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1631.pathWithminimumEffort.dijkstra.java
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1631.pathWithminimumEffort.dijkstra.java
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import java.util.Arrays;
import java.util.PriorityQueue;
class Solution {
int xd[]={1,-1,0,0};
int yd[]={0,0,1,-1};
public int minimumEffortPath(int[][] heights) {
// we may have multiple ways to reach end from start
// in each path we need to consider maximum difference
// from all this differences we need to return minimum difference
int n=heights.length,m=heights[0].length;
PriorityQueue<Pair> pq=new PriorityQueue<>((a,b)->a.diff-b.diff);
int minDis[][]=new int[n][m];
for(int row[]:minDis) Arrays.fill(row,(int)(1e9));
pq.add(new Pair(0,0,(int)0)); //starting node 0,0
minDis[0][0]=(int)0;
while (!pq.isEmpty()){
Pair node=pq.poll();
for(int i=0;i<xd.length;i++){
int nx=node.x+xd[i];
int ny=node.y+yd[i];
if(isValid(nx,ny,n,m)){
int newDiff=Math.abs(heights[nx][ny]-heights[node.x][node.y]); // this node's difference with parent node
int maxDiffSoFar=Math.max(newDiff,node.diff); //this path's maximum difference so far.
if(maxDiffSoFar<minDis[nx][ny]){
// if this maximum difference is lower than current node's stored difference.
pq.add(new Pair(nx,ny,maxDiffSoFar));
minDis[nx][ny]=maxDiffSoFar;
}
}
}
}
return minDis[n-1][m-1];
}
boolean isValid(int x,int y,int n,int m){
return x>=0 && y>=0 && x<n && y<m;
}
}
class Pair{
int x,y,diff;
Pair(int x,int y,int diff){
this.x=x;
this.y=y;
this.diff=diff;
}
}