6.二分查找
模板实现
二分查找的情况如图所示
模板如下:
while (left <= right) {
mid = (left + right) / 2;
if (key ? arr[mid]) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return ?;
只需要记住比较符号和返回值即可:
根据要求值的位置,可以先确定比较符号,再确定返回值。
比较符号:左<=, 右<;(左右方向)
返回值: 左right, 右left;(位置,这个最好确定)
#include <bits/stdc++.h>
using namespace std;
//二分查找
int binarySearch(int arr[], int len, int key)
{
int left = 0;
int right = len - 1;
int mid;
while (left <= right) {
mid = (left + right) / 2;
if (key < arr[mid]) {//key在左边
right = mid - 1;
} else if (arr[mid] < key) {//key在右边
left = mid + 1;
} else {
return mid;
}
}
return -1;
}
//1 查找最后一个小于key的元素
int findLastLess(int arr[], int len, int key)
{
int left = 0;
int right = len - 1;
int mid;
while (left <= right) {
mid = (left + right) / 2;
if (key <= arr[mid]) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return right;
}
//2 查找第一个大于等于key的元素
int findFirstGreaterEqual(int arr[], int len, int key)
{
int left = 0;
int right = len - 1;
int mid;
while (left <= right) {
mid = (left + right) / 2;
if (key <= arr[mid]) {
right = mid - 1;
}
else {
left = mid + 1;
}
}
return left;
}
//3 查找最后一个小于等于key的元素
int findLastLessEqual(int arr[], int len, int key)
{
int left = 0;
int right = len - 1;
int mid;
while (left <= right) {
mid = (left + right) / 2;
if (key < arr[mid]) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return right;
}
//4 查找第一个大于key的元素
int findFirstGreater(int arr[], int len, int key)
{
int left = 0;
int right = len - 1;
int mid;
while (left <= right) {
mid = (left + right) / 2;
if (key < arr[mid]) {
right = mid - 1;
}
else {
left = mid + 1;
}
}
return left;
}
//5 查找第一个与key相等的元素
int findFirstEqual(int arr[], int len, int key)
{
int left = 0;
int right = len - 1;
int mid;
while (left <= right) {
mid = (left + right) / 2;
if (key <= arr[mid]) {
right = mid - 1;
} else {//arr[mid] < key
left = mid + 1;
}
}
//arr[right] < key <= arr[left]
//right是最后一个小于key的
//left是第一个大于等于key的
if (left < len && arr[left] == key) {
return left;
}
return -1;
}
//6 查找最后一个与key相等的元素
int findLastEqual(int arr[], int len, int key)
{
int left = 0;
int right = len - 1;
int mid;
while (left <= right) {
mid = (left + right) / 2;
if (key < arr[mid]) {
right = mid - 1;
} else {//arr[mid] <= key
left = mid + 1;
}
}
//arr[right] <= key < arr[left]
//right是最后一个小于等于key的
//left是第一个大于key的
if (right >= 0 && arr[right] == key) {
return right;
}
return -1;
}
void test()
{
// int a[] = {0, 1, 2, 3, 4, 5, 6};
int a[] = {0, 1, 2, 2, 2, 5, 6};
int len = 7;
int key = 2;
int index;
int i;
for (i = 0; i < len; ++i) {
printf("%d ", i);
}
printf("\n");
for (i = 0; i < len; ++i) {
printf("%d ", a[i]);
}
printf("\n");
// index = binarySearch(a, 10, 2);
printf("%d binarySearch\n", binarySearch(a, len, key));
printf("%d findLastLess\n", findLastLess(a, len, key));
printf("%d findFirstGreaterEqual\n", findFirstGreaterEqual(a, len, key));
printf("%d findLastLessEqual\n", findLastLessEqual(a, len, key));
printf("%d findFirstGreater\n", findFirstGreater(a, len, key));
printf("%d findFirstEqual\n", findFirstEqual(a, len, key));
printf("%d findLastEqual\n", findLastEqual(a, len, key));
}
int main()
{
test();
return 0;
}
旋转数组查找最小值
class Solution:
def minArray(self, numbers: List[int]) -> int:
# 简单二分, 当m=e时无脑直接e-1...
# 最后返回跳出循环后的numbers[s]
# 注意m<e时要把e设为m, 因为最小值可能就是m
s, e = 0, len(numbers) - 1
while s < e:
m = (s + e) >> 1
if numbers[m] < numbers[e]:
# m可能是最小值, 不能排除它
e = m
elif numbers[m] > numbers[e]:
# m一定不是最小值, 排除它
s = m + 1
else:
# 退化的情况
e -= 1
return numbers[s]
参考链接:
二分查找的总结,这个链接绝了