Enhance space complexity

Author: bky373

unique-paths/bky373.java

@@ -1,5 +1,8 @@
-// time: O(m*n)
-// space: O(m*n)
+/*
+   [Approch 1]
+   - time: O(m*n)
+   - space: O(m*n)
+ */
 class Solution {
 
     public int uniquePaths(int m, int n) {
@@ -18,3 +21,27 @@ public int uniquePaths(int m, int n) {
         return dp[m - 1][n - 1];
     }
 }
+
+/*
+   [Approch 2]
+   - time: O(m*n)
+   - space: O(n)
+ */
+class Solution {
+
+    public int uniquePaths(int m, int n) {
+        int[] upper = new int[n];
+
+        Arrays.fill(upper, 1);
+
+        for (int i = 1; i < m; i++) {
+            int left = 1;
+            for (int j = 1; j < n; j++) {
+                left += upper[j];
+                upper[j] = left;
+            }
+        }
+
+        return upper[n - 1];
+    }
+}