Using custom comparator for priority_queue increases time C++

Question

For this question on leetcode, using dijkstra algo :

You are a hiker preparing for an upcoming hike. You are given heights, a 2D array of size rows x columns, where heights[row][col] represents the height of cell (row, col). You are situated in the top-left cell, (0, 0), and you hope to travel to the bottom-right cell, (rows-1, columns-1) (ie, 0-indexed). You can move up, down, left, or right, and you wish to find a route that requires the minimum effort.

A route's effort is the maximum absolute difference in heights between two consecutive cells of the route.

Return the minimum effort required to travel from the top-left cell to the bottom-right cell.

I am getting TLE time limit exceeded if I use priority_queue with struct . Can anyone help me figure out the reason?

TLE code :

struct heapNode
{
    int w;
    int i;
    int j;

    heapNode(int n1, int n2, int n3) : w(n1), i(n2), j(n3)
    {
    }
};

struct Comp {
    bool operator()(heapNode const& p1, heapNode const& p2)
    {
        // return "true" if "p1" is ordered
        // before "p2", for example:
        return p1.w < p2.w;
    }
};



class Solution {
public:
    int minimumEffortPath(vector<vector<int>>& heights) {
        
        int r  = heights.size(), c = heights[0].size();
        
        int dirs[5] = {-1, 0, 1, 0, -1};
        
        priority_queue<heapNode,vector<heapNode>,Comp> minheap; 
        vector<vector<int>> effort(r,vector<int>(c,INT_MAX));
        
        // effort[0][0] = 0;
        
        minheap.push(heapNode(0,0,0)); 
        
    
        while(!minheap.empty())
        {
            auto top = minheap.top(); minheap.pop();
            int w = top.w;
            int i = top.i;
            int j = top.j;
            
            if (w >= effort[i][j]) continue;
                effort[i][j] = w;
            
            for(int k = 0;k<4;k++)
            {
                int x = i + dirs[k], y = j + dirs[k + 1];
                
                if(x>=0 && y>=0 && x<r && y<c)
                {
                    
                    
                        int t = max(w, abs(heights[i][j] - heights[x][y]));
                        minheap.push(heapNode(t,x,y));
                    
                }
            }
            
        }
        
        return effort[r-1][c-1];
        
    }
};

Working Code :

using pii = pair<int,int>;

class Solution {
public:
    int minimumEffortPath(vector<vector<int>>& heights) {
        
        int r  = heights.size(), c = heights[0].size();
        
        int dirs[5] = {-1, 0, 1, 0, -1};
        
        priority_queue<pii,vector<pii>,greater<pii>> minheap; 
        vector<vector<int>> effort(r,vector<int>(c,INT_MAX));
        
        effort[0][0] = 0;
        
        minheap.push({effort[0][0],0}); 
        
    
        while(!minheap.empty())
        {
            auto top = minheap.top(); minheap.pop();
            int w = top.first;
            int i = top.second / 100, j = top.second % 100;
            
            for(int k = 0;k<4;k++)
            {
                int x = i + dirs[k], y = j + dirs[k + 1];
                
                if(x>=0 && y>=0 && x<r && y<c)
                {
                    if(effort[x][y] > max(w, abs(heights[i][j] - heights[x][y])))
                    {
                        effort[x][y] = max(w, abs(heights[i][j] - heights[x][y]));
                        minheap.push({effort[x][y],x*100+y});
                    }
                }
            }
            
        }
        
        return effort[r-1][c-1];
        
    }
};

Answer 1

Your question does not describe how "effort" is to be calculated.

Assuming that effort to travel from adjacent cells a,b is calculated as

sqrt( 1 + ( height(a) - (height(b) )^2 )

An application to solve this problem is described here https://github.com/JamesBremner/PathFinder2/wiki/Hills

There are two steps.

1. Convert the orthogonal grid to a graph with costed links

2. Run Dijsktra to find the cheapest route from source to destination

The github repo linked to above has c++ code that can solve this very quickly ( one hundred thousand cells in less than a second. )