Question

780. Reaching Points

中文文档

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).

 

Example 1:

Input: sx = 1, sy = 1, tx = 3, ty = 5
Output: true
Explanation:
One series of moves that transforms the starting point to the target is:
(1, 1) -> (1, 2)
(1, 2) -> (3, 2)
(3, 2) -> (3, 5)

Example 2:

Input: sx = 1, sy = 1, tx = 2, ty = 2
Output: false

Example 3:

Input: sx = 1, sy = 1, tx = 1, ty = 1
Output: true

 

Constraints:

• 1 <= sx, sy, tx, ty <= 109

Solutions

Solution 1

class Solution:
  def reachingPoints(self, sx: int, sy: int, tx: int, ty: int) -> bool:
    while tx > sx and ty > sy and tx != ty:
      if tx > ty:
        tx %= ty
      else:
        ty %= tx
    if tx == sx and ty == sy:
      return True
    if tx == sx:
      return ty > sy and (ty - sy) % tx == 0
    if ty == sy:
      return tx > sx and (tx - sx) % ty == 0
    return False

class Solution {
  public boolean reachingPoints(int sx, int sy, int tx, int ty) {
    while (tx > sx && ty > sy && tx != ty) {
      if (tx > ty) {
        tx %= ty;
      } else {
        ty %= tx;
      }
    }
    if (tx == sx && ty == sy) {
      return true;
    }
    if (tx == sx) {
      return ty > sy && (ty - sy) % tx == 0;
    }
    if (ty == sy) {
      return tx > sx && (tx - sx) % ty == 0;
    }
    return false;
  }
}

class Solution {
public:
  bool reachingPoints(int sx, int sy, int tx, int ty) {
    while (tx > sx && ty > sy && tx != ty) {
      if (tx > ty)
        tx %= ty;
      else
        ty %= tx;
    }
    if (tx == sx && ty == sy) return true;
    if (tx == sx) return ty > sy && (ty - sy) % tx == 0;
    if (ty == sy) return tx > sx && (tx - sx) % ty == 0;
    return false;
  }
};

func reachingPoints(sx int, sy int, tx int, ty int) bool {
  for tx > sx && ty > sy && tx != ty {
    if tx > ty {
      tx %= ty
    } else {
      ty %= tx
    }
  }
  if tx == sx && ty == sy {
    return true
  }
  if tx == sx {
    return ty > sy && (ty-sy)%tx == 0
  }
  if ty == sy {
    return tx > sx && (tx-sx)%ty == 0
  }
  return false
}