap, 0, sizeof(stmap));
        memset(vis, 0, sizeof(vis));
        cin >> s >> e;
        for (int i = 0; i < 4; i++)
        {
            ss.num[i] = s[i] - '0';
            ee.num[i] = e[i] - '0';
        }
        s_num = get_Num(ss.num);
        e_num = get_Num(ee.num);
        ss.step = 0;
        ee.step = 0;
        vis[s_num] = 1;
        vis[e_num] = 2;
        q.push(ss);
        p.push(ee);
        bfs();
    }
    return 0;
}