Codewars:Path Finder #3: the Alpinist in C++ - c++

Question

I just tried to finish a problem:Path Finder #3: the Alpinist in Codewars. I had passed all basic test cases and there were any errors under my own test cases. But when i submited my solution, my code failed for random test cased. My solution of problem is graph searching based Dijkstra algorithm and priority_queue. I think there my some potential errors i didn't consider. Please help me check it. I have tried achieve it for three hours.
My solution is below.
#include <iostream>
#include <cmath>
#include <vector>
#include <queue>
using namespace std;
const int INF = 1e9;
const int WHITE = -1;
const int GRAY = 0;
const int BLACK = 1;
int path_finder(string maze)
{
int result = 0;
vector<pair<int, int>> element;
vector<vector<pair<int, int>>> altitude;
int width = (-1 + sqrt(5 + 4 * maze.size())) / 2;
auto tem = maze.find('\n');
while (tem != string::npos)
{
maze.erase(tem, 1);
tem = maze.find('\n');
}
for (int i = 0; i < width; ++i)
{
for (int j = 0; j < width; ++j)
{
altitude.push_back(element);
if (i >= 1)
altitude[i * width + j].push_back(make_pair(i * width + j - width, abs(maze[i * width + j] - maze[i * width + j - width])));
if (i < width - 1)
altitude[i * width + j].push_back(make_pair(i * width + j + width, abs(maze[i * width + j] - maze[i * width + j + width])));
if (j >= 1)
altitude[i * width + j].push_back(make_pair(i * width + j - 1, abs(maze[i * width + j] - maze[i * width + j - 1])));
if (j < width - 1)
altitude[i * width + j].push_back(make_pair(i * width + j + 1, abs(maze[i * width + j] - maze[i * width + j + 1])));
}
}
int* distance = new int[width * width];
int* state = new int[width * width];
for (int i = 0; i < width * width; ++i)
{
distance[i] = INF;
state[i] = WHITE;
}
priority_queue<pair<int, int>> unfinished;
unfinished.push(make_pair(0, 0));
state[0] = GRAY;
distance[0] = 0;
while (!unfinished.empty())
{
pair<int, int> tem = unfinished.top();
unfinished.pop();
state[tem.second] = BLACK;
if(distance[tem.second] < tem.first * (-1))
continue;
for (int i = 0; i < altitude[tem.second].size(); ++i)
{
if(state[altitude[tem.second][i].first] != BLACK)
{
unfinished.push(make_pair(-1 * altitude[tem.second][i].second, altitude[tem.second][i].first));
if (distance[tem.second] + altitude[tem.second][i].second < distance[altitude[tem.second][i].first])
{
distance[altitude[tem.second][i].first] = distance[tem.second] + altitude[tem.second][i].second;
state[altitude[tem.second][i].first] = GRAY;
}
}
}
}
result = distance[width * width - 1];
return result;
}

Answer 1

Here is a test case where your code has the wrong answer.
"53072\n"
"09003\n"
"29977\n"
"31707\n"
"59844"
The least cost is 13, with this path:
{1 1 0 0 0}
{0 1 0 0 0}
{0 1 1 1 1}
{0 0 0 0 1}
{0 0 0 0 1}
But your program outputs 15.