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
.
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class Solution { | |
public boolean reachingPoints(int sx, int sy, int tx, int ty) { | |
// filter abnormal cases | |
if (sx > tx || sy > ty) { | |
return false; | |
} | |
if (sx == tx) { | |
return (ty - sy) % sx == 0; | |
} | |
if (sy == ty) { | |
return (tx - sx) % sy == 0; | |
} | |
if (Math.min(sx, sy) > Math.min(tx, ty)) { | |
System.out.println(1); | |
return reachingPoints1(sx, sy, tx, ty); | |
} else { | |
System.out.println(2); | |
return reachingPoints2(sx, sy, tx, ty); | |
} | |
} | |
private int sx; | |
private int sy; | |
HashSet<Entry> isVisited2 = new HashSet<>(); | |
public boolean reachingPoints2(int sx, int sy, int tx, int ty) { | |
// filter abnormal cases | |
if (sx > tx || sy > ty) { | |
return false; | |
} | |
if (sx == tx) { | |
return (ty - sy) % sx == 0; | |
} | |
if (sy == ty) { | |
return (tx - sx) % sy == 0; | |
} | |
isVisited2.clear(); | |
this.sx = sx; | |
this.sy = sy; | |
return helper2(tx, ty); | |
} | |
public boolean helper2(int tx, int ty) { | |
if (isVisited2.contains(new Entry(tx, ty))) { | |
return false; | |
} | |
if (this.sx == tx && this.sy == ty) { | |
return true; | |
} | |
if (sx > tx || sy > ty) { | |
return false; | |
} | |
if (sx == tx) { | |
return (ty - sy) % sx == 0; | |
} | |
if (sy == ty) { | |
return (tx - sx) % sy == 0; | |
} | |
isVisited2.add(new Entry(tx, ty)); | |
return helper2(tx - ty, ty) || helper2(tx, ty - tx); | |
} | |
private int tx; | |
private int ty; | |
HashSet<Entry> isVisited = new HashSet<>(); | |
public boolean reachingPoints1(int sx, int sy, int tx, int ty) { | |
// filter abnormal cases | |
if (sx > tx || sy > ty) { | |
return false; | |
} | |
if (sx == tx) { | |
return (ty - sy) % sx == 0; | |
} | |
if (sy == ty) { | |
return (tx - sx) % sy == 0; | |
} | |
isVisited.clear(); | |
this.tx = tx; | |
this.ty = ty; | |
return helper(sx, sy); | |
} | |
public boolean helper(int sx, int sy) { | |
if (isVisited.contains(new Entry(sx, sy))) { | |
return false; | |
} | |
if (sx == this.tx && sy == this.ty) { | |
return true; | |
} | |
if (sx > tx || sy > ty) { | |
return false; | |
} | |
if (sx == tx) { | |
return (ty - sy) % sx == 0; | |
} | |
if (sy == ty) { | |
return (tx - sx) % sy == 0; | |
} | |
isVisited.add(new Entry(sx, sy)); | |
return helper(sx + sy, sy) || helper(sx, sx + sy); | |
} | |
class Entry { | |
int x; | |
int y; | |
public Entry(int x, int y) { | |
this.x = x; | |
this.y = y; | |
} | |
} | |
} |
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