67 lines
2.0 KiB
C++
67 lines
2.0 KiB
C++
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/**
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* File: binary_search_edge.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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/* 二分查找插入点（存在重复元素） */
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int binarySearchInsertion(const vector<int> &nums, int target) {
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int i = 0, j = nums.size() - 1; // 初始化双闭区间 [0, n-1]
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while (i <= j) {
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int m = i + (j - i) / 2; // 计算中点索引 m
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if (nums[m] < target) {
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i = m + 1; // target 在区间 [m+1, j] 中
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} else {
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j = m - 1; // 首个小于 target 的元素在区间 [i, m-1] 中
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}
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}
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// 返回插入点 i
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return i;
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}
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/* 二分查找最左一个 target */
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int binarySearchLeftEdge(vector<int> &nums, int target) {
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// 等价于查找 target 的插入点
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int i = binarySearchInsertion(nums, target);
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// 未找到 target ，返回 -1
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if (i == nums.size() || nums[i] != target) {
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return -1;
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}
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// 找到 target ，返回索引 i
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return i;
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}
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/* 二分查找最右一个 target */
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int binarySearchRightEdge(vector<int> &nums, int target) {
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// 转化为查找最左一个 target + 1
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int i = binarySearchInsertion(nums, target + 1);
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// j 指向最右一个 target ，i 指向首个大于 target 的元素
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int j = i - 1;
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// 未找到 target ，返回 -1
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if (j == -1 || nums[j] != target) {
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return -1;
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}
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// 找到 target ，返回索引 j
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return j;
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}
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/* Driver Code */
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int main() {
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// 包含重复元素的数组
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vector<int> nums = {1, 3, 6, 6, 6, 6, 6, 10, 12, 15};
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cout << "\n数组 nums = ";
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printVector(nums);
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// 二分查找左边界和右边界
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for (int target : {6, 7}) {
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int index = binarySearchLeftEdge(nums, target);
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cout << "最左一个元素 " << target << " 的索引为 " << index << endl;
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index = binarySearchRightEdge(nums, target);
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cout << "最右一个元素 " << target << " 的索引为 " << index << endl;
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}
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return 0;
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}
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