From c3955ad3909540854b0e51771529ee61386d5a72 Mon Sep 17 00:00:00 2001 From: MH Hung Date: Fri, 5 Sep 2025 16:52:45 +0800 Subject: [PATCH 1/2] docs(makeTheIntegerZero): add README --- .../README.md | 101 ++++++++++++++++++ 1 file changed, 101 insertions(+) create mode 100644 problems/2749-minimum-operations-to-make-the-integer-zero/README.md diff --git a/problems/2749-minimum-operations-to-make-the-integer-zero/README.md b/problems/2749-minimum-operations-to-make-the-integer-zero/README.md new file mode 100644 index 0000000..253e45d --- /dev/null +++ b/problems/2749-minimum-operations-to-make-the-integer-zero/README.md @@ -0,0 +1,101 @@ +# [2749] Minimum Operations To Make The Integer Zero + +## 題目資訊 +- **難度**: Medium +- **標籤**: Bit Manipulation, Brainteaser, Enumeration +- **題目連結**: [LeetCode](https://leetcode.com/problems/minimum-operations-to-make-the-integer-zero/) +- **練習日期**: 2025-09-05 + +## 題目描述 +You are given two integers `num1` and `num2`. + +In one operation, you can choose integer i in the range `[0, 60]` and subtract `2^i + num2` from `num1`. + +Return the integer denoting the *minimum* number of operations needed to make `num1` equal to `0`. + +If it is impossible to make `num1` equal to `0`, return `-1`. + +## 解題思路 + +### 初步分析 +- 這題主要考察什麼概念？ + 1. 位元操作 (Bit Manipulation)：需要理解二進制表示和位元運算 + 2. 數學建模：將實際問題轉換為數學等式 + 3. 枚舉 (Enumeration)：嘗試不同的操作次數 k + 4. 約束條件判斷：理解多個限制條件的邏輯關係 +- 有什麼關鍵限制條件？ + 1. target ≥ 0 + 2. bitCount(target) ≤ k + 3. k ≤ target +- 預期時間/空間複雜度？ + - 時間複雜度：O(60 × log(target)) ≈ O(1) + - 空間複雜度：O(1) + +### 解法概述 +1. **解法**: + - 思路： + - 目標：讓 num1 變成 0 + - 每次操作：num1 = num1 - (2^i + num2) + - k 次操作後：num1 - k*num2 - (2^i1 + 2^i2 + ... + 2^ik) = 0 + - 重新整理：target = num1 - k*num2 = 2^i1 + 2^i2 + ... + 2^ik + - 時間複雜度：O(1) + - 空間複雜度：O(1) + +## 測試案例 + +### 範例輸入輸出 +``` +Input: num1 = 3, num2 = -2 +Output: 3 +Explanation: +We can make 3 equal to 0 with the following operations: +- We choose i = 2 and subtract 22 + (-2) from 3, 3 - (4 + (-2)) = 1. +- We choose i = 2 and subtract 22 + (-2) from 1, 1 - (4 + (-2)) = -1. +- We choose i = 0 and subtract 20 + (-2) from -1, (-1) - (1 + (-2)) = 0. +It can be proven, that 3 is the minimum number of operations that we need to perform. +``` + +### 邊界情況 + - `1 <= num1 <= 10^9` + - `-10^9 <= num2 <= 10^9` + +## 學習筆記 + +### 今天學到什麼？ +- 二位元的操作寫法 + +### 遇到的困難 +- 二位元的操作 + 1. 方法一: 逐位檢查法 + - 程式碼： + ``` C# + count += (int)(n & 1); + n >>= 1; + ``` + - 運作原理： + 1. n & 1：檢查最右邊的位元是否為 1 + 2. count += (int)(n & 1)：如果是 1 就加到計數器 + 3. n >>= 1：把 n 右移一位（去掉已檢查的位元） + 4. 重複直到 n 變成 0 + 2. 方法二: 移除最右邊 1 + - 程式碼： + ``` C# + count++; + n &= n - 1; + ``` + - 運作原理： + 1. n - 1：讓最右邊的 1 變成 0，其右邊的 0 都變成 1 + 2. n & (n - 1)：神奇地移除了最右邊的 1 + 3. count++：每移除一個 1，計數器就加 1 + 4. 重複直到 n 變成 0 + +### 改善方向 +- + +### 相關題目 +- [#991](https://leetcode.com/problems/broken-calculator) Broken Calculator +- [#1658](https://leetcode.com/problems/minimum-operations-to-reduce-x-to-zero/) Minimum Operations to Reduce X to Zero + +--- +**總結**: +1. 學習二位元的使用技巧 From 63880d47170dec8549421bde49c79d7f7705da39 Mon Sep 17 00:00:00 2001 From: MH Hung Date: Fri, 5 Sep 2025 16:54:03 +0800 Subject: [PATCH 2/2] feat(makeTheIntegerZeio): add C# solution --- .../csharp/Program.cs | 84 +++++++++++++++++++ .../csharp/csharp.csproj | 10 +++ 2 files changed, 94 insertions(+) create mode 100644 problems/2749-minimum-operations-to-make-the-integer-zero/csharp/Program.cs create mode 100644 problems/2749-minimum-operations-to-make-the-integer-zero/csharp/csharp.csproj diff --git a/problems/2749-minimum-operations-to-make-the-integer-zero/csharp/Program.cs b/problems/2749-minimum-operations-to-make-the-integer-zero/csharp/Program.cs new file mode 100644 index 0000000..7a81016 --- /dev/null +++ b/problems/2749-minimum-operations-to-make-the-integer-zero/csharp/Program.cs @@ -0,0 +1,84 @@ +// LeetCode 2749: Minimum Operations To Make The Integer Zero +// 難度: Medium +// 日期: 2025-09-05 + +using System; +using System.Collections.Generic; +using System.Linq; + +public class Solution +{ + public int MakeTheIntegerZero(int num1, int num2) + { + for (int k = 1; k <= 60; k++) + { + long target = (long)num1 - (long)k * num2; + + if (target < 0) continue; + + int bitCount = CountSetBits(target); + + if (bitCount <= k && k <= target) + { + return k; + } + } + + return -1; + } + + private int CountSetBits(long n) + { + int count = 0; + while (n > 0) + { + // 方法一 + // count += (int)(n & 1); + // n >>= 1; + + // 方法二 + count++; + n &= n - 1; + } + return count; + } +} + +public class Program +{ + public static void Main() + { + Solution solution = new Solution(); + TestCase1(solution); + TestCase2(solution); + } + + static void TestCase1(Solution solution) + { + int num1 = 3, num2 = -2; + int expected = 3; + int actual = solution.MakeTheIntegerZero(num1, num2); + + Console.WriteLine("Test 1:"); + Console.WriteLine($"Input: num1 = {num1}, num2 = {num2}"); + Console.WriteLine($"Expected: {expected}"); + Console.WriteLine($"Actual: {actual}"); + Console.WriteLine($"Result: {(actual == expected ? "PASS" : "FAIL")}"); + Console.WriteLine(); + } + + static void TestCase2(Solution solution) + { + int num1 = 5, num2 = 7; + int expected = -1; + int actual = solution.MakeTheIntegerZero(num1, num2); + + Console.WriteLine("Test 2:"); + Console.WriteLine($"Input: num1 = {num1}, num2 = {num2}"); + Console.WriteLine($"Expected: {expected}"); + Console.WriteLine($"Actual: {actual}"); + Console.WriteLine($"Result: {(actual == expected ? "PASS" : "FAIL")}"); + Console.WriteLine(); + } + +} diff --git a/problems/2749-minimum-operations-to-make-the-integer-zero/csharp/csharp.csproj b/problems/2749-minimum-operations-to-make-the-integer-zero/csharp/csharp.csproj new file mode 100644 index 0000000..2150e37 --- /dev/null +++ b/problems/2749-minimum-operations-to-make-the-integer-zero/csharp/csharp.csproj @@ -0,0 +1,10 @@ + + + + Exe + net8.0 + enable + enable + + +