讓面試官滿意的排序算法（圖文解析）
這種排序算法能夠讓面試官面露微笑
這種排序算法集各排序算法之大成
這種排序算法邏輯性十足
-
這種排序算法能夠展示自己對Java底層的了解
這種排序算法出自Vladimir Yaroslavskiy晾腔、Jon Bentley和Josh Bloch三位大牛之手，它就是JDK的排序算法——java.util.DualPivotQuicksort（雙支點快排）
DualPivotQuicksort
先看一副邏輯圖（如有錯誤請大牛在評論區(qū)指正）
插排指的是改進版插排——哨兵插排
快排指的是改進版快排——雙支點快排
DualPivotQuickSort沒有Object數(shù)組排序的邏輯，此邏輯在Arrays中涩金，好像是歸并+Tim排序
圖像應(yīng)該很清楚：對于不同的數(shù)據(jù)類型婚苹，Java有不同的排序策略：
- byte、short、char 他們的取值范圍有限矢否，使用計數(shù)排序占用的空間也不過256/65536個單位慎陵，只要排序的數(shù)量不是特別少（有一個計數(shù)排序閾值眼虱，低于這個閾值的話就沒有不要用空間換時間了），都應(yīng)使用計數(shù)排序
- int荆姆、long蒙幻、float、double 他們的取值范圍非常的大胆筒，不適合使用計數(shù)排序
-
float和double 他們又有特殊情況：
- NAN（not a number）邮破，NAN不等于任何數(shù)字，甚至不等于自己
- +0.0仆救，-0.0抒和，float和double無法精確表示十進制小數(shù)，我們所看到的十進制小數(shù)其實都是取得近似值彤蔽，因而會有+0.0（接近0的正浮點數(shù)）和-0.0（接近0的負(fù)浮點數(shù))摧莽，在排序流程中統(tǒng)一按0來處理，因而最后要調(diào)整一下-0.0和+0.0的位置關(guān)系
- Object
計數(shù)排序
計數(shù)排序是以空間換時間的排序算法顿痪，它時間復(fù)雜度O(n)镊辕，空間復(fù)雜度O(m)（m為排序數(shù)值可能取值的數(shù)量），只有在范圍較小的時候才應(yīng)該考慮計數(shù)排序
（源碼以short為例）
int[] count = new int[NUM_SHORT_VALUES]; //1 << 16 = 65536蚁袭，即short的可取值數(shù)量
//計數(shù)征懈，left和right為數(shù)組要排序的范圍的左界和右界
//注意，直接把
for (int i = left - 1; ++i <= right;count[a[i] - Short.MIN_VALUE]++);
//排序
for (int i = NUM_SHORT_VALUES, k = right + 1; k > left; ) {
while (count[--i] == 0);
short value = (short) (i + Short.MIN_VALUE);
int s = count[i];
do {
a[--k] = value;
} while (--s > 0);
}
哨兵插排
當(dāng)數(shù)組元素較少時揩悄，時間O(n2)和O(logn)其實相差無幾卖哎，而插排的空間占用率要少于快排和歸并排序，因而當(dāng)數(shù)組元素較少時（<插排閾值）删性，優(yōu)先使用插排
哨兵插排是對插排的優(yōu)化亏娜，原插排每次取一個值進行遍歷插入，而哨兵插排則取兩個蹬挺，較大的一個（小端在前的排序）作為哨兵维贺，當(dāng)哨兵遍歷到自己的位置時，另一個值可以直接從哨兵當(dāng)前位置開始遍歷巴帮，而不用再重頭遍歷
只畫了靜態(tài)圖幸缕，如果有好的繪制Gif的工具請在評論區(qū)告訴我哦
我們來看一下源碼：
if (leftmost) {
//傳統(tǒng)插排（無哨兵Sentinel）
//遍歷
//循環(huán)向左比較（<左側(cè)元素——換位）-直到大于左側(cè)元素
for (int i = left, j = i; i < right; j = ++i) {
int ai = a[i + 1];
while (ai < a[j]) {
a[j + 1] = a[j];
if (j-- == left) {
break;
}
}
a[j + 1] = ai;
}
//哨兵插排
} else {
//如果一開始就是排好序的——直接返回
do {
if (left >= right) {
return;
}
} while (a[++left] >= a[left - 1]);
//以兩個為單位遍歷群发，大的元素充當(dāng)哨兵，以減少小的元素循環(huán)向左比較的范圍
for (int k = left; ++left <= right; k = ++left) {
int a1 = a[k], a2 = a[left];
if (a1 < a2) {
a2 = a1; a1 = a[left];
}
while (a1 < a[--k]) {
a[k + 2] = a[k];
}
a[++k + 1] = a1;
while (a2 < a[--k]) {
a[k + 1] = a[k];
}
a[k + 1] = a2;
}
//確保最后一個元素被排序
int last = a[right];
while (last < a[--right]) {
a[right + 1] = a[right];
}
a[right + 1] = last;
}
return;
雙支點快排
重頭戲：雙支點快排发乔！
快排雖然穩(wěn)定性不如歸并排序熟妓，但是它不用復(fù)制來復(fù)制去，省去了一段數(shù)組的空間栏尚，在數(shù)組元素較少的情況下穩(wěn)定性影響也會下降（>插排閾值 起愈，<快排閾值），優(yōu)先使用快排
雙支點快排在原有的快排基礎(chǔ)上译仗，多加一個支點抬虽，左右共進，效率提升
看圖：
-
第一步纵菌，取支點
注意：如果5個節(jié)點有相等的任兩個節(jié)點阐污，說明數(shù)據(jù)不夠均勻，那就要使用單節(jié)點快排
-
快排
源碼（int為例咱圆，這么長估計也沒人看）
// Inexpensive approximation of length / 7
// 快排閾值是286 其7分之一小于等于1/8+1/64+1
int seventh = (length >> 3) + (length >> 6) + 1;
// 獲取分成7份的五個中間點
int e3 = (left + right) >>> 1; // The midpoint
int e2 = e3 - seventh;
int e1 = e2 - seventh;
int e4 = e3 + seventh;
int e5 = e4 + seventh;
// 保證中間點的元素從小到大排序
if (a[e2] < a[e1]) {
int t = a[e2]; a[e2] = a[e1]; a[e1] = t; }
if (a[e3] < a[e2]) {
int t = a[e3]; a[e3] = a[e2]; a[e2] = t;
if (t < a[e1]) { a[e2] = a[e1]; a[e1] = t; }
}
if (a[e4] < a[e3]) {
int t = a[e4]; a[e4] = a[e3]; a[e3] = t;
if (t < a[e2]) { a[e3] = a[e2]; a[e2] = t;
if (t < a[e1]) { a[e2] = a[e1]; a[e1] = t; }
}
}
if (a[e5] < a[e4]) {
int t = a[e5]; a[e5] = a[e4]; a[e4] = t;
if (t < a[e3]) { a[e4] = a[e3]; a[e3] = t;
if (t < a[e2]) { a[e3] = a[e2]; a[e2] = t;
if (t < a[e1]) { a[e2] = a[e1]; a[e1] = t; }
}
}
}
// Pointers
int less = left; // The index of the first element of center part
int great = right; // The index before the first element of right part
//點彼此不相等——分三段快排笛辟，否則分兩段
if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
/*
* Use the second and fourth of the five sorted elements as pivots.
* These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*/
int pivot1 = a[e2];
int pivot2 = a[e4];
/*
* The first and the last elements to be sorted are moved to the
* locations formerly occupied by the pivots. When partitioning
* is complete, the pivots are swapped back into their final
* positions, and excluded from subsequent sorting.
*/
a[e2] = a[left];
a[e4] = a[right];
while (a[++less] < pivot1);
while (a[--great] > pivot2);
/*
* Partitioning:
*
* left part center part right part
* +--------------------------------------------------------------+
* | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 |
* +--------------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*/
outer:
for (int k = less - 1; ++k <= great; ) {
int ak = a[k];
if (ak < pivot1) { // Move a[k] to left part
a[k] = a[less];
/*
* Here and below we use "a[i] = b; i++;" instead
* of "a[i++] = b;" due to performance issue.
*/
a[less] = ak;
++less;
} else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] < pivot1) { // a[great] <= pivot2
a[k] = a[less];
a[less] = a[great];
++less;
} else { // pivot1 <= a[great] <= pivot2
a[k] = a[great];
}
/*
* Here and below we use "a[i] = b; i--;" instead
* of "a[i--] = b;" due to performance issue.
*/
a[great] = ak;
--great;
}
}
// Swap pivots into their final positions
a[left] = a[less - 1]; a[less - 1] = pivot1;
a[right] = a[great + 1]; a[great + 1] = pivot2;
// Sort left and right parts recursively, excluding known pivots
sort(a, left, less - 2, leftmost);
sort(a, great + 2, right, false);
/*
* If center part is too large (comprises > 4/7 of the array),
* swap internal pivot values to ends.
*/
if (less < e1 && e5 < great) {
/*
* Skip elements, which are equal to pivot values.
*/
while (a[less] == pivot1) {
++less;
}
while (a[great] == pivot2) {
--great;
}
/*
* Partitioning:
*
* left part center part right part
* +----------------------------------------------------------+
* | == pivot1 | pivot1 < && < pivot2 | ? | == pivot2 |
* +----------------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (*, less) == pivot1
* pivot1 < all in [less, k) < pivot2
* all in (great, *) == pivot2
*
* Pointer k is the first index of ?-part.
*/
outer:
for (int k = less - 1; ++k <= great; ) {
int ak = a[k];
if (ak == pivot1) { // Move a[k] to left part
a[k] = a[less];
a[less] = ak;
++less;
} else if (ak == pivot2) { // Move a[k] to right part
while (a[great] == pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] == pivot1) { // a[great] < pivot2
a[k] = a[less];
/*
* Even though a[great] equals to pivot1, the
* assignment a[less] = pivot1 may be incorrect,
* if a[great] and pivot1 are floating-point zeros
* of different signs. Therefore in float and
* double sorting methods we have to use more
* accurate assignment a[less] = a[great].
*/
a[less] = pivot1;
++less;
} else { // pivot1 < a[great] < pivot2
a[k] = a[great];
}
a[great] = ak;
--great;
}
}
}
// Sort center part recursively
sort(a, less, great, false);
} else { // Partitioning with one pivot
/*
* Use the third of the five sorted elements as pivot.
* This value is inexpensive approximation of the median.
*/
int pivot = a[e3];
/*
* Partitioning degenerates to the traditional 3-way
* (or "Dutch National Flag") schema:
*
* left part center part right part
* +-------------------------------------------------+
* | < pivot | == pivot | ? | > pivot |
* +-------------------------------------------------+
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot
* all in [less, k) == pivot
* all in (great, right) > pivot
*
* Pointer k is the first index of ?-part.
*/
for (int k = less; k <= great; ++k) {
if (a[k] == pivot) {
continue;
}
int ak = a[k];
if (ak < pivot) { // Move a[k] to left part
a[k] = a[less];
a[less] = ak;
++less;
} else { // a[k] > pivot - Move a[k] to right part
while (a[great] > pivot) {
--great;
}
if (a[great] < pivot) { // a[great] <= pivot
a[k] = a[less];
a[less] = a[great];
++less;
} else { // a[great] == pivot
/*
* Even though a[great] equals to pivot, the
* assignment a[k] = pivot may be incorrect,
* if a[great] and pivot are floating-point
* zeros of different signs. Therefore in float
* and double sorting methods we have to use
* more accurate assignment a[k] = a[great].
*/
a[k] = pivot;
}
a[great] = ak;
--great;
}
}
/*
* Sort left and right parts recursively.
* All elements from center part are equal
* and, therefore, already sorted.
*/
sort(a, left, less - 1, leftmost);
sort(a, great + 1, right, false);
}
歸并排序
你不會以為元素多（>快排閾值）就一定要用歸并了吧？
錯序苏！元素多時確實對算法的穩(wěn)定性有要求手幢，可是如果這些元素能夠穩(wěn)定快排呢？
開發(fā)JDK的大牛顯然考慮了這一點：他們在歸并排序之前對元素進行了是否能穩(wěn)定快排的判斷：
- 如果數(shù)組本身幾乎已經(jīng)排好了（可以看出幾段有序數(shù)組的拼接）忱详，那還排什么围来，理一理返回就行了
- 如果出現(xiàn)連續(xù)33個相等元素——使用快排（實話說，我沒弄明白為什么匈睁，有無大牛給我指點迷津监透？）
//判斷結(jié)構(gòu)是否適合歸并排序
int[] run = new int[MAX_RUN_COUNT + 1];
int count = 0; run[0] = left;
// Check if the array is nearly sorted
for (int k = left; k < right; run[count] = k) {
if (a[k] < a[k + 1]) { // ascending
while (++k <= right && a[k - 1] <= a[k]);
} else if (a[k] > a[k + 1]) { // descending
while (++k <= right && a[k - 1] >= a[k]);
for (int lo = run[count] - 1, hi = k; ++lo < --hi; ) {
int t = a[lo]; a[lo] = a[hi]; a[hi] = t;
}
} else {
//連續(xù)MAX_RUN_LENGTH（33）個相等元素，使用快排
for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k]; ) {
if (--m == 0) {
sort(a, left, right, true);
return;
}
}
}
//count達到MAX_RUN_LENGTH航唆，使用快排
if (++count == MAX_RUN_COUNT) {
sort(a, left, right, true);
return;
}
}
// Check special cases
// Implementation note: variable "right" is increased by 1.
if (run[count] == right++) { // The last run contains one element
run[++count] = right;
} else if (count == 1) { // The array is already sorted
return;
}
歸并排序源碼
byte odd = 0;
for (int n = 1; (n <<= 1) < count; odd ^= 1);
// Use or create temporary array b for merging
int[] b; // temp array; alternates with a
int ao, bo; // array offsets from 'left'
int blen = right - left; // space needed for b
if (work == null || workLen < blen || workBase + blen > work.length) {
work = new int[blen];
workBase = 0;
}
if (odd == 0) {
System.arraycopy(a, left, work, workBase, blen);
b = a;
bo = 0;
a = work;
ao = workBase - left;
} else {
b = work;
ao = 0;
bo = workBase - left;
}
// Merging
for (int last; count > 1; count = last) {
for (int k = (last = 0) + 2; k <= count; k += 2) {
int hi = run[k], mi = run[k - 1];
for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
b[i + bo] = a[p++ + ao];
} else {
b[i + bo] = a[q++ + ao];
}
}
run[++last] = hi;
}
if ((count & 1) != 0) {
for (int i = right, lo = run[count - 1]; --i >= lo;
b[i + bo] = a[i + ao]
);
run[++last] = right;
}
int[] t = a; a = b; b = t;
int o = ao; ao = bo; bo = o;
}
技術(shù)不分領(lǐng)域胀蛮，思想一脈相承，歡迎訪問橙味菌的博客
本文由博客一文多發(fā)平臺 OpenWrite 發(fā)布佛点！
