{
  "id": 16376173,
  "title": "Trace Path: Why Net Displacement Is the Wrong Check",
  "url": "https://urgent.news/2026/10/24/trace-path-why-net-displacement-is-the-wrong-check",
  "topic": "tech",
  "section": "Tech",
  "published": "2026-10-24T21:50:37.000Z",
  "source": {
    "name": "Dev.to",
    "slug": "dev-to",
    "url": "https://dev.to/obrutus/trace-path-why-net-displacement-is-the-wrong-check-3gkh"
  },
  "original_language": "en",
  "account": "The Trace Path problem on GeeksforGeeks asks whether a given sequence of moves can be completed within the bounds of an n x m grid, starting from any cell. At first glance, the solution might seem to involve simulating the path from every possible starting position, but this brute-force approach quickly becomes infeasible for large grids.\n\nThe key insight is that horizontal moves (L and R) do not affect the row, and vertical moves (U and D) do not affect the column. This means the path must be valid both horizontally and vertically independently. The interviewer highlights that the answer for the grid depends only on the net displacement along each axis, not the order of moves.\n\nTo determine if a start position is valid, the interviewer proposes checking whether the path's span (the difference between the farthest offset to the left and right, or the farthest offset up and down) fits within the grid dimensions. For example, if the maximum horizontal displacement is greater than the grid width, no valid start exists.\n\nRather than attempting to brute-force every possible start, the interviewer suggests a more efficient approach. By considering all starting positions simultaneously, the problem can be reduced to tracking the minimum and maximum offsets along each axis as the path progresses. The valid start positions correspond to those whose offsets remain within the grid bounds throughout the entire sequence.\n\nThe interviewer provides a compact solution in Java that implements this approach. The `isPossible` function checks the validity of the path on both axes by maintaining a shrinking interval for each axis. As it iterates through the move string, it updates the interval boundaries based on the move type. If at any point the minimum offset exceeds the maximum, the interval becomes invalid, indicating that no valid start position exists.\n\nThis elegant solution leverages the independence of horizontal and vertical movements to reduce the problem to two one-dimensional checks, each operating in linear time relative to the length of the move string. The final result is the logical conjunction of the two checks, yielding a boolean indicating whether the move sequence can be completed within the grid boundaries.",
  "summary": "Most grid problems tempt you to simulate. This one gives you a free choice of starting cell, which makes simulation look even more natural: try every cell and see if one survives. Then the constraints arrive, and you need a different idea. So this post is written as an interview transcript. You get the vague version of the problem, ask questions, propose something slightly wrong, and get…",
  "key_points": [
    "Net displacement determines path validity, not move order",
    "Track min/max offsets along each axis to validate path",
    "Solution reduces problem to two 1D checks in linear time"
  ],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}