added Unique Binary Search Tree with dynamic programming

dynamic_programming/unique_binary_search_tree.dart

@@ -0,0 +1,34 @@
+import 'package:test/test.dart';
+
+// Problem - https://leetcode.com/problems/unique-binary-search-trees/description/
+// Given an integer n, return the number of structurally unique BST's (binary search trees)
+// which has exactly n nodes of unique values from 1 to n.
+
+class UniqueBST {
+  int solve(int i, List<int> dp) {
+    if (i == 0 || i == 1) return 1;
+    if (dp[i] != -1) return dp[i];
+
+    int total = 0;
+    for (int k = 1; k <= i; k++) {
+      total += solve(k - 1, dp) * solve(i - k, dp);
+    }
+    return dp[i] = total;
+  }
+
+  int numTrees(int n) {
+    List<int> dp = List.filled(n + 1, -1);
+    return this.solve(n, dp);
+  }
+}
+
+void main() {
+  var uniqueBST = UniqueBST();
+  test('Test Case 1: Input 3, Output - 5', () {
+    expect(uniqueBST.numTrees(3), 5);
+  });
+
+  test('Test Case 2: Input 1, Output - 1', () {
+    expect(uniqueBST.numTrees(1), 1);
+  });
+}