feat: 1201. Ugly Number III.js : 二分 + 数论

Author: upupming

leetcode/残酷刷题/1201. Ugly Number III.js

@@ -0,0 +1,24 @@
+/**
+ * @param {number} n
+ * @param {number} a
+ * @param {number} b
+ * @param {number} c
+ * @return {number}
+ */
+const gcd = (a, b) => b ? gcd(b, a % b) : a
+const lcm = (a, b) => a * b / gcd(a, b)
+const nthUglyNumber = function (n, a, b, c) {
+  const min = BigInt(Math.min(a, b, c))
+  n = BigInt(n), a = BigInt(a), b = BigInt(b), c = BigInt(c)
+  let l = 1n; let r = n * min
+  while (l < r) {
+    const mid = l + r >> 1n
+    if (valid(mid)) r = mid
+    else l = mid + 1n
+  }
+  function valid (m) {
+    const cnt = (d) => m / d
+    return (cnt(a) + cnt(b) + cnt(c) - cnt(lcm(a, b)) - cnt(lcm(b, c)) - cnt(lcm(a, c)) + cnt(lcm(lcm(a, b), c))) >= n
+  }
+  return l
+}

leetcode/残酷刷题/README.md

@@ -141,6 +141,8 @@
 - 1751. Maximum Number of Events That Can Be Attended II
 - 1300. Sum of Mutated Array Closest to Target
 - 1802. Maximum Value at a Given Index in a Bounded Array
+- 1201. Ugly Number III.js
+- 二分 + 容斥原理 + lcm
 
 ### 并查集