780. Reaching Points

A move consists of taking a point (x, y) and transforming it to either (x, x+y) or (x+y, y).

Given a starting point (sx, sy) and a target point (tx, ty), return True if and only if a sequence of moves exists to transform the point (sx, sy) to (tx, ty). Otherwise, return False.

Examples:
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)

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

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

Note:

  • sx, sy, tx, ty will all be integers in the range [1, 10^9].

Rust Solution

struct Solution;

impl Solution {
    fn reaching_points(sx: i32, sy: i32, mut tx: i32, mut ty: i32) -> bool {
        while sx < tx && sy < ty {
            if tx < ty {
                ty %= tx;
            } else {
                tx %= ty;
            }
        }
        sx == tx && sy <= ty && (ty - sy) % sx == 0 || sy == ty && sx <= tx && (tx - sx) % sy == 0
    }
}

#[test]
fn test() {
    let sx = 1;
    let sy = 1;
    let tx = 3;
    let ty = 5;
    let res = true;
    assert_eq!(Solution::reaching_points(sx, sy, tx, ty), res);
    let sx = 1;
    let sy = 1;
    let tx = 2;
    let ty = 2;
    let res = false;
    assert_eq!(Solution::reaching_points(sx, sy, tx, ty), res);
    let sx = 1;
    let sy = 1;
    let tx = 1;
    let ty = 1;
    let res = true;
    assert_eq!(Solution::reaching_points(sx, sy, tx, ty), res);
}

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