java 二分查找算法

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编程之美在于算法之美，先来看看二分查找的算法：

隐藏条件：二分查找必须是有序的，从小到大，或从大到小的排序才能进行二分查找，下面来看看代码：

package com.cn.daming;public class MainActivity {/** * @param args */public static void main(String[] args) {int[] aInts = new int[]{1,3,5,8,11,14,16,24,37,47,49,56,63,83,223}; //排序是从小到大int[] aInts2 = new int[]{322,243,211,156,98,85,79,68,53,47,38,24,13,6,2}; //排序是从大到小// TODO Auto-generated method stubMainActivity main = new MainActivity();System.out.println("aInts  the reault is : " + main.binarySearch(aInts, 0, aInts.length, 24));System.out.println("aInts2 the reault is : " + main.binarySearch2(aInts2, 0, aInts2.length, 243));}//从小到大的二分查找private int binarySearch(int[] a, int start, int len, int key) {        int high = start + len, low = start - 1, guess;        while (high - low > 1) {            guess = (high + low) / 2;            if (a[guess] < key)                low = guess;            else                high = guess;        }        if (high == start + len)            return ~(start + len);        else if (a[high] == key)            return high;        else            return ~high;    }//从大到小的二分查找private int binarySearch2(int[] a, int start, int len, int key) {        int high = start + len, low = start - 1, guess;        while (high - low > 1) {            guess = (high + low) / 2;            if (a[guess] > key)                low = guess;            else                high = guess;        }        if (high == start + len)            return ~(start + len);        else if (a[high] == key)            return high;        else            return ~high;    }}

返回值就是返回要查的key的下标；

看结果如图：

2014-05-10 11:06 补充：

以上的二分查找理解起来比较费劲，下面我用个可读性强的二分查找，效率估计没有上面的高，但是程序的可读性会很强，

       /** * Java Binary search Algorithm *  * @param a * @param key * @return Subscript */public int binarySearch(int[] a, int key) {if (a.length == 0)return -1;int first = 0;int last = a.length - 1;int mid;while (first <= last) {mid = (first + last) / 2;if (a[mid] == key) {return mid;} else if (a[mid] > key) {last = mid - 1;} else {first = mid + 1;}}return -1;}

这个binarySearch()返回的是数组的下标，我验证过，没有问题的，可以直接copy过来使用的。

对二分查找求平均查找长度二分查找的过程相当与一棵二叉排序树，所以总节点数为n=2^h-1,h=Log2 (n+1)。第i层上的节点数为2^(1－1)；在等概率的情况下，平均查找长度ASL=Log2 (n+1)-1。