Create ugly-number-iii.cpp

Author: kamyu104

C++/ugly-number-iii.cpp

@@ -0,0 +1,42 @@
+// Time:  O(logn)
+// Space: O(1)
+
+class Solution {
+public:
+    int nthUglyNumber(int n, int a, int b, int c) {
+        int64_t lcm_a_b = lcm(a, b), lcm_b_c = lcm(b, c), lcm_c_a = lcm(c, a);
+        int64_t lcm_a_b_c = lcm(lcm_a_b, lcm_b_c);
+        int64_t left = 1, right = 2 * 1e9;
+        while (left <= right) {
+            const auto& mid = left + (right - left) / 2;
+            if (count(mid, a, b, c,
+                      lcm_a_b, lcm_b_c, lcm_c_a, lcm_a_b_c) >= n) {
+                right = mid - 1;
+            } else {
+                left = mid + 1;
+            }
+        }
+        return left;
+    }
+
+private:
+    int64_t count (int64_t x,
+                   int64_t a, int64_t b, int64_t c,
+                   int64_t lcm_a_b, int64_t lcm_b_c, int64_t lcm_c_a,
+                   int64_t lcm_a_b_c) {
+        return x / a + x / b + x / c - (x / lcm_a_b + x / lcm_b_c + x / lcm_c_a) + x / lcm_a_b_c;
+    }
+
+    int64_t gcd(int64_t a, int64_t b) {
+        while (b != 0) {
+            const auto tmp = b;
+            b = a % b;
+            a = tmp;
+        }
+        return a;
+    }
+    
+    int64_t lcm(int64_t a, int64_t b) {
+        return a / gcd(a, b) * b;
+    }
+};