娴呮瀽涓冪缁忓吀鎺掑簭绠楁硶
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鏍囩锛?a href='http://www.mamicode.com/so/1/%e6%80%9d%e8%b7%af' title='鎬濊矾'>鎬濊矾
鍙樺寲 鎻忚堪 璧勬枡 鐩稿 瑙ｉ噴 detail 棰樻剰 鍑芥暟鏈枃鍒嗘瀽鍐掓场銆佸揩閫熴€侀€夋嫨銆佹彃鍏ャ€佸笇灏斻€佸綊骞跺拰鍫嗘帓搴忥紝涓轰簡瀵逛互涓嬪悇涓畻娉曡繘琛屾柟渚跨殑娴嬭瘯锛屾祴璇曚富鏂规硶浣撳涓嬶紙Java 瀹炵幇锛夛細
public class Sort {
public static void main(String[] args) {
int[] input = {5, 4, 7, 1, 6, 2, 8, 9, 10};
// 姝ゅ璋冪敤鏂规硶锛屼互璋冪敤鍐掓场鎺掑簭涓轰緥
bubbleSort(input);
for (int i = 1; i <= input.length; i++) {
System.out.println(input[i - 1]);
}
}
}
鏈瘒鍗氭枃鎵€鏈夋帓搴忓疄鐜板潎榛樿 浠庡皬鍒板ぇ銆?/p>
鍐掓场鎺掑簭锛圔ubble Sort锛?/h2>
姣忎竴娆￠€氳繃涓や袱姣旇緝鎵惧埌鏈€澶э紙灏忥級鐨勫厓绱犳斁鍦ㄦ湭鎺掑簭搴忓垪鐨勬渶鍚庯紝鐩磋嚦鏈夊簭銆?/p>
姝ラ
- 姣旇緝涓や釜鐩搁偦鐨勫厓绱犮€傚鏋滃墠闈㈡瘮鍚庨潰涓ぇ锛堝皬锛夛紝灏变氦鎹㈤『搴忋€?/li>
- 浠庣 1 涓暟涓庣 2 涓暟寮€濮嬫瘮杈冿紝鐩村埌绗?n-1 涓暟涓庣 n 涓暟缁撴潫銆傚埌鏈€鍚庯紝鏈€澶э紙灏忥級鐨勬暟灏?" 娴?" 鍦ㄤ簡鏈€涓婇潰銆?/li>
- 鎸佺画姣忔瀵瑰墠闈㈣秺鏉ヨ秺灏戠殑鏈帓搴忓厓绱犻噸澶嶄笂闈㈢殑姝ラ锛岀洿鍒版墍鏈夊厓绱犳湁搴忋€?/li>
鎺掑簭婕旂ず
婧愪唬鐮侊紙Java 瀹炵幇锛?/h3>
public static void bubbleSort(int[] input) {
for (int i = 1; i <= input.length; i++) {
for (int j = 1; j <= input.length - i; j++) {
if (input[j - 1] > input[j]) {
int temp = input[j - 1];
input[j - 1] = input[j];
input[j] = temp;
}
}
}
}
绠楁硶鎸囨爣鍒嗘瀽
public static void bubbleSort(int[] input) {
for (int i = 1; i <= input.length; i++) {
for (int j = 1; j <= input.length - i; j++) {
if (input[j - 1] > input[j]) {
int temp = input[j - 1];
input[j - 1] = input[j];
input[j] = temp;
}
}
}
}
鏈€濂芥椂闂村鏉傚害锛歄(n^2)銆傚綋鍏冪礌鏈夊簭鏃讹紝瑕佹瘮杈冦€俷 涓厓绱狅紝姣忎釜鍏冪礌姣旇緝 n娆°€?/p>
鏈€鍧忔椂闂村鏉傚害锛歄(n^2)銆傚綋鍏冪礌鏃犲簭鏃讹紝涔熻姣旇緝銆?/p>
骞冲潎鏃堕棿澶嶆潅搴︼細O(n^2)銆?/p>
杈呭姪绌洪棿锛氫笉闇€瑕侀涓存椂鐨勫瓨鍌ㄧ┖闂存潵杩愯绠楁硶锛屾墍浠ヤ负 O(1)銆?/p>
绋冲畾鎬э細鍥犱负鎺掑簭鏂瑰紡鏄浉閭绘暟姣旇緝鍚庝氦鎹紝濡傛灉搴忓垪涓湁鐩哥瓑鐨勪袱涓暟锛屽緟涓ゆ暟鐩搁偦鏃讹紝涓嶄細浜ゆ崲涓よ€呯殑浣嶇疆锛屾墍浠ョǔ瀹氥€?/p>
鍐掓场鎺掑簭鐨勪袱绉嶄紭鍖栨柟寮?/h3>
浼樺寲 1锛?/h4>
鏌愪竴瓒熼亶鍘嗗鏋滄病鏈夊厓绱犱氦鎹紝flag 鏍囪渚濇棫涓?true銆傝鏄庡凡缁忔帓濂藉簭浜嗭紝缁撴潫杩唬銆?/p>
public static void bubbleSort2(int[] input) {
for (int i = 1; i <= input.length; i++) {
boolean flag = true;
for (int j = 1; j <= input.length - i; j++) {
if (input[j - 1] > input[j]) {
int temp = input[j - 1];
input[j - 1] = input[j];
input[j] = temp;
}
flag = false;
}
if (flag)
break;
}
}
绠楁硶鎸囨爣鍒嗘瀽
鏈€濂芥椂闂村鏉傚害锛氬綋搴忓垪鏈夊簭鏃躲€傜涓€涓?for 寰幆涓紝绗?2/3/11/12 琛岃鍙ユ墽琛?1 娆★紝鍗抽搴︿负 1锛涚浜屼釜 for 寰幆涓紝绗?4銆?銆? 琛岃鍙ユ墽琛?n-1 娆★紝鍗抽搴︿负 n-1銆俆(n) = 3*(n-1)+4 = 3n+1 = O(n)銆傛墍浠ユ渶濂芥椂闂村鏉傚害涓?O(n)銆?/p>
鏈€鍧忔椂闂村鏉傚害锛氬綋搴忓垪涓洪€嗗簭鏃躲€傜涓€涓?for 寰幆鐨勯搴︿负 n锛涚浜屼釜 for 寰幆涓紝j 鍙互鍙?1,2,...,n-1锛屾墍浠ョ 3/4/6/7/8 璇彞锛岄搴﹀潎涓?(1+n-1)??(n-1)/2銆俆(n) = n??(n-1)/2+n = O(n^2)銆傛墍浠ユ渶鍧忔椂闂村鏉傚害涓?O(n^2)銆?/p>
鎴戜滑鍙互鐪嬪嚭鍦ㄥ祵濂楀眰鏁板鐨勫惊鐜鍙ヤ腑锛岀敱鏈€鍐呭眰璇彞鐨勯搴?f(n) 鍐冲畾鏃堕棿澶嶆潅搴︺€?/p>
浼樺寲 2锛?/h4>
璁板綍鏌愭閬嶅巻鏃舵渶鍚庡彂鐢熷厓绱犱氦鎹㈢殑浣嶇疆锛圠astExchange锛夛紝杩欎釜浣嶇疆涔嬪悗鐨勬暟鎹樉鐒跺凡缁忔湁搴忥紝涓嶇敤鍐嶆帓搴忎簡銆傚洜姝ら€氳繃璁板綍鏈€鍚庡彂鐢熷厓绱犱氦鎹㈢殑浣嶇疆灏卞彲浠ョ‘瀹氫笅娆″惊鐜殑鑼冨洿銆?/p>
public static void bubbleSort3(int[] input) {
int LastExchange = input.length;
boolean flag = true;
for (int i = 1; i <= input.length; i++) {
int k = LastExchange;
for (int j = 1; j <= k - 1; j++) {
if (input[j - 1] > input[j]) {
int temp = input[j - 1];
input[j - 1] = input[j];
input[j] = temp;
}
LastExchange = j;
flag = false;
}
if (flag)
break;
}
}
蹇€熸帓搴忥紙Quick Sort锛?/h2>
鍙堢О鍒掑垎浜ゆ崲鎺掑簭锛坧artition-exchange sort锛夈€傞噰鐢ㄤ簡鍒嗚€屾不涔嬬殑鎬濇兂銆?/p>
鎬濊矾
- 閫掑綊缁撴潫鏉′欢锛? 涓暟鎴?0 涓暟涓嶇敤鎺掑簭
- 鎵句竴涓熀鍑嗗€硷紝浠庝袱杈瑰悜涓棿閬嶅巻锛屽皢宸﹁竟澶т簬鍩哄噯鍊间笌鍙宠竟灏忎簬鍩哄噯鍊间氦鎹€?strong>涓€娆℃帓搴忓悗锛屽乏杈规墍鏈夌殑鏁版瘮鍙宠竟鎵€鏈夌殑鏁板皬
閫夋嫨鏈熬鏁颁负鍩哄噯鍊?/p>
- 濡傛灉閫夋嫨涓綅鏁颁綔涓哄熀鍑嗗€硷紝鑰冭檻鏉′欢澶锛屾瘮濡?
20, 2, 10 ,1, 6, 9
鎺掑簭婕旂ず
6 5 3 1 8 7 2 4
鈫? 鈫? ^
2 5 3 1 8 7 6 4
鈫? 鈫? ^
2 1 3 5 8 7 6 4
鈫? ^
2 1 3 [4] 8 7 6 5
婧愪唬鐮?/h3>
// Java
public static void quickSort(int[] input) {
quick_sort(input, 0, input.length - 1);
}
private static void quick_sort(int[] input, int start, int end) {
if (start >= end) {
return;
}
int left = start, right = end - 1;
int pivot = input[end];
while (left < right) {
// 璺宠繃
while (input[left] <= pivot && left < right) {
left++;
}
while (input[right] >= pivot && left < right) {
right--;
}
int temp = input[left];
input[left] = input[right];
input[right] = temp;
}
// 姝ゆ椂宸﹀彸鎸囬拡閲嶅悎锛坙eft == right锛夛紝鍏舵寚鍚戝厓绱犲彲鑳藉ぇ浜庡熀鍑嗗€? if (input[left] >= pivot) {
int temp = input[left];
input[left] = pivot;
input[end] = temp;
} else
left++; // 璺宠繃宸茬粡鏈夊簭鐨勪腑鏁? quick_sort(input, start, left - 1);
quick_sort(input, left, end);
}
绠楁硶鎸囨爣鍒嗘瀽
// Java
public static void quickSort(int[] input) {
quick_sort(input, 0, input.length - 1);
}
private static void quick_sort(int[] input, int start, int end) {
if (start >= end) {
return;
}
int left = start, right = end - 1;
int pivot = input[end];
while (left < right) {
// 璺宠繃
while (input[left] <= pivot && left < right) {
left++;
}
while (input[right] >= pivot && left < right) {
right--;
}
int temp = input[left];
input[left] = input[right];
input[right] = temp;
}
// 姝ゆ椂宸﹀彸鎸囬拡閲嶅悎锛坙eft == right锛夛紝鍏舵寚鍚戝厓绱犲彲鑳藉ぇ浜庡熀鍑嗗€? if (input[left] >= pivot) {
int temp = input[left];
input[left] = pivot;
input[end] = temp;
} else
left++; // 璺宠繃宸茬粡鏈夊簭鐨勪腑鏁? quick_sort(input, start, left - 1);
quick_sort(input, left, end);
}
鏈€濂芥椂闂村鏉傚害锛歯*log n銆俷锛氫氦鎹紱log n锛氳皟鐢ㄦ爤鐨勯珮搴︼紙2^(high-1) = n锛夛紝鏁扮粍鏈夊簭涓斿熀鍑嗗€兼瘡娆￠兘鏄腑闂村€笺€?/p>
鏈€鍧忔椂闂村鏉傚害锛歯^2銆傝皟鐢ㄦ爤鐨勯珮搴︿负 n锛屽熀鍑嗗€兼瘡娆￠兘鏄渶鍊笺€?/p>
骞冲潎鏃堕棿澶嶆潅搴︼細O(n log n)銆傞殢鏈洪€夋嫨鍩哄噯鍊?(log n + n)/2 = log n
杈呭姪绌洪棿锛氶渶瑕侀涓存椂鐨勫瓨鍌ㄧ┖闂存潵杩愯绠楁硶锛屾墍浠ヤ负 O(n log n)~O(n)銆?/p>
绋冲畾鎬э細涓嶇ǔ瀹氥€?/p>
鏇村瀹炵幇鏂瑰紡锛?a href="https://depp.wang/2020/06/18/several-implementations-of-quick-sort/">蹇€熸帓搴忕殑鍑犵瀹炵幇鏂瑰紡
閫夋嫨鎺掑簭锛圫election Sort锛?/h2>
姣忎竴娆￠€氳繃閫夋嫨鎵惧埌鏈帓搴忓簭鍒楃殑鏈€灏忥紙澶э級鍏冪礌鏀惧湪宸叉帓搴忓簭鍒楃殑鏈熬锛堜氦鎹綅缃級锛岀洿鑷虫湁搴忋€?/p>
鎬濊矾
- 閫夋嫨鎺掑簭涓€閬嶉亶鍘嗭紝鍙氦鎹竴娆★紝鑰屽啋娉℃帓搴忎細浜ゆ崲澶氭銆?/li>
姝ラ
- 鏈帓搴忓簭鍒椾腑鎵惧埌鏈€灏忥紙澶э級鍏冪礌锛屽瓨鏀惧埌搴忓垪鐨勮捣濮嬩綅缃€?/li>
- 鍐嶄粠鍓╀綑鏈帓搴忓厓绱犱腑缁х画鎵惧埌鏈€灏忥紙澶э級鍏冪礌锛屾斁鍒板凡鎺掑簭搴忓垪鐨勬湯灏俱€?/li>
- 浠ユ绫绘帹锛岀洿鍒版墍鏈夊厓绱犲潎鎺掑簭瀹屾瘯銆?/li>
鎺掑簭婕旂ず
婧愪唬鐮侊紙Java 瀹炵幇锛?/h3>
public static void selectionSort(int[] input) {
for (int i = 1; i <= input.length; i++) {
int minIndex = i - 1;
for (int j = i; j < input.length; j++) {
if (input[minIndex] > input[j])
minIndex = j;
}
if (minIndex != i - 1) {
int temp = input[minIndex];
input[minIndex] = input[i - 1];
input[i - 1] = temp;
}
}
}
绠楁硶鎸囨爣鍒嗘瀽
public static void selectionSort(int[] input) {
for (int i = 1; i <= input.length; i++) {
int minIndex = i - 1;
for (int j = i; j < input.length; j++) {
if (input[minIndex] > input[j])
minIndex = j;
}
if (minIndex != i - 1) {
int temp = input[minIndex];
input[minIndex] = input[i - 1];
input[i - 1] = temp;
}
}
}
涓嶇搴忓垪鏈夊簭杩樻槸閫嗗簭锛岀浜屼釜 for 寰幆鐨勯搴︿负 n*(n-1)/2銆傛墍浠ユ渶鍧忔椂闂村鏉傚害鍜屾渶濂芥椂闂村鏉傚害鍧囦负 O(n^2)銆?/p>
骞冲潎鏃堕棿澶嶆潅搴︼細O(n^2)
杈呭姪绌洪棿锛氫笉闇€瑕侀涓存椂鐨勫瓨鍌ㄧ┖闂存潵杩愯绠楁硶锛屾墍浠ヤ负 O(1)銆?/p>
绋冲畾鎬э細涓嶇ǔ瀹氥€備妇渚嬶紝5銆?銆?銆?銆?锛屾壘鍒版渶灏?2 鏃讹紝2 涓?5 浜ゆ崲锛屾鏃朵袱涓?5 鐨勭浉瀵逛綅缃彂鐢熸敼鍙樸€?/p>
鎻掑叆鎺掑簭锛圛nsertion Sort锛?/h2>
瀵逛簬姣忎釜鏈帓搴忓厓绱狅紝鍦ㄥ凡鎺掑簭搴忓垪涓?strong>浠庡悗鍚戝墠鎵弿锛屾壘鍒扮浉搴斾綅缃苟鎻掑叆銆?/p>
鎬濊矾
- 鎻掑叆鏃讹紝闇€瑕佺Щ鍔ㄥ悗闈㈢殑鍏冪礌锛熸彃鍏ュ苟涓嶆槸鐪熸鐨勬彃鍏ワ紝鑰屾槸浠庡悗寰€鍓嶄袱涓や氦鎹紝鏈€缁堟晥鏋滃儚鎻掑叆涓€鏍枫€?/li>
姝ラ
- 绗?1 涓厓绱犺涓哄凡缁忚鎺掑簭
- 鍙栨湭鎺掑簭鐨勭 1 涓厓绱狅紝鍦ㄥ凡鎺掑簭搴忓垪涓粠鍚庡悜鍓嶆壂鎻?/li>
- 濡傛灉琚壂鎻忕殑鍏冪礌澶т簬鏂板厓绱狅紝灏嗚鍏冪礌鍚庣Щ涓€浣?/li>
- 閲嶅姝ラ 3锛岀洿鍒版壘鍒板凡鎺掑簭鐨勫厓绱犲皬浜庢垨鑰呯瓑浜庢柊鍏冪礌鐨勪綅缃?/li>
- 灏嗘柊鍏冪礌鎻掑叆鍒拌浣嶇疆鍚?/li>
- 閲嶅姝ラ 2~5
- 濡傛灉鍏ㄩ儴鏈夊簭锛岀粨鏉熻凯浠?/li>
鎺掑簭婕旂ず
6 5 3 1 8 7 2 4
5 6 3 1 8 7 2 4 5 6 浜ゆ崲
5 3 6 1 8 7 2 4 6 3 浜ゆ崲
3 5 6 1 8 7 2 4 3 5 浜ゆ崲
婧愪唬鐮?(Java 瀹炵幇)
public static void insertionSort(int[] input) {
for (int i = 1; i < input.length; i++) {
for (int j = i; j > 0; j--) {
if (input[j] < input[j - 1]) {
int temp = input[j];
input[j] = input[j - 1];
input[j - 1] = temp;
}
else break;
}
}
}
绠楁硶鎸囨爣鍒嗘瀽
鏈€濂芥椂闂村鏉傚害锛氬綋搴忓垪鏈夊簭鏃躲€傚綋绗竴涓?for 寰幆杩愯鏃讹紝鍦ㄧ浜屼釜 for 寰幆涓紝鍥犱负搴忓垪鏈夊簭锛屾墍浠ュ彧浼氱浉閭绘瘮杈?1 娆★紝灏辫烦鍑哄惊鐜€傛墍浠ヤ袱涓惊鐜殑棰戝害鍧囦负 n-1锛屾墍浠ユ渶濂芥椂闂村鏉傚害鍧囦负 O(n)銆?/p>
鏈€鍧忔椂闂村鏉傚害锛氬綋搴忓垪閫嗗簭鏃躲€傜浜屼釜 for 寰幆鐨勯搴︿负 n(n-1)/2銆傛墍浠ユ渶鍧忔椂闂村鏉傚害鍧囦负 O(n^2)銆?/p>
骞冲潎鏃堕棿澶嶆潅搴︼細O((n+n^2)/2) = O(n^2)銆?/p>
杈呭姪绌洪棿锛氫笉闇€瑕侀涓存椂鐨勫瓨鍌ㄧ┖闂存潵杩愯绠楁硶锛屾墍浠ヤ负 O(1)銆?/p>
绋冲畾鎬э細鍥犱负鎺掑簭鏂瑰紡鏄袱涓ゆ瘮杈冿紝搴忓垪涓鏋滅浉閭讳袱涓暟鐩哥瓑锛屼笉浼氫氦鎹袱鑰呯殑浣嶇疆锛屾墍浠ョǔ瀹氥€?/p>
甯屽皵鎺掑簭锛圫hell Sort锛?/h2>
甯屽皵鎺掑簭锛屼篃绉伴€掑噺澧為噺鎺掑簭绠楁硶锛屽疄璐ㄤ笂鏄竴绉嶅垎缁勬彃鍏ユ帓搴忕畻娉曘€傛槸鎻掑叆鎺掑簭鐨勪竴绉嶆洿楂樻晥鐨勬敼杩涚増鏈€?甯屽皵鎺掑簭鏄熀浜庢彃鍏ユ帓搴忕殑浠ヤ笅涓ょ偣鎬ц川鑰屾彁鍑烘敼杩涙柟娉曠殑锛?/p>
- 鎻掑叆鎺掑簭鍦ㄥ鍑犱箮宸茬粡鎺掑ソ搴忕殑鏁版嵁鎿嶄綔鏃讹紝鏁堢巼楂橈紝鍗冲彲浠ヨ揪鍒扮嚎鎬ф帓搴忕殑鏁堢巼
- 浣嗘彃鍏ユ帓搴忎竴鑸潵璇存槸浣庢晥鐨勶紝鍥犱负鎻掑叆鎺掑簭姣忔鍙兘灏嗘暟鎹Щ鍔ㄤ竴浣?/li>
姝ラ
- 鍋囪鏁扮粍涓?
{5, 4, 7, 1, 6, 2, 8, 9, 10}锛屽鏋滄垜浠互姝ラ暱涓?4 寮€濮嬭繘琛屾帓搴忥紝鎴戜滑鍙互閫氳繃灏嗚繖鍒楄〃鏀惧湪鏈?4 鍒楃殑琛ㄤ腑鏉ユ洿濂藉湴鎻忚堪绠楁硶锛岃繖鏍蜂粬浠氨搴旇鐪嬭捣鏉ユ槸杩欐牱锛?/li>
5, 4, 7, 1 6, 2, 8, 9 10
- 灏嗘暟缁勫垪鍦ㄤ竴涓〃涓苟瀵瑰垪鍒嗗埆杩涜鎻掑叆鎺掑簭
5, 2, 7, 1 6, 4, 8, 9 10
- 閲嶅杩欒繃绋嬶紝涓嶈繃姣忔鐢ㄦ洿闀跨殑鍒楋紙姝ラ暱鏇村皬锛屽垪鏁版洿灏戯級鏉ヨ繘琛岋紝濡備笅姝ラ暱涓?2銆?/li>
5, 2
7, 1
6, 4
8, 9
10
- 鏈€鍚庢暣涓〃灏卞彧鏈変竴鍒椾簡锛?鍐嶈繘琛屾彃鍏ユ帓搴忥級
5, 1, 6, 2, 7, 4, 8, 9, 10
婧愪唬鐮侊紙Java 瀹炵幇锛?/h3>
public static void shellSort(int[] input) {
int len = input.length, j;
int gap = Math.round(len / 2);
for (; gap > 0; gap /= 2) // 姝ラ暱姣忔灏卞噺灏戜竴鍊? for (int i = gap; i < len; i++) {
int temp = input[i];
for (j = i - gap; j >= 0 && temp < input[j]; j -= gap) {// 鍒楁帓搴? input[j + gap] = input[j];
input[j] = temp;
}
}
}
绠楁硶鎸囨爣鍒嗘瀽
public static void shellSort(int[] input) {
int len = input.length, j;
int gap = Math.round(len / 2);
for (; gap > 0; gap /= 2) // 姝ラ暱姣忔灏卞噺灏戜竴鍊? for (int i = gap; i < len; i++) {
int temp = input[i];
for (j = i - gap; j >= 0 && temp < input[j]; j -= gap) {// 鍒楁帓搴? input[j + gap] = input[j];
input[j] = temp;
}
}
}
鏈€濂芥椂闂村鏉傚害锛氬綋搴忓垪鏈夊簭鏃躲€傛渶濂芥椂闂村鏉傚害鍧囦负 O(n^s)锛?<s<2锛岃窡绠楁硶姝ラ暱鏈夊叧銆?/p>
鏈€鍧忔椂闂村鏉傚害锛氬綋搴忓垪閫嗗簭鏃躲€傛渶鍧忔椂闂村鏉傚害鍧囦负 O(n^2)銆?/p>
骞冲潎鏃堕棿澶嶆潅搴︼細O(n log n)~O(n^2)銆?/p>
杈呭姪绌洪棿锛氫笉闇€瑕侀涓存椂鐨勫瓨鍌ㄧ┖闂存潵杩愯绠楁硶锛屾墍浠ヤ负 O(1)銆?/p>
绋冲畾鎬э細涓嶇ǔ瀹氥€傝В閲婂涓嬶細
鍋囪锛屽簭鍒椾负 5,5,7,3,2锛屽彇姝ラ暱涓?3 鍒嗙粍涓?5,5,7
3,6
3 鍜?5 浜ゆ崲浣嶇疆鍚庯紝涓や釜 5 鐨勭浉瀵归『搴忓彂鐢熸敼鍙橈紝鎵€浠ヤ笉绋冲畾
鍫嗘帓搴忥紙HeapSort锛?/h2>
浣跨敤鍒颁簩鍙夊爢杩欑鏁版嵁缁撴瀯锛屼簩鍙夊爢鏄钩琛′簩鍙夋爲銆傚畠鍏锋湁浠ヤ笅鎬ц川锛?/p>
- 鐖惰妭鐐圭殑鍊煎ぇ浜庣瓑浜庡乏鍙宠妭鐐圭殑鍊硷紝涓烘渶澶у爢锛堝ぇ椤跺爢锛夛紱鐖惰妭鐐圭殑鍊煎皬浜庝簬绛変簬宸﹀彸鑺傜偣鐨勫€硷紝涓烘渶灏忓爢锛堝ぇ椤跺爢锛?/li>
- 姣忎釜鐖惰妭鐐圭殑宸﹀彸鑺傜偣閮芥槸浜屽弶鍫嗭紙澶ч《鍫嗘垨灏忛《鍫嗭級
鏈川涓婂爢鎺掑簭鏄敱鏁扮粍瀹炵幇銆?/p>
姝ラ
- 璋冪敤鏋勯€犲ぇ椤跺爢鏂规硶锛屽皢鏁扮粍鏋勯€犳垚澶ч《鍫嗐€傚彾瀛愯妭鐐圭浉褰撲簬澶ч《鍫嗭紝鍋囪鏁扮粍涓嬫爣鑼冨洿涓?0~n-1锛屽垯浠庝笅鏍?n/2 寮€濮嬬殑鍏冪礌锛堝彾瀛愯妭鐐癸級鍧囦负澶ч《鍫嗐€傛墍浠ヤ粠涓嬫爣 n/2-1 寮€濮嬬殑鍏冪礌锛堢埗鑺傜偣锛夊紑濮嬶紝鍚戝墠渚濇锛堜笅鏍囧噺 1锛夋瀯閫犲ぇ椤跺爢銆?/li>
- 鍫嗘帓搴忥細鐢变簬鍫嗘槸鐢ㄦ暟缁勬ā鎷熺殑銆傛瀯閫犵殑澶ч《鍫嗙浉褰撲簬鍦ㄦ暟缁勪腑鏃犲簭銆傚洜姝ら渶瑕佸皢鏁扮粍鏈夊簭鍖栥€傛€濇兂鏄惊鐜皢鏍硅妭鐐逛笌鏈€鍚庝竴涓湭鎺掑簭鍏冪礌浜ゆ崲锛屽啀璋冪敤鏋勯€犲ぇ椤跺爢鏂规硶銆傚惊鐜粨鏉熷悗锛屾暣涓暟缁勫氨鏄湁搴忕殑浜嗐€?/li>
- 鏋勯€犲ぇ椤跺爢鏂规硶锛氳皟鏁磋妭鐐癸紝浣垮緱宸﹀彸瀛愯妭鐐瑰皬浜庣埗鑺傜偣锛屼繚璇佹牴鑺傜偣鏄綋鍓嶅爢涓渶澶х殑鍏冪礌銆?/li>
鎺掑簭婕旂ず锛?/h3>
绗竴娆″皢鏁扮粍鏋勯€犳垚澶ч《鍫嗘椂锛岃窡姝ゆ紨绀虹◢鏈変笉鍚岋紝榛樿鎸夋暟缁勯『搴忔斁鍏ヤ簩鍙夊爢锛屾病鏈夎竟鏀捐竟鏋勯€犮€?/p>
婧愪唬鐮侊紙Java 瀹炵幇锛?/h3>
public static void heapSort(int[] input) {
int i = input.length/ 2 - 1;// 鏈€鍚庝竴涓潪鍙跺瓙鑺傜偣
// 灏嗘暟缁勬瀯閫犳垚澶ч《鍫? for (; i >= 0; i--)
maxHeapify(input, i, input.length - 1);
// 鍫嗘帓锛屽皢澶ч《鍫嗚浆鎹㈡垚鏈夊簭鏁扮粍
for (i = input.length - 1; i >= 0; i--) {
int temp = input[0];
input[0] = input[i];
input[i] = temp;
maxHeapify(input, 0, i - 1);
}
}
// 鏋勯€犲ぇ椤跺爢
public static void maxHeapify(int[] input, int start, int end) {
int child;
int root = start;
// 鐖惰妭鐐逛笉鏄彾瀛愯妭鐐规椂寰幆锛涘彧鏈変竴涓牴鑺傜偣鏃朵笉鍐嶆瘮杈? for (; root <= (end - 1) / 2 && end > 0; ) {
child = root * 2 + 1;// 璋冩暣瀛愯妭鐐? // 鍙栬緝澶х殑瀛愯妭鐐? if (child + 1 <= end && input[child] < input[child + 1])
child += 1;
if (input[root] < input[child]) {
// 浜ゆ崲杈冨皬鐖惰妭鐐瑰拰杈冨ぇ瀛愯妭鐐圭殑浣嶇疆
int temp = input[root];
input[root] = input[child];
input[child] = temp;
root = child;// 杈冨ぇ鐨勫瓙鑺傜偣鎴愪负鐖惰妭鐐? } else
break;
}
}
绠楁硶鎸囨爣鍒嗘瀽
public static void heapSort(int[] input) {
int i = input.length/ 2 - 1;// 鏈€鍚庝竴涓潪鍙跺瓙鑺傜偣
// 灏嗘暟缁勬瀯閫犳垚澶ч《鍫? for (; i >= 0; i--)
maxHeapify(input, i, input.length - 1);
// 鍫嗘帓锛屽皢澶ч《鍫嗚浆鎹㈡垚鏈夊簭鏁扮粍
for (i = input.length - 1; i >= 0; i--) {
int temp = input[0];
input[0] = input[i];
input[i] = temp;
maxHeapify(input, 0, i - 1);
}
}
// 鏋勯€犲ぇ椤跺爢
public static void maxHeapify(int[] input, int start, int end) {
int child;
int root = start;
// 鐖惰妭鐐逛笉鏄彾瀛愯妭鐐规椂寰幆锛涘彧鏈変竴涓牴鑺傜偣鏃朵笉鍐嶆瘮杈? for (; root <= (end - 1) / 2 && end > 0; ) {
child = root * 2 + 1;// 璋冩暣瀛愯妭鐐? // 鍙栬緝澶х殑瀛愯妭鐐? if (child + 1 <= end && input[child] < input[child + 1])
child += 1;
if (input[root] < input[child]) {
// 浜ゆ崲杈冨皬鐖惰妭鐐瑰拰杈冨ぇ瀛愯妭鐐圭殑浣嶇疆
int temp = input[root];
input[root] = input[child];
input[child] = temp;
root = child;// 杈冨ぇ鐨勫瓙鑺傜偣鎴愪负鐖惰妭鐐? } else
break;
}
}
鏈€濂芥椂闂村鏉傚害锛氬綋搴忓垪鏈夊簭鏃躲€傛渶濂芥椂闂村鏉傚害鍧囦负 O(n log n)锛岃窡绠楁硶姝ラ暱鏈夊叧銆?/p>
鏈€鍧忔椂闂村鏉傚害锛氬綋搴忓垪閫嗗簭鏃躲€傛渶鍧忔椂闂村鏉傚害鍧囦负 O(n log n)銆?/p>
骞冲潎鏃堕棿澶嶆潅搴︼細O(n log n)銆?/p>
杈呭姪绌洪棿锛氫笉闇€瑕侀涓存椂鐨勫瓨鍌ㄧ┖闂存潵杩愯绠楁硶锛屾墍浠ヤ负 O(1)銆?/p>
绋冲畾鎬э細涓嶇ǔ瀹氥€?/p>
浜屽垎褰掑苟鎺掑簭锛圡ergeSort锛?/h2>
鍏堥€掑綊鍒嗚В搴忓垪锛屽啀鍚堝苟搴忓垪銆備篃閲囩敤浜嗗垎娌绘硶鐨勬€濇兂銆?/p>
姝ラ
- 鍚堝苟锛氬悎骞剁殑鏉′欢鏄袱涓簭鍒楅兘鏈夊簭锛屽綋搴忓垪涓彧鏈?1 涓厓绱犳椂鎴戜滑璁や负涔熸槸鏈夊簭鐨勶紱鍚堝苟鐨勬柟娉曟槸閫氳繃姣旇緝灏嗚緝灏忓厓绱犲厛鏀惧叆涓存椂鏁扮粍锛屽啀灏嗗乏銆佸彸搴忓垪鍓╀綑鍏冪礌鏀惧叆銆?/li>
- 鍒嗚В锛氬厛灏嗘簮搴忓垪浠庝腑浣嶆暟锛堜腑鏁帮級鍒嗗紑涓哄乏鍙冲簭鍒楋紝閫掑綊鍒嗚В宸﹀簭鍒楋紝涓暟涓嶆柇鍑忓皬锛岀洿鍒颁负 1銆傛鏃跺乏銆佸彸搴忓垪涓彧鏈変竴涓厓绱狅紝閫氳繃姣旇緝灏嗗乏銆佸彸搴忓垪鍚堝苟涓哄乏搴忓垪鍚庯紝鍐嶉€掑綊鍒嗚В鍙冲簭鍒楋紙涔熷垎瑙ｅ埌鍙湁涓€涓厓绱狅級銆?/li>
鎺掑簭婕旂ず
姝ゅ浘涓昏鎬濇兂涓€鑷达紝浣嗕唬鐮佸疄鐜拌繃绋嬩腑锛?531 鍚堝苟瀹屾垚鏃讹紝8724 杩樻病鍒嗚В銆?/p>
婧愪唬鐮侊紙Java 瀹炵幇锛?/h3>
public static void mergeSort(int[] input) {
merge_sort(input, 0, input.length - 1);
}
public static void merge_sort(int[] input, int start, int end) {
int middle;
// 褰撳簭鍒椾腑鍙湁涓€涓厓绱犳椂锛岀粨鏉熷綋鍓嶉€掑綊
if (start < end) {
middle = (start + end) / 2;// 鎵惧嚭涓綅鏁帮紙涓暟锛夛紝涓暟瓒婃潵瓒婂皬
merge_sort(input, start, middle);// 涓暟宸︿晶搴忓垪浜屽垎
merge_sort(input, middle + 1, end);// 涓暟鍙充晶搴忓垪浜屽垎
merge(input, start, middle, end);// 鍚堝苟鎴愭簮搴忓垪
}
}
// 鍚堝苟鎴愭簮搴忓垪
public static void merge(int[] input, int left, int middle, int right) {
int[] temp = new int[right - left + 1];// 鐢ㄤ簬瀛樻斁鏂版帓濂藉簭鐨勫簭鍒? int i = left;// 宸﹀簭鍒楃殑璧峰涓嬫爣
int j = middle + 1;// 鍙冲簭鍒楃殑璧峰涓嬫爣
int n = 0;//temp[] 鏁扮粍鐨勮捣濮嬩笅鏍? // 閫氳繃姣旇緝灏嗚緝灏忓厓绱犲厛鏀惧叆 temp 鏁扮粍
while (i <= middle && j <= right) {
if (input[i] < input[j]) {
temp[n] = input[i];
i++;
} else {
temp[n] = input[j];
j++;
}
n++;
}
// 灏嗙涓€涓簭鍒楃殑鍓╀綑鍏冪礌鏀惧叆 temp[]
while (i <= middle) {
temp[n] = input[i];
i++;
n++;
}
// 灏嗙浜屼釜搴忓垪鐨勫墿浣欏厓绱犳斁鍏?temp[]
while (j <= right) {
temp[n] = input[j];
j++;
n++;
}
// 灏?num[] 涓殑鍏冪礌澶嶅埗鍒版暟缁?input
for (int x = 0, y = left; x <= n && y <= right; x++, y++)
input[y] = temp[x];
}
绠楁硶鎸囨爣鍒嗘瀽
public static void mergeSort(int[] input) {
merge_sort(input, 0, input.length - 1);
}
public static void merge_sort(int[] input, int start, int end) {
int middle;
// 褰撳簭鍒椾腑鍙湁涓€涓厓绱犳椂锛岀粨鏉熷綋鍓嶉€掑綊
if (start < end) {
middle = (start + end) / 2;// 鎵惧嚭涓綅鏁帮紙涓暟锛夛紝涓暟瓒婃潵瓒婂皬
merge_sort(input, start, middle);// 涓暟宸︿晶搴忓垪浜屽垎
merge_sort(input, middle + 1, end);// 涓暟鍙充晶搴忓垪浜屽垎
merge(input, start, middle, end);// 鍚堝苟鎴愭簮搴忓垪
}
}
// 鍚堝苟鎴愭簮搴忓垪
public static void merge(int[] input, int left, int middle, int right) {
int[] temp = new int[right - left + 1];// 鐢ㄤ簬瀛樻斁鏂版帓濂藉簭鐨勫簭鍒? int i = left;// 宸﹀簭鍒楃殑璧峰涓嬫爣
int j = middle + 1;// 鍙冲簭鍒楃殑璧峰涓嬫爣
int n = 0;//temp[] 鏁扮粍鐨勮捣濮嬩笅鏍? // 閫氳繃姣旇緝灏嗚緝灏忓厓绱犲厛鏀惧叆 temp 鏁扮粍
while (i <= middle && j <= right) {
if (input[i] < input[j]) {
temp[n] = input[i];
i++;
} else {
temp[n] = input[j];
j++;
}
n++;
}
// 灏嗙涓€涓簭鍒楃殑鍓╀綑鍏冪礌鏀惧叆 temp[]
while (i <= middle) {
temp[n] = input[i];
i++;
n++;
}
// 灏嗙浜屼釜搴忓垪鐨勫墿浣欏厓绱犳斁鍏?temp[]
while (j <= right) {
temp[n] = input[j];
j++;
n++;
}
// 灏?num[] 涓殑鍏冪礌澶嶅埗鍒版暟缁?input
for (int x = 0, y = left; x <= n && y <= right; x++, y++)
input[y] = temp[x];
}
鏈€濂芥椂闂村鏉傚害锛氬綋搴忓垪鏈夊簭鏃躲€傛渶濂芥椂闂村鏉傚害鍧囦负 O(n log n)銆?/p>
鏈€鍧忔椂闂村鏉傚害锛氬綋搴忓垪閫嗗簭鏃躲€傛渶鍧忔椂闂村鏉傚害鍧囦负 O(n log n)銆?/p>
骞冲潎鏃堕棿澶嶆潅搴︼細O(n log n)銆?/p>
杈呭姪绌洪棿锛氶渶瑕佹柊寤洪澶栦复鏃剁殑瀛樺偍绌洪棿鏉ュ瓨鍌ㄦ柊鎺掑ソ搴忕殑搴忓垪锛屾瘡涓€娆″綊骞堕兘闇€瑕侀噸鏂版柊寤猴紝鏂板缓棰戝害涓?n锛屾墍浠ヨ緟鍔╃┖闂翠负 O(n)銆?/p>
绋冲畾鎬э細绋冲畾銆傚洜涓轰袱涓ゆ瘮杈冦€?/p>
鏃堕棿澶嶆潅搴?/h2>
鏃堕棿棰戝害锛氫竴涓畻娉曡姳璐圭殑鏃堕棿涓庣畻娉曚腑璇彞鐨勬墽琛屾鏁版垚姝ｆ瘮渚嬶紝鍝釜绠楁硶涓鍙ユ墽琛屾鏁板锛屽畠鑺辫垂鏃堕棿灏卞銆備竴涓畻娉曚腑鐨勮鍙ユ墽琛屾鏁扮О涓鸿鍙ラ搴︽垨鏃堕棿棰戝害銆傝涓?T(n)銆?/p>
鏃堕棿澶嶆潅搴?/strong>锛氬湪鍒氭墠鎻愬埌鐨勬椂闂撮搴︿腑锛宯 绉颁负闂鐨勮妯★紝褰?n 涓嶆柇鍙樺寲鏃讹紝鏃堕棿棰戝害 T(n) 涔熶細涓嶆柇鍙樺寲銆備絾鏈夋椂鎴戜滑鎯崇煡閬撳畠鍙樺寲鏃跺憟鐜颁粈涔堣寰嬨€備负姝わ紝鎴戜滑寮曞叆鏃堕棿澶嶆潅搴︽蹇点€?涓€鑸儏鍐典笅锛岀畻娉曚腑鍩烘湰鎿嶄綔閲嶅鎵ц鐨勬鏁版槸闂瑙勬ā n 鐨勬煇涓嚱鏁帮紝鐢?T(n) 琛ㄧず锛岃嫢鏈夋煇涓緟鍔╁嚱鏁?f(n), 浣垮緱褰?n 瓒嬭繎浜庢棤绌峰ぇ鏃讹紝T(n)/f(n) 鐨勬瀬闄愬€间负涓嶇瓑浜庨浂鐨勫父鏁?C锛屽垯绉?f(n) 鏄?T(n) 鐨勫悓鏁伴噺绾у嚱鏁般€傝浣?T(n)=O(f(n)), 绉?O(f(n)) 涓虹畻娉曠殑娓愯繘鏃堕棿澶嶆潅搴︼紝绠€绉版椂闂村鏉傚害銆?/p>
铏界劧瀵?f(n) 娌℃湁瑙勫畾锛屼絾鏄竴鑸兘鏄彇灏藉彲鑳界畝鍗曠殑鍑芥暟銆備緥濡傦紝O(2n^2+n+1) = O(3n^2+n+3) = O(7n^2 + n) = O(n^2) 锛屼竴鑸兘鍙敤 O(n^2) 琛ㄧず灏卞彲浠ヤ簡銆傛敞鎰忓埌澶?O 绗﹀彿閲岄殣钘忕潃涓€涓父鏁?C锛屾墍浠?f(n) 閲屼竴鑸笉鍔犵郴鏁般€傚鏋滄妸 T(n) 褰撳仛涓€妫垫爲锛岄偅涔?O(f(n)) 鎵€琛ㄨ揪鐨勫氨鏄爲骞诧紝鍙叧蹇冨叾涓殑涓诲共锛屽叾浠栫殑缁嗘灊鏈妭鍏ㄩ兘鎶涘純涓嶇銆?/p>
鏃堕棿棰戝害锛氫竴涓畻娉曡姳璐圭殑鏃堕棿涓庣畻娉曚腑璇彞鐨勬墽琛屾鏁版垚姝ｆ瘮渚嬶紝鍝釜绠楁硶涓鍙ユ墽琛屾鏁板锛屽畠鑺辫垂鏃堕棿灏卞銆備竴涓畻娉曚腑鐨勮鍙ユ墽琛屾鏁扮О涓鸿鍙ラ搴︽垨鏃堕棿棰戝害銆傝涓?T(n)銆?/p>
鏃堕棿澶嶆潅搴?/strong>锛氬湪鍒氭墠鎻愬埌鐨勬椂闂撮搴︿腑锛宯 绉颁负闂鐨勮妯★紝褰?n 涓嶆柇鍙樺寲鏃讹紝鏃堕棿棰戝害 T(n) 涔熶細涓嶆柇鍙樺寲銆備絾鏈夋椂鎴戜滑鎯崇煡閬撳畠鍙樺寲鏃跺憟鐜颁粈涔堣寰嬨€備负姝わ紝鎴戜滑寮曞叆鏃堕棿澶嶆潅搴︽蹇点€?涓€鑸儏鍐典笅锛岀畻娉曚腑鍩烘湰鎿嶄綔閲嶅鎵ц鐨勬鏁版槸闂瑙勬ā n 鐨勬煇涓嚱鏁帮紝鐢?T(n) 琛ㄧず锛岃嫢鏈夋煇涓緟鍔╁嚱鏁?f(n), 浣垮緱褰?n 瓒嬭繎浜庢棤绌峰ぇ鏃讹紝T(n)/f(n) 鐨勬瀬闄愬€间负涓嶇瓑浜庨浂鐨勫父鏁?C锛屽垯绉?f(n) 鏄?T(n) 鐨勫悓鏁伴噺绾у嚱鏁般€傝浣?T(n)=O(f(n)), 绉?O(f(n)) 涓虹畻娉曠殑娓愯繘鏃堕棿澶嶆潅搴︼紝绠€绉版椂闂村鏉傚害銆?/p>
铏界劧瀵?f(n) 娌℃湁瑙勫畾锛屼絾鏄竴鑸兘鏄彇灏藉彲鑳界畝鍗曠殑鍑芥暟銆備緥濡傦紝O(2n^2+n+1) = O(3n^2+n+3) = O(7n^2 + n) = O(n^2) 锛屼竴鑸兘鍙敤 O(n^2) 琛ㄧず灏卞彲浠ヤ簡銆傛敞鎰忓埌澶?O 绗﹀彿閲岄殣钘忕潃涓€涓父鏁?C锛屾墍浠?f(n) 閲屼竴鑸笉鍔犵郴鏁般€傚鏋滄妸 T(n) 褰撳仛涓€妫垫爲锛岄偅涔?O(f(n)) 鎵€琛ㄨ揪鐨勫氨鏄爲骞诧紝鍙叧蹇冨叾涓殑涓诲共锛屽叾浠栫殑缁嗘灊鏈妭鍏ㄩ兘鎶涘純涓嶇銆?/p>
鐢变笂鍥惧彲瑙侊紝甯歌鐨勭畻娉曟椂闂村鏉傚害鐢卞皬鍒板ぇ渚濇涓猴細螣(1)锛溛?log n)锛溛?n)锛溛?nlog n)锛溛?n^2)锛溛?n^3)锛溾€︼紲螣(2^n)锛溛?n!)銆?/p>
鍒嗘瀽浠ヤ笅浠ｇ爜鐨勬椂闂村鏉傚害銆?/p>
i=1;
while (i<=n)
i=i*2;
绗?1 琛岃鍙ョ殑棰戝害涓?1
璁剧 3 琛岃鍙ョ殑鏃堕棿棰戝害涓?f(n)k锛?f(n) = n; -->f(n) = log n
绗?2 琛岃鍙ヨ窡绗?2 涓夎鐨勯搴︿竴鏍凤紝涓?log n
浠ヤ笂浠ｇ爜鐨?T(n) = 2log n+1 = O(log n)
鐢辨鍙锛孴(n) 鐢辨渶澶х殑 f(n) 鍐冲畾銆傚湪宓屽灞傛暟澶氱殑寰幆璇彞涓紝鐢辨渶鍐呭眰璇彞鐨勯搴?f(n) 鍐冲畾 T(n)銆?娉細log n = log?n = lg n锛涘鏉傚害涓互 2 涓哄簳锛屼笉鏄暟瀛︿腑浠?10 涓哄簳銆?/p>
绌洪棿澶嶆潅搴?/h2>
涓€涓畻娉曠殑绌洪棿澶嶆潅搴?(Space Complexity) 瀹氫箟涓鸿绠楁硶鎵€鑰楄垂鐨勫瓨鍌ㄧ┖闂达紝瀹冧篃鏄棶棰樿妯?n 鐨勫嚱鏁般€傛笎杩戠┖闂村鏉傚害涔熷父甯哥畝绉颁负绌洪棿澶嶆潅搴︺€?/p>
涓€涓畻娉曠殑绌洪棿澶嶆潅搴?(Space Complexity) 瀹氫箟涓鸿绠楁硶鎵€鑰楄垂鐨勫瓨鍌ㄧ┖闂达紝瀹冧篃鏄棶棰樿妯?n 鐨勫嚱鏁般€傛笎杩戠┖闂村鏉傚害涔熷父甯哥畝绉颁负绌洪棿澶嶆潅搴︺€?/p>
涓€涓畻娉曞湪璁＄畻鏈哄瓨鍌ㄥ櫒涓婃墍鍗犵敤鐨勫瓨鍌ㄧ┖闂达紝鍖呮嫭锛?/p>
- 瀛樺偍绠楁硶鏈韩鎵€鍗犵敤鐨勫瓨鍌ㄧ┖闂?/li>
- 绠楁硶鐨勮緭鍏ヨ緭鍑烘暟鎹墍鍗犵敤鐨勫瓨鍌ㄧ┖闂?/li>
- 绠楁硶鍦ㄨ繍琛岃繃绋嬩腑涓存椂鍗犵敤鐨勫瓨鍌ㄧ┖闂?/li>
鎴戜滑灏嗙畻娉曞湪杩愯杩囩▼涓复鏃跺崰鐢ㄧ殑瀛樺偍绌洪棿绉颁负杈呭姪绌洪棿锛屽畠闅忕畻娉曠殑涓嶅悓鑰屽紓锛屽彟澶栦袱绉嶅瓨鍌ㄧ┖闂翠笌绠楁硶鏈韩鏃犲叧銆?/p>
濡傚綋涓€涓畻娉曠殑绌洪棿澶嶆潅搴︿负涓€涓父閲忥紝鍗充笉闅忚澶勭悊鏁版嵁閲?n 鐨勫ぇ灏忚€屾敼鍙樻椂锛岃緟鍔╃┖闂村彲琛ㄧず涓?O(1)锛涘綋涓€涓畻娉曠殑绌洪棿澶嶆潅搴︿笌浠?2 涓哄簳鐨?n 鐨勫鏁版垚姝ｆ瘮鏃讹紝杈呭姪绌洪棿鍙〃绀轰负 O(1og?n)锛涘綋涓€涓畻娉曠殑绌洪棿澶嶆潅搴︿笌 n 鎴愮嚎鎬ф瘮渚嬪叧绯绘椂锛岃緟鍔╃┖闂村彲琛ㄧず涓?O(n)銆?/p>
绋冲畾鎬?/h2>
鍦ㄦ帓搴忚繃绋嬩腑锛屽叿鏈夌浉鍚屾暟鍊肩殑瀵硅薄鐨勭浉瀵归『搴忚涓嶈鎵撲贡銆傚鏋滃彲浠ヤ繚璇佷笉琚墦涔卞氨鏄ǔ瀹氱殑锛屽鏋滀笉鑳戒繚璇佸氨鏄笉绋冲畾鐨勩€?/p>
鎬荤粨
鏍规嵁姣忎釜鎺掑簭绠楁硶鍏充簬绋冲畾鎬х殑鎸囨爣鍒嗘瀽锛屽彲浠ュ緱鍑轰互涓嬬粨璁猴細
- 濡傛灉姣忔鍙樻崲閮藉彧鏄氦鎹㈢浉閭荤殑涓や釜鍏冪礌锛岄偅涔堝氨鏄ǔ瀹氱殑銆?/li>
- 濡傛灉姣忔閮芥湁鏌愪釜鍏冪礌鍜屾瘮杈冭繙鐨勫厓绱犵殑浜ゆ崲鎿嶄綔锛岄偅涔堝氨鏄笉绋冲畾鐨勩€?/li>
浠ヤ笂绠楁硶鍗氫富浜叉祴閮借兘姝ｇ‘杩愯銆備互涓嬫槸涓婅堪涓冪绠楁硶鐨勬€ц兘鎸囨爣鍒嗘瀽瀵规瘮鎯呭喌銆?/p>
| 鎺掑簭鏂瑰紡 | 骞冲潎鏃堕棿澶嶆潅搴?/th> | 鏈€濂芥椂闂村鏉傚害 | 鏈€鍧忔椂闂村鏉傚害 | 绌洪棿澶嶆潅搴? 锛堣緟鍔╃┖闂达級 |
绋冲畾鎬?/th> |
|---|---|---|---|---|---|
| 鍐掓场鎺掑簭 | O(n^2) | O(n^2) | O(n^2) | O(1) | 绋冲畾 |
| 蹇€熸帓搴?/td> | O(n log n) | O(n log n) | O(n^2) | O(log n)~O(n) | 涓嶇ǔ瀹?/td> |
| 閫夋嫨鎺掑簭 | O(n^2) | O(n^2) | O(n^2) | O(1) | 涓嶇ǔ瀹?/td> |
| 鎻掑叆鎺掑簭 | O(n^2) | O(n) | O(n^2) | O(1) | 绋冲畾 |
| 甯屽皵鎺掑簭 | O(n log n)~O(n^2) | O(n^s) 锛?<s<1锛岃窡姝ラ暱鏈夊叧锛?/td> | O(n^2) | O(1) | 涓嶇ǔ瀹?/td> |
| 鍫嗘帓搴?/td> | O(n log n) | O(n log n) | O(n log n) | O(1) | 涓嶇ǔ瀹?/td> |
| 浜屽垎褰掑苟鎺掑簭 | O(n log n) | O(n log n) | O(n log n) | O(n) | 绋冲畾 |
鍙傝€冭祫鏂?/h2>
- 缁村熀鐧剧锛?a href="https://zh.wikipedia.org/wiki/%E5%B8%8C%E5%B0%94%E6%8E%92%E5%BA%8F#Java">甯屽皵鎺掑簭 銆?a href="https://zh.wikipedia.org/wiki/%E5%BF%AB%E9%80%9F%E6%8E%92%E5%BA%8F#Java">蹇€熸帓搴?/a>
- 缁忓吀鎺掑簭绠楁硶鎬荤粨涓庡疄鐜?/a> ---Python 瀹炵幇
- 鐧借瘽缁忓吀绠楁硶绯诲垪涔嬩竴 鍐掓场鎺掑簭鐨勪笁绉嶅疄鐜?/a>
- 鍑犵缁忓吀鎺掑簭绠楁硶
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- 鎺掑簭绠楁硶鐨勭ǔ瀹氭€?/a>
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