关于二分查找及变体
/********************************************
* All Rights Reserved By www.laughing.ren
* @author:Laughing_Lz
* @version:2018年11月22日 下午11:28:28
* ******************************************/
package ren.laughing.code.Test;
import java.util.Arrays;
public class Search {
/**
* 简单的二分查找，前提是数组是有序，且无重复值
*
* @param arr arr
*/
public static int binarySearch(int value, int[] arr) {
int low = 0, high = arr.length - 1, middle;
// 为什么要是<=呢？
while (low <= high) {
middle = low + ((high - low) >> 1);
if (arr[middle] < value) {
low = middle + 1;
} else if (arr[middle] > value) {
high = middle - 1;
} else {
return middle;
}
}
return -1;
}
/**
* 递归方法实现简单二分查找，前提同上：数组有序，且无重复值
*
* @param value value
* @param arr arr
* @param low low
* @param high high
* @return
*/
public static int recursionBinarySearch(int value, int[] arr, int low, int high) {
if (low > high) {
return -1;
}
int middle = low + ((high - low) >> 1);
if (arr[middle] == value) {
return middle;
} else if (arr[middle] > value) {
return recursionBinarySearch(value, arr, low, middle - 1);
} else {
return recursionBinarySearch(value, arr, middle + 1, high);
}
}
/**
* 求解一个数的平方根，精确到小数六位
*
* @param n n
* @return
*/
public static float square(float n) {
if (n == 0 || n == 1) {
return 1;
}
float low = 0, high = n;
float middle = low + (high - low) / 2;
while (Math.abs(middle * middle - n) > 0.000001) {
if (middle * middle > n) {
high = middle;
} else if (middle * middle < n) {
low = middle;
} else {
return middle;
}
middle = low + (high - low) / 2;
}
return middle;
}
/**
* 利用二分查找返回数组中第一个出现value的位置,注意边界条件middle==0
*
* @param arr arr
* @param value value
* @return
*/
public static int firstEqual(int[] arr, int value) {
int low = 0, high = arr.length - 1, middle = low + ((high - low) >> 1);
while (low <= high) {
if (arr[middle] > value) {
high = middle - 1;
} else if (arr[middle] < value) {
low = middle + 1;
} else {
if ((middle == 0) || (arr[middle - 1] < value)) {
return middle;
} else {
high = middle - 1;
}
}
middle = low + ((high - low) >> 1);
}
return -1;
}
/**
* 利用二分查找返回数组中最后一个出现value的位置
*
* @param arr arr
* @param value value
* @return
*/
public static int lastEqual(int[] arr, int value) {
int low = 0, high = arr.length - 1, middle = low + ((high - low) >> 1);
while (low < high) {
if (arr[middle] > value) {
high = middle - 1;
} else if (arr[middle] < value) {
low = middle + 1;
} else {
if ((middle == arr.length - 1) || (arr[middle + 1] > value)) {
return middle;
} else {
low = middle + 1;
}
}
middle = low + ((high - low) >> 1);
}
return -1;
}
/**
* 利用二分查找返回数组中第一个大于value的位置
*
* @param arr arr
* @param value value
* @return
*/
public static int firstGreat(int[] arr, int value) {
int low = 0, high = arr.length - 1, middle = low + ((high - low) >> 1);
while (low <= high) {
if (arr[middle] > value && arr[middle - 1] <= value) {
return middle;
} else if (arr[middle] <= value) {
low = middle + 1;
} else {
high = middle - 1;
}
middle = low + ((high - low) >> 1);
}
return -1;
}
/**
* 利用二分查找返回数组中最后一个小于value的位置
*
* @param arr arr
* @param value value
* @return
*/
public static int lastLess(int[] arr, int value) {
int low = 0, high = arr.length - 1, middle = low + ((high - low) >> 1);
while (low <= high) {
if (arr[middle] < value && arr[middle + 1] >= value) {
return middle;
} else if (arr[middle] >= value) {
high = middle - 1;
} else {
low = middle + 1;
}
middle = low + ((high - low) >> 1);
}
return -1;
}
/**
* 循环数组中使用二分查找获取value所在位置
*
* @param arr arr
* @param value value
* @return
*/
public static int loopBinarySearch(int[] arr, int value) {
if(arr.length < 1) {
return -1;
}
if (arr.length == 1) {
if (arr[0] == value) {
return 0;
} else {
return -1;
}
}
int low = 0, high = arr.length, middle = 0;
// 首先获取首末位置
for (int i = 0; i < arr.length - 1; i++) {
if (arr[i] > arr[i + 1]) {
high = i;
low = i + 1;
}
}
if (arr[arr.length - 1] > arr[0]) {
low = 0;
high = arr.length - 1;
}
// 经过和arr[0]判断后筛选出可能包含value的子数组
if (arr[0] == value) {
return 0;
} else if (arr[0] < value) {
low = 1;
} else if (arr[0] > value) {
high = arr.length - 1;
}
// 使用简单二分查找获取value位置
while (low <= high) {
middle = low + ((high - low) >> 1);
if (arr[middle] > value) {
high = middle - 1;
} else if (arr[middle] < value) {
low = middle + 1;
} else {
return middle;
}
}
return -1;
}
public static void main(String[] args) {
int[] arr = { 2, 1, 4, 6, 7, 3, 0, 9, 8, 5 };
Arrays.sort(arr);
// System.out.println(binarySearch(5, arr));
// System.out.println(recursionBinarySearch(5, arr, 0, arr.length - 1));
System.out.println(square(5f));
int[] arr1 = { 0, 1, 2, 3, 4, 4, 5, 5, 5, 8, 9 };
System.out.println(firstEqual(arr1, 5));
System.out.println(lastEqual(arr1, 5));
System.out.println(firstGreat(arr1, 5));
System.out.println(lastLess(arr1, 5));
int[] arr2 = { 7, 8, 9, 0, 1, 2, 3, 4, 5, 6 };
System.out.println(loopBinarySearch(arr2, 8));
}
}
