import(solutions): Add problem 96 .

1 files changed, 14 insertions, 0 deletions

diff --git a/works/solutions/cpp/96.cpp b/works/solutions/cpp/96.cpp
new file mode 100644
index 0000000..a67a59a
--- /dev/null
+++ b/works/solutions/cpp/96.cpp
@@ -0,0 +1,14 @@
+class Solution {
+public:
+    // catalan number:
+    // f(n) = f(0) * f(n-1) + f(1) * f(n-2) + ... + f(n-1)*f(0)
+    // f(n) = 2(2n-1) * f(n-1) / (n+1)
+    // f(n) = C(2n, n) / (n+1)
+    int numTrees(int n) {
+        long long result = 1;
+        for (int i = 2; i <= n; i++) {
+            result = 2 * (2 * i - 1) * result / (i + 1);
+        }
+        return result;
+    }
+};