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65 lines
2.3 KiB
65 lines
2.3 KiB
/**
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* File: binary_search_insertion.cs
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* Created Time: 2023-08-06
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* Author: hpstory (hpstory1024@163.com)
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*/
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namespace hello_algo.chapter_searching;
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public class binary_search_insertion {
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/* 二分搜尋插入點（無重複元素） */
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public static int BinarySearchInsertionSimple(int[] nums, int target) {
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int i = 0, j = nums.Length - 1; // 初始化雙閉區間 [0, n-1]
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while (i <= j) {
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int m = i + (j - i) / 2; // 計算中點索引 m
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if (nums[m] < target) {
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i = m + 1; // target 在區間 [m+1, j] 中
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} else if (nums[m] > target) {
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j = m - 1; // target 在區間 [i, m-1] 中
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} else {
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return m; // 找到 target ，返回插入點 m
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}
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}
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// 未找到 target ，返回插入點 i
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return i;
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}
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/* 二分搜尋插入點（存在重複元素） */
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public static int BinarySearchInsertion(int[] nums, int target) {
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int i = 0, j = nums.Length - 1; // 初始化雙閉區間 [0, n-1]
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while (i <= j) {
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int m = i + (j - i) / 2; // 計算中點索引 m
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if (nums[m] < target) {
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i = m + 1; // target 在區間 [m+1, j] 中
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} else if (nums[m] > target) {
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j = m - 1; // target 在區間 [i, m-1] 中
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} else {
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j = m - 1; // 首個小於 target 的元素在區間 [i, m-1] 中
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}
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}
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// 返回插入點 i
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return i;
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}
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[Test]
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public void Test() {
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// 無重複元素的陣列
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int[] nums = [1, 3, 6, 8, 12, 15, 23, 26, 31, 35];
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Console.WriteLine("\n陣列 nums = " + nums.PrintList());
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// 二分搜尋插入點
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foreach (int target in new int[] { 6, 9 }) {
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int index = BinarySearchInsertionSimple(nums, target);
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Console.WriteLine("元素 " + target + " 的插入點的索引為 " + index);
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}
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// 包含重複元素的陣列
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nums = [1, 3, 6, 6, 6, 6, 6, 10, 12, 15];
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Console.WriteLine("\n陣列 nums = " + nums.PrintList());
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// 二分搜尋插入點
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foreach (int target in new int[] { 2, 6, 20 }) {
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int index = BinarySearchInsertion(nums, target);
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Console.WriteLine("元素 " + target + " 的插入點的索引為 " + index);
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}
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}
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}
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