BFS "Digit Jump" solution working fine on machine, get TLE on online judge - infinite-loop

Question

This code is for problem DIGJUMP.
It gives me correct output for all inputs i have tried (i have tried a lot of them). But the problem is that it is getting TLE while submitting it on codechef. I checked the editorial and the same solution (concept-wise) gets accepted, so it means algorithmic approach is correct. I must have something wrong in the implementation.
I tried it for a long time, but could not figure out what is wrong.
#include <string.h>
#include <vector>
#include <queue>
#include <stdio.h>
using namespace std;
class Node
{
public:
int idx, steps;
};
int main()
{
char str[100001];
scanf("%s", str);
int len = strlen(str);
vector<int> adj[10];
for(int i = 0; i < len; i++)
adj[str[i] - '0'].push_back(i);
int idx, chi, size, steps;
Node tmpn;
tmpn.idx = 0;
tmpn.steps = 0;
queue<Node> que;
que.push(tmpn);
bool * visited = new bool[len];
for(int i = 0; i < len; i++)
visited[i] = false;
while(!que.empty())
{
tmpn = que.front();
que.pop();
idx = tmpn.idx;
steps = tmpn.steps;
chi = str[idx] - '0';
if(visited[idx])
continue;
visited[idx] = true;
if(idx == len - 1)
{
printf("%d\n", tmpn.steps);
return 0;
}
if(visited[idx + 1] == false)
{
tmpn.idx = idx + 1;
tmpn.steps = steps + 1;
que.push(tmpn);
}
if(idx > 0 && visited[idx - 1] == false)
{
tmpn.idx = idx - 1;
tmpn.steps = steps + 1;
que.push(tmpn);
}
size = adj[chi].size();
for(int j = 0; j < size; j++)
{
if(visited[adj[chi][j]] == false)
{
tmpn.idx = adj[chi][j];
tmpn.steps = steps + 1;
que.push(tmpn);
}
}
}
return 0;
}

Answer 1

This solution won't finish in acceptable time for the problem. Remember that BFS is O(E). In a string with O(n) digits of some kind there are O(n^2) edges between those digits. For N=10^5 O(N^2) is too much.
This will need some optimizations like if we came to current node from a similar node, we wont skip further to similar nodes.