From aa48a1ba631846f3452f2f68fc05be6e6d911de5 Mon Sep 17 00:00:00 2001
From: kamyu <kamyu104@users.noreply.github.com>
Date: Sun, 18 Sep 2016 22:45:05 +0800
Subject: [PATCH] Create nth-digit.cpp

---
 C++/nth-digit.cpp | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)
 create mode 100644 C++/nth-digit.cpp

diff --git a/C++/nth-digit.cpp b/C++/nth-digit.cpp
new file mode 100644
index 000000000..c30adbf0b
--- /dev/null
+++ b/C++/nth-digit.cpp
@@ -0,0 +1,20 @@
+// Time:  O(logn)
+// Space: O(1)
+
+class Solution {
+public:
+    int findNthDigit(int n) {
+        int digit_len = 1;
+        while (n > digit_len * 9 * pow(10, digit_len - 1)) {
+            n -= digit_len  * 9 * pow(10, digit_len - 1);
+            ++digit_len;
+        }
+
+        const int num = pow(10, digit_len - 1) + (n - 1) / digit_len;
+
+        int nth_digit = num / pow(10, (digit_len - 1) - (n - 1) % digit_len);
+        nth_digit %= 10;
+
+        return nth_digit;
+    }
+};