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67 lines
2.1 KiB
67 lines
2.1 KiB
/**
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* File: binary_search_insertion.cpp
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* Created Time: 2023-08-04
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 二分搜尋插入點（無重複元素） */
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int binarySearchInsertionSimple(vector<int> &nums, int target) {
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int i = 0, j = nums.size() - 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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int binarySearchInsertion(vector<int> &nums, int target) {
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int i = 0, j = nums.size() - 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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/* Driver Code */
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int main() {
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// 無重複元素的陣列
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vector<int> nums = {1, 3, 6, 8, 12, 15, 23, 26, 31, 35};
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cout << "\n陣列 nums = ";
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printVector(nums);
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// 二分搜尋插入點
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for (int target : {6, 9}) {
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int index = binarySearchInsertionSimple(nums, target);
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cout << "元素 " << target << " 的插入點的索引為 " << index << endl;
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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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cout << "\n陣列 nums = ";
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printVector(nums);
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// 二分搜尋插入點
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for (int target : {2, 6, 20}) {
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int index = binarySearchInsertion(nums, target);
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cout << "元素 " << target << " 的插入點的索引為 " << index << endl;
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}
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return 0;
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}
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