使用示例
vector<int> nums = {1, 2, 2, 2, 3, 4, 5};
int target = 2;
cout << "第一个 >= 2: " << lowerBound(nums, target) << endl; // 1
cout << "第一个 > 2: " << upperBound(nums, target) << endl; // 4
cout << "最后一个 <= 2: " << lastLessEqual(nums, target) << endl; // 3
cout << "最后一个 < 2: " << lastLess(nums, target) << endl; // 0
记忆技巧
| 查找类型 | 条件判断 | 返回值 | 等价关系 |
|---|
| 第一个 >= target | nums[mid] < target | left | lower_bound |
| 第一个 > target | nums[mid] <= target | left | upper_bound |
| 最后一个 <= target | nums[mid] <= target | left - 1 | upper_bound - 1 |
| 最后一个 < target | nums[mid] < target | left - 1 | lower_bound - 1 |
所有实现都使用左闭右开区间 [left, right)，保持一致性。
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85 | /****************************************************************
* 代码作者: Alex Li
* 创建时间: 2025-09-03 01:06:56
* 最后修改: 2025-09-03 01:10:23
* 文件描述: 二分法查找边界
****************************************************************/
#include <iostream>
#include <vector>
using namespace std;
// 1. 第一个 >= target
int lowerBound(vector<int>& nums, int target) {
int left = 0, right = nums.size(); // [left, right)
while (left < right) {
int mid = left + (right - left) / 2;
if (nums[mid] < target) {
left = mid + 1;
} else {
right = mid;
}
}
return left; // 或 right
}
// 2. 第一个 > target
int upperBound(vector<int>& nums, int target) {
int left = 0, right = nums.size(); // [left, right)
while (left < right) {
int mid = left + (right - left) / 2;
if (nums[mid] <= target) {
left = mid + 1;
} else {
right = mid;
}
}
return left; // 或 right
}
// 3. 最后一个 <= target
int lastLE(vector<int>& nums, int target) {
int left = 0, right = nums.size(); // [left, right)
while (left < right) {
int mid = left + (right - left) / 2;
if (nums[mid] <= target) {
left = mid + 1;
} else {
right = mid;
}
}
return left - 1; // 注意：可能为 -1
}
// 4. 最后一个 < target
int lastLT(vector<int>& nums, int target) {
int left = 0, right = nums.size(); // [left, right)
while (left < right) {
int mid = left + (right - left) / 2;
if (nums[mid] < target) {
left = mid + 1;
} else {
right = mid;
}
}
return left - 1; // 注意：可能为 -1
}
int main() {
int n,target;
cout<<"input nubmer: ";
cin>>n;
vector<int> nums(n);
for (int k =0; k < n; ++k) {
cin>>nums[k];
}
// sort(a.begin(),a.end()); //如果输入数组不保证升序，就排序。
cout<<"input number that your want to find: ";
cin>>target;
cout << "lowerBound (>= " << target << "): " << lowerBound(nums, target) << endl;
cout << "upperBound (> " << target << "): " << upperBound(nums, target) << endl;
cout << "lastLE (<= " << target << "): " << lastLE(nums, target) << endl;
cout << "lastLT (< " << target << "): " << lastLT(nums, target) << endl;
return 0;
}
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