C++ 0ms使用inclusion exclusion, bitmask DP, 二元搜尋解Leetcode難題3116 Kth Smallest Amount With Denomination
[codes on Leetcode]https://leetcode.com/problems/kth-smallest-amount-with-single-denomination-combination/solutions/8473317/reduced-coins-mask-dpbinary-searchbeats-6acqj/
核心思路：
二元搜尋 (Binary Search)：將「找出第 K 小的金額」轉化為「判定某金額下有多少組合」的判定問題。
排容原理 (Inclusion-Exclusion Principle)：精確計算多個面額組合出的金額數量，避免重複計數。
Bitmask DP 預處理：透過位元遮罩與動態規劃預先計算所有組合的最小公倍數 (LCM)，將排容原理的計算複雜度降至最低。
這是一場結合了數學推導與程式優化的深度教學，適合想挑戰高階演算法的你！
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In this video, we tackle LeetCode 3116 (Hard) and achieve a blazing-fast 0ms runtime using C++.
Key Algorithmic Techniques:
Binary Search: Transforming the search for the K-th smallest amount into a decision problem.
Inclusion-Exclusion Principle: Systematically counting valid amounts across multiple denominations without double-counting.
Bitmask DP Preprocessing: Optimizing the calculation of Least Common Multiples (LCM) for all subsets to make the Inclusion-Exclusion step extremely efficient.
Perfect for developers looking to master advanced algorithm optimization and mathematical reasoning in C++.
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00:00 – Introduction and LeetCode Problem 3116 Overview
00:14 – Demonstration of Test Cases and Submission (0ms Result)
00:33 – Explanation of Problem: Kth Smallest Amount With Denominations
01:45 – Example 1: Simplifying Coins (3, 6, 9 to 3)
02:10 – Example 2: Union and Intersection of Sets (Coins 5 and 2)
03:13 – Analyzing Constraints and K-value Magnitude
03:55 – Core Theory: Inclusion-Exclusion Principle (IEP)
06:22 – Visualization using Venn Diagrams (LCM and Subsets)
07:23 – Strategy: Optimizing Performance by Reducing Unnecessary Coins
08:28 – Implementing Bitmask Dynamic Programming (DP) for Subsets
10:42 – Calculating LCM for All Possible Combinations
12:22 – Defining the Counting Function (Using popcount for IEP)
13:32 – Applying Binary Search to Find the Kth Smallest Amount
14:18 – Walkthrough of a Complex Test Case Example
15:33 – Code Review: Counting Function, Coin Reduction, and Search Logic
16:28 – Final Submission and Performance Confirmation
#LeetCode3116 #InclusionExclusion #CPP #LeetCodeHard #BitmaskDP #BinarySearch #DynamicProgramming #anwendeng
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