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;//+1if(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; //-1if(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; //+1if (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; //-1if (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;
}