Reaching Points

Author: gouthampradhan

README.md

@@ -235,6 +235,7 @@ My accepted leetcode solutions to some of the common interview problems.
 - [Global and Local Inversions](problems/src/math/GlobalAndLocalInversions.java) (Medium)
 - [Solve the Equation](problems/src/math/SolveTheEquation.java) (Medium)
 - [Couples Holding Hands](problems/src/math/CouplesHoldingHands.java) (Hard)
+- [Reaching Points](problems/src/math/ReachingPoints.java) (Hard)
 
 #### [Reservoir Sampling](problems/src/reservoir_sampling)
 

problems/src/math/ReachingPoints.java

@@ -0,0 +1,88 @@
+package math;
+
+/**
+ * Created by gouthamvidyapradhan on 14/07/2018.
+ * 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].
+
+ Solution: Start from the target, reduce the target value to start value.
+ If at any stage the target value goes below start value then there exist no solution hence return false.
+ */
+public class ReachingPoints {
+
+    class Pair{
+        int x, y;
+        Pair(int x, int y){
+            this.x = x;
+            this.y = y;
+        }
+    }
+
+    /**
+     * Main method
+     * @param args
+     * @throws Exception
+     */
+    public static void main(String[] args) throws Exception{
+        System.out.println(new ReachingPoints().reachingPoints(1, 1, 153, 10));
+    }
+
+    public boolean reachingPoints(int sx, int sy, int tx, int ty) {
+        Pair target = new Pair(tx, ty);
+        Pair start = new Pair(sx, sy);
+        while(true){
+            if(start.x == target.x && start.y == target.y){
+                return true;
+            } else if(start.x > target.x || start.y > target.y || target.x == target.y){
+                return false;
+            } else if(start.x == target.x){
+                int t = target.y - start.y;
+                return (t % target.x) == 0;
+            } else if(start.y == target.y){
+                int t = target.x - start.x;
+                return (t % target.y) == 0;
+            } else{
+                if(target.x > target.y){
+                    int[] R = reduce(target.x, target.y);
+                    target.x = R[0];
+                    target.y = R[1];
+                } else {
+                    int[] R = reduce(target.y, target.x);
+                    target.x = R[1];
+                    target.y = R[0];
+                }
+            }
+        }
+    }
+
+    private int[] reduce(int x, int y){
+        int t = x - y;
+        int q = t / y;
+        x -= (y * q);
+        if((t % y) != 0){
+            x -= y;
+        }
+        return new int[]{x, y};
+    }
+}