深入JDK源码之Arrays类中的排序查找算法（转）

原文出处：陶邦仁

binarySearch()方法

二分法查找算法，算法思想：当数据量很大适宜采用该方法。采用二分法查找时，数据需是排好序的。基本思想：假设数据是按升序排序的，对于给定值x，从序列的中间位置开始比较，如果当前位置值等于x，则查找成功；若x小于当前位置值，则在数列的前半段中查找；若x大于当前位置值则在数列的后半段中继续查找，直到找到为止。

//针对int类型数组的二分法查找，key为要查找数的下标

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;//无符号左移一位，相当于除以二

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.

}

sort()方法

针对引用类型数组采取的算法是归并排序，算法思想：归并（Merge）排序法是将两个（或两个以上）有序表合并成一个新的有序表，即把待排序序列分为若干个子序列，每个子序列是有序的。然后再把有序子序列合并为整体有序序列。

private static final int INSERTIONSORT_THRESHOLD = 7;//插入排序门槛

public static void sort(Object[] a) {

Object[] aux = (Object[])a.clone();

mergeSort(aux, a, 0, a.length, 0);

}

//归并排序

private static void mergeSort(Object[] src, Object[] dest, int low, int high, int off) {

int length = high - low;

if (length < INSERTIONSORT_THRESHOLD) { //若数组长度小于7，则用冒泡排序

for (int i=low; i<high; i++)

for (int j=i; j>low && ((Comparable) dest[j-1]).compareTo(dest[j])>0; j--)

swap(dest, j, j-1);

return;

}

// Recursively sort halves of dest into src

int destLow = low;

int destHigh = high;

low += off;

high += off;

int mid = (low + high) >>> 1; //无符号左移一位，

mergeSort(dest, src, low, mid, -off);

mergeSort(dest, src, mid, high, -off);

// If list is already sorted, just copy from src to dest. This is an

// optimization that results in faster sorts for nearly ordered lists.

if (((Comparable)src[mid-1]).compareTo(src[mid]) <= 0) {

System.arraycopy(src, low, dest, destLow, length);

return;

}

// Merge sorted halves (now in src) into dest

for(int i = destLow, p = low, q = mid; i < destHigh; i++) {

if (q >= high || p < mid && ((Comparable)src[p]).compareTo(src[q])<=0)

dest[i] = src[p++];

else

dest[i] = src[q++];

}

sort()方法

采取的是快速排序算法，算法思想：通过一趟排序将要排序的数据分割成独立的两部分，其中一部分的所有数据都比另外一部分的所有数据都要小，然后再按此方法对这两部分数据分别进行快速排序，整个排序过程可以递归进行，以此达到整个数据变成有序序列。

/**

* Swaps x[a] with x[b].

*/

private static void swap(int x[], int a, int b) {

int t = x[a];

x[a] = x[b];

x[b] = t;

}

public static void sort(int[] a) {

sort1(a, 0, a.length);

}

private static int med3(int x[], int a, int b, int c) {//找出三个中的中间值

return (x[a] < x[b] ?

(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :

(x[b] > x[c] ? b : x[a] > x[c] ? c : a));

}

/**

* Sorts the specified sub-array of integers into ascending order.

*/

private static void sort1(int x[], int off, int len) {

// Insertion sort on smallest arrays

if (len < 7) {//采用冒泡排序

for (int i=off; i<len+off; i++)

for (int j=i; j>off && x[j-1]>x[j]; j--)

swap(x, j, j-1);

return;

}

//采用快速排序

// Choose a partition element, v

int m = off + (len >> 1); // Small arrays, middle element

if (len > 7) {

int l = off;

int n = off + len - 1;

if (len > 40) { // Big arrays, pseudomedian of 9

int s = len/8;

l = med3(x, l, l+s, l+2*s);

m = med3(x, m-s, m, m+s);

n = med3(x, n-2*s, n-s, n);

}

m = med3(x, l, m, n); // Mid-size, med of 3

}

int v = x[m];

// Establish Invariant: v* (<v)* (>v)* v*

int a = off, b = a, c = off + len - 1, d = c;

while(true) {

while (b <= c && x[b] <= v) {

if (x[b] == v)

swap(x, a++, b);

b++;

}

while (c >= b && x[c] >= v) {

if (x[c] == v)

swap(x, c, d--);

c--;

}

if (b > c)

break;

swap(x, b++, c--);

}

// Swap partition elements back to middle

int s, n = off + len;

s = Math.min(a-off, b-a ); vecswap(x, off, b-s, s);

s = Math.min(d-c, n-d-1); vecswap(x, b, n-s, s);

// Recursively sort non-partition-elements

if ((s = b-a) > 1)

sort1(x, off, s);

if ((s = d-c) > 1)

sort1(x, n-s, s);

}

sort()方法

针对double，float类型数组排序，采取了先把所有的数组元素值为-0.0d的转换成0.0d，再利用快速排序排好序，最后再还原。

public static void sort(double[] a) {

sort2(a, 0, a.length);

}

private static void sort2(double a[], int fromIndex, int toIndex) {

//static long doubleToLongBits(double value)

//根据 IEEE 754 浮点双精度格式 ("double format") 位布局，返回指定浮点值的表示形式。

final long NEG_ZERO_BITS = Double.doubleToLongBits(-0.0d);

/*

* The sort is done in three phases to avoid the expense of using

* NaN and -0.0 aware comparisons during the main sort.

*/

/*

* Preprocessing phase: Move any NaN's to end of array, count the

* number of -0.0's, and turn them into 0.0's.

*/

int numNegZeros = 0;

int i = fromIndex, n = toIndex;

while(i < n) {

if (a[i] != a[i]) { //这段搞不懂，源代码怪怪的，感觉多此一举

double swap = a[i];

a[i] = a[--n];

a[n] = swap;

} else {

if (a[i]==0 && Double.doubleToLongBits(a[i])==NEG_ZERO_BITS) {

a[i] = 0.0d;

numNegZeros++;

}

i++;

}

// Main sort phase: quicksort everything but the NaN's

sort1(a, fromIndex, n-fromIndex);

// Postprocessing phase: change 0.0's to -0.0's as required

if (numNegZeros != 0) {

int j = binarySearch0(a, fromIndex, n, 0.0d); // posn of ANY zero

do {

j--;

} while (j>=0 && a[j]==0.0d);

// j is now one less than the index of the FIRST zero

for (int k=0; k<numNegZeros; k++)

a[++j] = -0.0d;

}

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