Create UniquePaths.java

Author: techieJarek

UniquePaths.java

@@ -0,0 +1,47 @@
+import java.time.Instant;
+
+/**
+ * A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
+ *
+ * The robot can only move either down or right at any point in time.
+ * The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).
+ *
+ * How many possible unique paths are there?
+ */
+public class UniquePaths {
+    public static void main(String[] args){
+
+        Instant before = Instant.now();
+        int paths = uniquePathsWithMemo(20,10);
+        Instant after = Instant.now();
+        System.out.println("Unique paths with memo : " + paths + ", time : " + (after.toEpochMilli() - before.toEpochMilli()));
+
+        before = Instant.now();
+        paths = uniquePathsNoMemo(20,10);
+        after = Instant.now();
+        System.out.println("Unique paths no memo : " + paths + ", time : " + (after.toEpochMilli() - before.toEpochMilli()));
+
+    }
+
+    public static int uniquePathsWithMemo(int m, int n) {
+        return uniquePathsWithMemo(m,n,0,0,new int[m][n]);
+    }
+
+    public static int uniquePathsWithMemo(int m, int n, int x, int y, int[][] memo) {
+        if(x == m || y == n) return 0;
+        if(x == m-1 && y == n-1) return 1;
+        if(memo[x][y] != 0) return  memo[x][y];
+        memo[x][y] = uniquePathsWithMemo(m,n,x, y+1, memo) + uniquePathsWithMemo(m,n,x + 1, y, memo);
+        return memo[x][y];
+    }
+
+    public static int uniquePathsNoMemo(int m, int n) {
+        return uniquePathsNoMemo(m,n,0,0);
+    }
+
+    public static int uniquePathsNoMemo(int m, int n, int x, int y) {
+        if(x == m || y == n) return 0;
+        if(x == m -1 || y == n - 1) return 1;
+        return uniquePathsNoMemo(m,n,x, y + 1) + uniquePathsNoMemo(m,n,x + 1, y);
+    }
+}