780. Reaching Points

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

Python Code
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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

Java Code
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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;
    }
}

C++ Code
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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;
    }
};

Go Code
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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
}