二分查找算法解析（java版）

二分查找：

（1）确定该区间的中点位置：mid=（low+high）/2    

min代表区间中间的结点的位置，low代表区间最左结点位置，high代表区间最右结点位置

（2）将待查a值与结点mid的关键字（下面用R[mid].key）比较，若相等，则查找成功，否则确定新的查找区间：

如果R[mid].key>a，则由表的有序性可知，R[mid].key右侧的值都大于a，所以等于a的关键字如果存在，必然在R[mid].key左边的表中。这时high=mid-1

如果R[mid].key<a,则等于a的关键字如果存在，必然在R[mid].key右边的表中。这时low=mid

如果R[mid].key=a，则查找成功。

（3）下一次查找针对新的查找区间，重复步骤（1）和（2）

（4）在查找过程中，low逐步增加，high逐步减少，如果high<low，则查找失败。

实现方式有两种：

//1、递归实现：public static int binarySerach2(int[] array, int low, int high, int key){int middle = (low+high)/2;if (low > high) {return -1;}if (array[middle] == key) {return middle;}else if (array[middle] > key) {return binarySerach2(array, low, middle-1, key);}else {return binarySerach2(array, middle+1, high, key);}}

//2、while循环实现：public static int binarySerach(int[] array, int key){int low = 0;int high = array.length - 1;int middle = 0;while (low <= high) {middle = (low+high)/2;if (array[middle] == key) {return middle;}else if (array[middle] > key) {high = middle - 1;}else {low = middle + 1;}}return -1;}

JDK自带实现：位于java.util.Arrays包中

 public static int binarySearch(int[] a, int fromIndex, int toIndex,                                   int key) {        rangeCheck(a.length, fromIndex, toIndex);        return binarySearch0(a, fromIndex, toIndex, key);    }    // Like public version, but without range checks.    private static int binarySearch0(int[] a, int fromIndex, int toIndex,                                     int key) {        int low = fromIndex;        int high = toIndex - 1;        while (low <= high) {            int mid = (low + high) >>> 1;            int midVal = a[mid];            if (midVal < key)                low = mid + 1;            else if (midVal > key)                high = mid - 1;            else                return mid; // key found        }        return -(low + 1);  // key not found.    }//    健壮性判断 private static void rangeCheck(int length, int fromIndex, int toIndex) {        if (fromIndex > toIndex) {            throw new IllegalArgumentException(                "fromIndex(" + fromIndex + ") > toIndex(" + toIndex + ")");        }        if (fromIndex < 0) {            throw new ArrayIndexOutOfBoundsException(fromIndex);        }        if (toIndex > length) {            throw new ArrayIndexOutOfBoundsException(toIndex);        }    }