你真的会写二分查找吗？

二分查找

//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;
}

二分查找变形

随着二分查找的进行，如果找到key并不结束循环的话，最终的结束状态会是right < left，并且right + 1 = left。

当数组中存在key时，根据二分区间选择的不同，这里又分为两种情况，如下图（key为2时），

当数组中不存在key时，最后仅有一种情况，即把图中的黄色框框去掉。

#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;
}

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