#780 - Reaching Points

Hard • View on LeetCode • View on GitHub

Problem Description

Given four integers sx, sy, tx, and ty, return true if it is possible to convert the point (sx, sy) to the point (tx, ty) through some operations, or false otherwise.

The allowed operation on some point (x, y) is to convert it to either (x, x + y) or (x + y, y).

Solution

/**
 * @param {number} sx
 * @param {number} sy
 * @param {number} tx
 * @param {number} ty
 * @return {boolean}
 */
var reachingPoints = function(sx, sy, tx, ty) {
  while (tx >= sx && ty >= sy) {
    if (tx === sx && ty === sy) {
      return true;
    }

    if (tx > ty) {
      // If we can directly reach sx by making proper subtractions
      if (ty === sy) {
        return (tx - sx) % ty === 0;
      }
      tx %= ty;
    } else {
      // If we can directly reach sy by making proper subtractions
      if (tx === sx) {
        return (ty - sy) % tx === 0;
      }
      ty %= tx;
    }
  }

  return false;
};