銆愭暟鎹粨鏋勩€戝崄澶ф帓搴忕畻娉曗€斺€?C++瀹炵幇

Posted 2021-04-04 OAOA

馃槈馃グ馃槡馃槞馃ぉ馃槤馃榿馃槄馃き馃槃馃檪

浜虹被涓轰綍

閮界埍鐪嬪ぉ绌?/strong>

鈥?/span> 杩欐涓滆タ澶锛屽氨鍏堜笉瀛︿竴涓崟璇嶇儹鐑韩浜嗭紒鈥?/span>

---

Contents

• 0 绠楁硶姒傝堪
• 1 鍐掓场鎺掑簭
• 2 閫夋嫨鎺掑簭
• 3 鎻掑叆鎺掑簭
• 4 甯屽皵鎺掑簭
• 5 褰掑苟鎺掑簭
• 6 閫夋嫨鎺掑簭
• 7 鍫嗘帓搴忥紙Heap Sort锛?/span>
• 8 璁℃暟鎺掑簭
• 9 妗舵帓搴?/span>
• 10 鍩烘暟鎺掑簭

---

0 绠楁硶姒傝堪

0.1 绠楁硶鍒嗙被

鍗佺甯歌鎺掑簭绠楁硶鍙互鍒嗕负涓ゅぇ绫伙細

锛堥€夋场鎻掞紝蹇綊鍫嗗笇缁熻鍩猴級

鈥?鈥?鈥傛瘮杈冪被鎺掑簭锛氶€氳繃姣旇緝鏉ュ喅瀹氬厓绱犻棿鐨勭浉瀵规搴忥紝鐢变簬鍏舵椂闂村鏉傚害涓嶈兘绐佺牬O(nlogn)锛屽洜姝や篃绉颁负闈炵嚎鎬ф椂闂?/strong>姣旇緝绫绘帓搴忋€?/span>

鈥?鈥?鈥傞潪姣旇緝绫绘帓搴忥細涓嶉€氳繃姣旇緝鏉ュ喅瀹氬厓绱犻棿鐨勭浉瀵规搴忥紝鑰屾槸閫氳繃纭畾姣忎釜鍏冪礌涔嬪墠锛屽簲璇ユ湁澶氬皯涓厓绱犳潵鎺掑簭銆傚畠鍙互绐佺牬鍩轰簬姣旇緝鎺掑簭鐨勬椂闂翠笅鐣岋紝浠ョ嚎鎬ф椂闂碠(n)杩愯锛屽洜姝や篃绉颁负绾挎€ф椂闂?/strong>闈炴瘮杈冪被鎺掑簭銆?/span>

鍏充簬姣旇緝鍜岄潪姣旇緝鎺掑簭锛?/span>

鈥?鈥?鈥傚父瑙佺殑蹇€熸帓搴忋€佸綊骞舵帓搴忋€佸爢鎺掑簭銆佸啋娉℃帓搴?绛夊睘浜庢瘮杈冩帓搴?銆傚湪鎺掑簭鐨勬渶缁堢粨鏋滈噷锛屽厓绱犱箣闂寸殑娆″簭渚濊禆浜庡畠浠箣闂寸殑姣旇緝銆傛瘡涓暟閮藉繀椤诲拰鍏朵粬鏁拌繘琛屾瘮杈冿紝鎵嶈兘纭畾鑷繁鐨勪綅缃?銆?/span>

鈥?鈥?nbsp;鈥?/span>鍦ㄥ啋娉℃帓搴忎箣绫荤殑鎺掑簭涓紝闂瑙勬ā涓簄锛屽張鍥犱负闇€瑕佹瘮杈僴娆★紝鎵€浠ュ钩鍧囨椂闂村鏉傚害涓篛(n虏)銆傚湪褰掑苟鎺掑簭銆佸揩閫熸帓搴忎箣绫荤殑鎺掑簭涓紝闂瑙勬ā閫氳繃鍒嗘不娉曟秷鍑忎负logN娆★紝鎵€浠ユ椂闂村鏉傚害骞冲潎O(nlogn)銆?/span>

鈥?鈥?nbsp;鈥?/span>姣旇緝鎺掑簭鐨勪紭鍔挎槸锛岄€傜敤浜庡悇绉嶈妯＄殑鏁版嵁锛屼篃涓嶅湪涔庢暟鎹殑鍒嗗竷锛岄兘鑳借繘琛屾帓搴忋€傚彲浠ヨ锛屾瘮杈冩帓搴忛€傜敤浜庝竴鍒囬渶瑕佹帓搴忕殑鎯呭喌銆?br>

璁℃暟鎺掑簭銆佸熀鏁版帓搴忋€佹《鎺掑簭鍒欏睘浜庨潪姣旇緝鎺掑簭 銆傞潪姣旇緝鎺掑簭鏄€氳繃纭畾姣忎釜鍏冪礌涔嬪墠锛屽簲璇ユ湁澶氬皯涓厓绱犳潵鎺掑簭銆傞拡瀵规暟缁刟rr锛岃绠梐rr[i]涔嬪墠鏈夊灏戜釜鍏冪礌锛屽垯鍞竴纭畾浜哸rr[i]鍦ㄦ帓搴忓悗鏁扮粍涓殑浣嶇疆 銆?br>

鈥?鈥?nbsp;鈥?/span>闈炴瘮杈冩帓搴?/strong>鍙纭畾姣忎釜鍏冪礌涔嬪墠鐨勫凡鏈夌殑鍏冪礌涓暟鍗冲彲锛屾墍鏈変竴娆￠亶鍘嗗嵆鍙В鍐炽€傜畻娉曟椂闂村鏉傚害O(n)銆傞潪姣旇緝鎺掑簭鏃堕棿澶嶆潅搴﹀簳锛屼絾鐢变簬闈炴瘮杈冩帓搴忛渶瑕佸崰鐢ㄧ┖闂存潵纭畾鍞竴浣嶇疆銆傛墍浠ュ鏁版嵁瑙勬ā鍜屾暟鎹垎甯冩湁涓€瀹氱殑瑕佹眰銆?/span>

0.2 绠楁硶澶嶆潅搴?/span>

0.3 鐩稿叧姒傚康

绋冲畾锛?/span>濡傛灉a鍘熸湰鍦╞鍓嶉潰锛岃€宎=b锛屾帓搴忎箣鍚巃浠嶇劧鍦╞鐨勫墠闈€?/span>

涓嶇ǔ瀹氾細濡傛灉a鍘熸湰鍦╞鐨勫墠闈紝鑰宎=b锛屾帓搴忎箣鍚?a 鍙兘浼氬嚭鐜板湪 b 鐨勫悗闈€?/span>

鏃堕棿澶嶆潅搴︼細瀵规帓搴忔暟鎹殑鎬荤殑鎿嶄綔娆℃暟銆傚弽鏄犲綋n鍙樺寲鏃讹紝鎿嶄綔娆℃暟鍛堢幇浠€涔堣寰嬨€?/span>

绌洪棿澶嶆潅搴︼細鏄寚绠楁硶鍦ㄨ绠楁満鍐呮墽琛屾椂鎵€闇€瀛樺偍绌洪棿鐨勫害閲忥紝瀹冧篃鏄暟鎹妯鐨勫嚱鏁般€?/span>

---

01

鈥?/span>

鍐掓场鎺掑簭

鈥?鈥?鈥傝繖涓畻娉曞悕瀛楃殑鐢辨潵鏄洜涓鸿秺灏忕殑鍏冪礌浼氱粡浜ゆ崲鎱㈡參"娴?鍒版暟鍒楃殑椤剁銆備綔涓烘渶绠€鍗曠殑鎺掑簭绠楁硶涔嬩竴锛屽啋娉℃帓搴忕粰浜虹殑鎰熻灏卞儚 Abandon 鍦ㄥ崟璇嶄功閲屽嚭鐜扮殑鎰熻涓€鏍凤紝姣忔閮藉湪绗竴椤电涓€浣嶏紝鎵€浠ユ渶鐔熸倝銆?/span>

1. 姣旇緝鐩搁偦鐨勫厓绱犮€傚鏋滅涓€涓瘮绗簩涓ぇ锛屽氨浜ゆ崲浠栦滑涓や釜銆?/span>

2. 瀵规瘡涓€瀵圭浉閭诲厓绱犱綔鍚屾牱鐨勫伐浣滐紝浠庡紑濮嬬涓€瀵瑰埌缁撳熬鐨勬渶鍚庝竴瀵广€傝繖姝ュ仛瀹屽悗锛屾渶鍚庣殑鍏冪礌浼氭槸鏈€澶х殑鏁般€?/span>

3. 涓嬩竴瓒熷鍓峮-1涓暟鍋氬悓鏍风殑鎿嶄綔銆?/span>

4. 鎸佺画姣忔瀵硅秺鏉ヨ秺灏戠殑鍏冪礌閲嶅浠ヤ笂姝ラ锛岀洿鍒版病鏈変换浣曚竴瀵规暟瀛楅渶瑕佹瘮杈冦€?/span>

/********************鍐掓场鎺掑簭********************///鐩搁偦鍏冪礌姣旇緝锛氶€夋嫨澶х殑鍏冪礌鏀惧湪鍚庨潰//闈炵浉閭诲厓绱犳瘮杈冿紝鍒欐槸鎻掑叆娉曠殑鎬濇兂/********************鍐掓场鎺掑簭********************/void BubbleSort(int a[], int len) { bool exchange = true; for (int i = len - 1; i > 0 && exchange; i--) { int temp = 0; exchange = false; for (int j = 0; j < len - 1; j++) { if (a[j] > a[j + 1]) { temp = a[j]; a[j] = a[j + 1]; a[j + 1] = temp; exchange = true; } } }}

---

02

鈥?/span>

閫夋嫨鎺掑簭

 鈥?鈥傚寘鍚玭涓厓绱犵殑閫夋嫨鎺掑簭鍙粡杩噉-1瓒熼€夋嫨鎺掑簭寰楀埌鏈夊簭缁撴灉銆?/span>

1. 鍒濆鐘舵€侊細鏃犲簭鍖轰负R[1鈥]锛屾湁搴忓尯涓虹┖锛?/span>

2. 绗琲瓒熸帓搴?i=1,2,3鈥-1)寮€濮嬫椂锛屽綋鍓嶆湁搴忓尯鍜屾棤搴忓尯鍒嗗埆涓篟[1鈥-1]鍜孯(i鈥锛夈€傝瓒熸帓搴忎粠褰撳墠鏃犲簭鍖轰腑-閫夊嚭鍏抽敭瀛楁渶灏忕殑璁板綍 R[k]锛屽皢瀹冧笌鏃犲簭鍖虹殑绗?涓褰昍[i]浜ゆ崲锛屼娇R[1鈥]鍜孯[i+1鈥)鍒嗗埆鍙樹负璁板綍涓暟澧炲姞1涓殑鏂版湁搴忓尯鍜岃褰曚釜鏁板噺灏?涓殑鏂版棤搴忓尯锛?/span>

3. 缁忚繃n-1瓒熼€夋嫨鎺掑簭锛屾暟缁勬湁搴忓寲銆?/span>

鈥?鈥?鈥傞€夋嫨鎺掑簭鏄〃鐜版渶绋冲畾鐨勬帓搴忕畻娉曚箣涓€锛屽洜涓哄浜庝换浣曟暟鎹帓搴忕殑鏃堕棿澶嶆潅搴﹂兘鏄疧(n2)锛屾晠鏁版嵁瑙勬ā瓒婂ぇ琛ㄧ幇瓒婂樊銆傚敮涓€鐨勫ソ澶勬槸涓嶅崰鐢ㄩ澶栫殑鍐呭瓨绌洪棿銆?/span>

/********************閫夋嫨鎺掑簭********************///姣忔閫夋嫨鏃犲簭鍖轰腑鏈€灏忕殑鍏冪礌涓庢棤搴忓尯涓殑棣栧厓绱犱氦鎹?/span>//浜ゆ崲鍚庢湁搴忓尯闀垮害鍔犱竴锛屾棤搴忓尯闀垮害鍑忎竴/********************鍐掓场鎺掑簭********************/void SelectSort(int a[], int len) {
 for (int i = 0; i < len; i++) { for (int j = i+1; j < len ; j++) { int temp = 0; if (a[i] > a[j]) { temp = a[i]; a[i] = a[j]; a[j] = temp; } } }}

---

03

鈥?/span>

鎻掑叆鎺掑簭

鈥?鈥?鈥傛彃鍏ユ帓搴忥紙Insertion-Sort锛夋槸閫氳繃鏋勫缓鏈夊簭搴忓垪锛屽浜庢湭鎺掑簭鏁版嵁锛屽湪宸叉帓搴忓簭鍒椾腑浠庡悗鍚戝墠鎵弿锛屾壘鍒扮浉搴斾綅缃苟鎻掑叆銆備竴鑸潵璇达紝鎻掑叆鎺掑簭閮介噰鐢╥n-place鍦ㄦ暟缁勪笂瀹炵幇銆傚叿浣撶畻娉曟弿杩板涓嬶細

1. 浠庣涓€涓厓绱犲紑濮嬶紝璇ュ厓绱犲彲浠ヨ涓哄凡缁忚鎺掑簭锛?/span>

2. 鍙栧嚭涓嬩竴涓厓绱犵殑key锛屽湪宸茬粡鎺掑簭鐨勫厓绱犲簭鍒椾腑浠庡悗鍚戝墠鎵弿锛?/span>

3. 濡傛灉鎵弿鍒扮殑鍏冪礌锛堝凡鎺掑簭锛夊ぇ浜庢柊鍏冪礌key锛屽皢鎵弿鍒扮殑鍏冪礌绉诲埌涓嬩竴浣嶇疆锛?/span>

4. 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紱

5. 灏嗘柊鍏冪礌鎻掑叆鍒拌浣嶇疆鍚庯紱

鈥?鈥?鈥?/span>浠庢帴涓嬫潵鐨刵-1涓厓绱犲紑濮嬮噸澶嶆楠?~5銆?/span>

void Insertsort(int a[], int len) { for (int i = 1; i < len; i++) { int temp = a[i]; int pos = i; for (int j = i - 1; j >= 0 && a[j] > temp; j--) { a[j + 1] = a[j]; pos = j; } a[pos] = temp; }}

---

04

鈥?/span>

甯屽皵鎺掑簭

鈥?鈥?鈥?959骞碨hell鍙戞槑绗竴涓獊鐮碠(n2)鐨勬帓搴忕畻娉曪紝鏄畝鍗曟彃鍏ユ帓搴忕殑鏀硅繘鐗堛€傚畠涓庢彃鍏ユ帓搴忕殑涓嶅悓涔嬪鍦ㄤ簬锛屽畠浼氫紭鍏堟瘮杈冭窛绂昏緝杩滅殑鍏冪礌銆傚笇灏旀帓搴忓張鍙?span class="mq-204">缂╁皬澧為噺鎺掑簭銆傚叿浣撶畻娉曟弿杩板涓嬶細

鈥?鈥?鈥?/span>鍏堝皢鏁翠釜寰呮帓搴忕殑璁板綍搴忓垪鍒嗗壊鎴愪负鑻ュ共瀛愬簭鍒楀垎鍒繘琛岀洿鎺ユ彃鍏ユ帓搴忥紝杩欐牱鍙互璁╀竴涓厓绱犲彲浠ヤ竴娆℃€у湴鏈濇渶缁堜綅缃墠杩涗竴澶ф锛岀劧鍚庣畻娉曞啀鍙栬秺鏉ヨ秺灏忕殑姝ラ暱杩涜鎺掑簭銆備粎澧為噺鍥犲瓙涓?鏃讹紝鏁翠釜搴忓垪浣滀负涓€涓褰曞簭鍒楁潵澶勭悊锛屽嵆鏈€鍚庝竴姝ヨ繘琛屾櫘閫氱殑鎻掑叆鎺掑簭鍚庯紝搴忓垪鏈夊簭銆?/span>

void ShellSort(int a[], int len) { const int sublen = 2; int InsertNum = 0; unsigned gap = len / sublen; while(gap) { for (int i = gap; i < len; i++) { InsertNum = a[i]; int j = i; while (j >= gap && a[j - gap] > InsertNum) { a[i] = a[j - gap]; j -= gap; } a[j] = InsertNum; } gap = gap / sublen; }}

---

05

鈥?/span>

褰掑苟鎺掑簭

鈥?鈥?鈥傚綊骞舵帓搴忔槸寤虹珛鍦ㄥ綊骞舵搷浣滀笂鐨勪竴绉嶆湁鏁堢殑鎺掑簭绠楁硶銆傝绠楁硶鏄噰鐢ㄥ垎娌绘硶锛圖ivide and Conquer锛夌殑涓€涓潪甯稿吀鍨嬬殑搴旂敤銆傚皢宸叉湁搴忕殑瀛愬簭鍒楀悎骞讹紝寰楀埌瀹屽叏鏈夊簭鐨勫簭鍒楋紱鍗冲厛浣挎瘡涓瓙搴忓垪鏈夊簭锛屽啀浣垮瓙搴忓垪娈甸棿鏈夊簭銆傚叿浣撶畻娉曟弿杩板涓嬶細

1. 鎶婇暱搴︿负n鐨勮緭鍏ュ簭鍒楀垎鎴愪袱涓暱搴︿负n/2鐨勫瓙搴忓垪锛?/span>

2. 瀵硅繖涓や釜瀛愬簭鍒楀垎鍒噰鐢ㄥ綊骞舵帓搴忥紱

3. 灏嗕袱涓帓搴忓ソ鐨勫瓙搴忓垪鍚堝苟鎴愪竴涓渶缁堢殑鎺掑簭搴忓垪銆?/span>

鈥?鈥?鈥傚綊骞舵帓搴忔槸涓€绉嶇ǔ瀹氱殑鎺掑簭鏂规硶銆傚拰閫夋嫨鎺掑簭涓€鏍凤紝褰掑苟鎺掑簭鐨勬€ц兘涓嶅彈杈撳叆鏁版嵁鐨勫奖鍝嶏紝浣嗚〃鐜版瘮閫夋嫨鎺掑簭濂界殑澶氾紝鍥犱负濮嬬粓閮芥槸O(nlogn)鐨勬椂闂村鏉傚害銆備唬浠锋槸闇€瑕侀澶栫殑鍐呭瓨绌洪棿銆?/span>

void Merge(int a[], int low, int mid, int high) { int n = high - low + 1;//涓存椂鏁扮粍瀛樺悎骞跺悗鐨勬湁搴忓簭鍒?/span> int* tmp = new int[n]; int i = 0; int left = low; int right = mid + 1; while (left <= mid && right <= high) tmp[i++] = a[left] <= a[right] ? a[left++] : a[right++]; while (left <= mid) tmp[i++] = a[left++]; while (right <= high) tmp[i++] = a[right++];
 //灏嗚瀺鍚堝悗鐨勬暟鎹嫹璐濆埌鍘熸潵鐨勬暟鎹搴旂殑瀛愮┖闂翠腑 i = 0; while(low <= high) a[low++] = tmp[i++];
 delete[] tmp;//鍒犳帀鍫嗗尯鐨勫唴瀛?/span>}void MergeSort(int a[], int low, int high) { if (low == high) return; //閫掑綊鍩烘槸璁╂暟缁勪腑鐨勬瘡涓暟鍗曠嫭鎴愪负闀垮害涓?鐨勫尯闂?/span> int mid = (low + high) / 2; MergeSort(a, low, mid); MergeSort(a, mid+1, high); Merge(a, low, mid, high);}

---

06

鈥?/span>

蹇€熸帓搴?/span>

鈥?鈥?鈥傚叿浣撶畻娉曟弿杩板涓嬶細

1. 浠庢暟鍒椾腑鎸戝嚭涓€涓厓绱狅紝绉颁负 鈥滃熀鍑嗏€濓紙pivot锛夛紱

2. 閲嶆柊鎺掑簭鏁板垪锛屾墍鏈夊厓绱犳瘮鍩哄噯鍊煎皬鐨勬憜鏀惧湪鍩哄噯鍓嶉潰锛屾墍鏈夊厓绱犳瘮鍩哄噯鍊煎ぇ鐨勬憜鍦ㄥ熀鍑嗙殑鍚庨潰锛堢浉鍚岀殑鏁板彲浠ュ埌浠讳竴杈癸級銆傚湪杩欎釜鍒嗗尯閫€鍑轰箣鍚庯紝璇ュ熀鍑嗗氨澶勪簬鏁板垪鐨勪腑闂翠綅缃€傝繖涓О涓哄垎鍖猴紙partition锛夋搷浣滐紱

3. 閫掑綊鍦帮紙recursive锛夋妸灏忎簬鍩哄噯鍊煎厓绱犵殑瀛愭暟鍒楀拰澶т簬鍩哄噯鍊煎厓绱犵殑瀛愭暟鍒楁帓搴忋€?/span>

鈥?鈥?鈥傛牴鎹垎娌汇€侀€掑綊鐨勫鐞嗘€濇兂锛屽彲浠ョ敤閫掑綊鎺掑簭涓嬫爣浠?p 鍒?q-1 涔嬮棿鐨勬暟鎹拰涓嬫爣浠?q+1 鍒?r 涔嬮棿鐨勬暟鎹紝鐩村埌鍖洪棿缂╁皬涓?1锛屽氨璇存槑鎵€鏈夌殑鏁版嵁閮芥湁搴忎簡銆傝繖閲屾秹鍙婂埌鍩哄噯鐨勯€夋嫨闂锛屽洜姝ゅ繀椤绘湁鍑芥暟Partition()鏉ュ疄鐜扳€滃熀鍑嗏€濓紝璇ュ嚱鏁板簲杩斿洖鍩哄噯鐨勭储寮曘€?/span>

int partition(int a[], int low, int high) { int pivot = a[high]; int i = low; for (int j = i; j < high; j++) { if (a[j] < pivot) { swap(a[j], a[i]); i++; } } swap(a[high], a[i]); return i;}void QuickSort(int a[], int low, int high) { if (low < high) { int q = partition(a, low, high); QuickSort(a, low, q - 1); QuickSort(a, q + 1, high); }}

---

07

鈥?/span>

鍫嗘帓搴?/span>

鈥?鈥?鈥傚爢鏄畬鍏ㄤ簩鍙夋爲鐨勭粨鏋勶紝鍥犳瀵逛簬涓€涓湁n涓妭鐐圭殑鍫嗭紝楂樺害涓篛(logn)銆?/span>
鈥?鈥?鈥傛渶澶у爢锛氬爢涓殑鏈€澶у厓绱犲瓨鏀惧湪鏍硅妭鐐圭殑浣嶇疆銆傞櫎浜嗘牴鑺傜偣锛屽叾浠栨瘡涓妭鐐圭殑鍊兼渶澶氫笌鍏剁埗鑺傜偣鐨勫€间竴鏍峰ぇ銆備篃灏辨槸浠绘剰涓€涓瓙鏍戜腑鍖呭惈鐨勬墍鏈夎妭鐐圭殑鍊奸兘涓嶅ぇ浜庡叾鏍戞牴鑺傜偣鐨勫€笺€?/span>
鈥?鈥?鈥傚爢涓妭鐐圭殑浣嶇疆缂栧彿閮芥槸纭畾鐨勶紝鏍硅妭鐐圭紪鍙蜂负1锛屾瘡涓€灞備粠宸﹀埌鍙充緷娆＄紪鍙枫€傜敱鍫嗘槸瀹屽叏浜屽弶鏍戯紝鍙互鐭ラ亾褰撳爢涓煇涓妭鐐圭殑缂栧彿涓篿鏃讹紝濡傛灉杩欎釜鑺傜偣鏈夊乏鍙冲瓙鏍戯紝閭ｄ箞宸﹀瓙鏍戠殑鑺傜偣缂栧彿涓?脳i,鍙冲瓙鏍戠殑鑺傜偣缂栧彿涓?脳i+1锛堝湪鏍硅妭鐐圭紪鍙蜂负1鐨勬儏鍐垫椂锛夈€?/span>

鍫嗘帓搴忕畻娉曪細
鈥?鈥?鈥傚垵濮嬫椂锛岀畻娉曞埄鐢╞uildMaxHeap灏嗘暟缁凙[1鈥]寤烘垚鏈€澶у爢锛屽洜涓烘暟缁勪腑鏈€澶у厓绱犳€诲湪鏍硅妭鐐笰[1]澶勶紝閫氳繃鎶婂畠涓嶢[n]杩涜浜掓崲锛屽彲浠ヨ璇ュ厓绱犳斁鍒版纭綅缃€備箣鍚庝粠鍫嗕腑鍘绘帀缁撶偣n锛岃皟鐢╩axHeap锛圓, 1)锛屼粠鑰屽湪A[1鈥-1]涓婃瀯閫犱竴涓柊鐨勬渶澶у爢銆備箣鍚庝笉鏂噸澶嶈繖鏍风殑鎿嶄綔锛岀洿鍒板爢鐨勫ぇ灏忎粠n-1闄嶅埌2銆?/span>

/********************鍫嗘帓搴?*******************/// 鏈€澶у爢 鏍戞牴鑺傜偣鍏冪礌鏈€澶э紝姣忔灏嗘爲鏍硅妭鐐瑰厓绱犲彇鍑?鍗冲彇鍒颁簡搴忓垪鏈€澶у厓绱?/span>// 灏嗘渶澶у厓绱犲幓鎺夊悗鐨勫墿浣欏簭鍒楁瀯鎴愭渶澶у爢锛屼笉鏂彇鍑烘渶澶у爢鐨勬爲鏍硅妭鐐?/span>// 鐩村埌鏈€澶у爢鏈€鍚庡墿涓や釜鑺傜偣锛屾帓搴忓畬姣?/span>// 鍫嗘槸瀹屽叏浜屽弶鏍戯紝浠庝笅鍚戜笂鏋勫缓鏈€澶у爢/**********************End***********************/void heapSort(int a[], int n, int len);void maxHeap(int a[], int n, int len);void buildMaxHeap(int a[], int n, int len);
void heapSort(int a[], int n, int len){ buildMaxHeap(a, n, len); for (int i = len; i > 1; i--) { swap(a[0], a[i - 1]); len = len - 1; maxHeap(a, 1, len); }}void buildMaxHeap(int a[], int n, int len){ int i = n / 2; for (i; i > 0; i--) maxHeap(a, i, len);}void maxHeap(int a[], int n, int len){ int leftChild, rightChild, largest; leftChild = 2 * n; rightChild = 2 * n + 1; if (leftChild <= len && a[leftChild - 1] > a[n - 1]) largest = leftChild; else largest = n; if (rightChild <= len && a[rightChild - 1] > a[largest - 1]) largest = rightChild; if (largest != n) { swap(a[n - 1], a[largest - 1]); maxHeap(a, largest, len); }}

---

08

鈥?/span>

璁℃暟鎺掑簭

鈥?鈥?鈥傝鏁版帓搴忎笉鏄熀浜庢瘮杈冪殑鎺掑簭绠楁硶锛屽叾鏍稿績鍦ㄤ簬灏嗚緭鍏ョ殑鏁版嵁鍊艰浆鍖栦负閿瓨鍌ㄥ湪棰濆寮€杈熺殑鏁扮粍绌洪棿涓€備綔涓轰竴绉嶇嚎鎬ф椂闂村鏉傚害鐨勬帓搴廜(n)锛岃鏁版帓搴忚姹傝緭鍏ョ殑鏁版嵁蹇呴』鏄湁纭畾鑼冨洿鐨勬暣鏁般€傦紙鏁翠釜杩囩▼鍙鎷负鍏堣繘琛岀洿鏂瑰浘缁熻锛屽啀鎸夌収椤哄簭鎵斿嚭鏉ワ級銆傚叿浣撶畻娉曟弿杩板涓嬶細

1. 鎵惧嚭寰呮帓搴忕殑鏁扮粍涓渶澶у拰鏈€灏忕殑鍏冪礌锛?/span>

2. 缁熻鏁扮粍涓瘡涓€间负i鐨勫厓绱犲嚭鐜扮殑娆℃暟锛屽瓨鍏ユ暟缁凜鐨勭i椤癸紱

3. 瀵规墍鏈夌殑璁℃暟绱姞锛堜粠C涓殑绗竴涓厓绱犲紑濮嬶紝姣忎竴椤瑰拰鍓嶄竴椤圭浉鍔狅級锛?/span>

4. 鍙嶅悜濉厖鐩爣鏁扮粍锛氬皢姣忎釜鍏冪礌i鏀惧湪鏂版暟缁勭殑绗珻(i)椤癸紝姣忔斁涓€涓厓绱犲氨灏咰(i)鍑忓幓1銆?/span>

/********************璁℃暟鎺掑簭********************/// 闇€瑕佸緱鍒板簭鍒椾腑鐨勬暟鎹垎甯冭寖鍥达紝鍗冲簭鍒楃殑鏈€澶у€煎拰鏈€灏忓€?/span>// 瑕佹眰寰呮帓搴忓簭鍒楀繀椤绘槸闈炶礋鏁存暟// 鍦ㄦ柊寮€杈熺┖闂翠腑璁板綍鍘熷搴忓垪涓瘡涓€煎嚭鐜扮殑娆℃暟// 涔嬪悗鍐嶆牴鎹柊寮€杈熺┖闂翠腑瀵瑰簲绱㈠紩瀛樺偍鍊肩殑涓暟鏉ヨ繑鍥炴湁搴忓簭鍒?/span>/**********************End***********************/void CountSort(int a[], int len) {
 int temp[100] = { 0 }; int n = 0; int sortIndex = 0; for (int i = 0; i < len; i++) { temp[a[i]]++; } for (int i = 0; i < 100; i++) { while (temp[i] > 0) { a[sortIndex++] = i; temp[i]--; } }}

---

09

鈥?/span>

妗舵帓搴?/span>

鈥?鈥?鈥傛《鎺掑簭鏄鏁版帓搴忕殑鍗囩骇鐗堛€傚畠鍒╃敤浜嗗嚱鏁扮殑鏄犲皠鍏崇郴锛岄珮鏁堜笌鍚︾殑鍏抽敭灏卞湪浜庤繖涓槧灏勫嚱鏁扮殑纭畾銆傛《鎺掑簭 (Bucket sort)鐨勫伐浣滅殑鍘熺悊鏄皢鏁版嵁鍒嗗埌鏈夐檺鏁伴噺鐨勬《閲岋紝姣忎釜妗跺啀鍒嗗埆鎺掑簭锛堟湁鍙兘鍐嶄娇鐢ㄥ埆鐨勬帓搴忕畻娉曟垨鏄互閫掑綊鏂瑰紡缁х画浣跨敤妗舵帓搴忚繘琛屾帓锛夈€傚叿浣撶畻娉曟弿杩板涓嬶細

1. 璁剧疆涓€涓畾閲忕殑鏁扮粍褰撲綔绌烘《锛?/span>

2. 閬嶅巻杈撳叆鏁版嵁锛屽苟涓旀妸鏁版嵁涓€涓竴涓斁鍒板搴旂殑妗堕噷鍘伙紱

3. 瀵规瘡涓笉鏄┖鐨勬《杩涜鎺掑簭锛?/span>

4. 浠庝笉鏄┖鐨勬《閲屾妸鎺掑ソ搴忕殑鏁版嵁鎷兼帴璧锋潵銆?/span>

/********************妗舵帓搴?*********************/// 棣栧厛寰楀埌寰呮帓搴忓簭鍒楃殑鏈€澶ф渶灏忓€?/span>// 鏍规嵁缁欏畾妗剁殑瀹归噺 鏉ョ‘瀹氭《鐨勪釜鏁?/span>// 灏嗗緟鎺掑簭搴忓垪鍒嗗埆鏀惧叆涓嶅悓鐨勬《涓?/span>// 瀵逛簬涓嶅悓鐨勬《 鍒╃敤浠ヤ笂浠绘剰涓€绉嶆帓搴忕畻娉曟帓搴?/span>// 灏嗘《涓殑鏁版嵁鎸夌収妗剁殑椤哄簭杩涜鏁翠綋杩炴帴鎺掑簭// 鏈閫夌敤璁℃暟鎺掑簭瀵?妗朵腑鐨勫簭鍒楁帓搴?/span>/**********************End***********************/
void CountSort_vct(vector<int>& a) { int temp[100] = { 0 }; int n = 0; int sortIndex = 0; for (int i = 0; i < a.size(); i++) { temp[a[i]]++; } for (int i = 0; i < 100; i++) { while (temp[i] > 0) { a[sortIndex++] = i; temp[i]--; } }}void bucketSort(vector<int>& arr, int bucketSize = 10) { if (arr.size() == 0) { return; } int i; int minValue = arr[0]; int maxValue = arr[0]; for (i = 1; i < arr.size(); i++) { if (arr[i] < minValue) { minValue = arr[i]; // 寰呮帓搴忓簭鍒楁渶灏忓€?/span> } else if (arr[i] > maxValue) { maxValue = arr[i]; // 寰呮帓搴忓簭鍒楁渶澶у€?/span> } } int bucketCount = int((maxValue - minValue) / bucketSize) + 1; //鏍规嵁鏈€澶ф渶灏忓€艰绠楁《鐨勪釜鏁?/span>
 vector<vector<int>> buckets(bucketCount, vector<int>()); // 鍒╃敤鏄犲皠鍑芥暟灏嗘暟鎹垎閰嶅埌鍚勪釜妗朵腑  for (i = 0; i < arr.size(); i++) { int idx = int((arr[i] - minValue) / bucketSize); buckets[idx].push_back(arr[i]); } arr.clear(); for (i = 0; i < buckets.size(); i++) { CountSort_vct(buckets[i]); // 瀵规瘡涓《杩涜鎺掑簭锛岃繖閲屼娇鐢ㄤ簡璁℃暟鎺掑簭锛屽彲浠ョ敤涓婇潰鐨勪换鎰忎竴绉嶆帓搴忎唬鏇?/span> for (int j = 0; j < buckets[i].size(); j++) { arr.push_back(buckets[i][j]); } } return;}

---

10

鈥?/span>

鍩烘暟鎺掑簭

鈥?鈥?鈥傚熀鏁版帓搴忔槸鎸夌収浣庝綅鍏堟帓搴忥紝鐒跺悗鏀堕泦锛涘啀鎸夌収楂樹綅鎺掑簭锛岀劧鍚庡啀鏀堕泦锛涗緷娆＄被鎺紝鐩村埌鏈€楂樹綅銆傛湁鏃跺€欐湁浜涘睘鎬ф槸鏈変紭鍏堢骇椤哄簭鐨勶紝鍏堟寜浣庝紭鍏堢骇鎺掑簭锛屽啀鎸夐珮浼樺厛绾ф帓搴忋€傛渶鍚庣殑娆″簭灏辨槸楂樹紭鍏堢骇涓洿楂樼殑鍦ㄥ墠锛岄珮浼樺厛绾х浉鍚屾椂浣庝紭鍏堢骇楂樼殑鍦ㄥ墠銆傚叿浣撶畻娉曟弿杩板涓嬶細

1. 鍙栧緱鏁扮粍涓殑鏈€澶ф暟锛屽苟鍙栧緱鍏朵綅鏁帮紱
2. arr涓哄師濮嬫暟缁勶紝浠庢渶浣庝綅寮€濮嬪彇姣忎釜浣嶇粍鎴恟adix鏁扮粍锛?/span>
3. 瀵箁adix杩涜璁℃暟鎺掑簭锛堝埄鐢ㄨ鏁版帓搴忛€傜敤浜庡皬鑼冨洿鏁扮殑鐗圭偣锛夛紱

鈥?鈥?鈥傚拰璁℃暟鎺掑簭涓€鏍凤紝鍩烘暟鎺掑簭浠呬粎鍙互瀵归潪璐熸暣鏁拌繘琛屾帓搴忥紝鍏舵椂闂村鏉傚害涓篛(n)锛屼笖璁℃暟鎺掑簭銆佹《鎺掑簭銆佸熀鏁版帓搴忓潎涓虹ǔ瀹氭帓搴忕畻娉曘€?/span>

/********************鍩烘暟鎺掑簭**********************/// 鑾峰緱寰呮帓搴忓簭鍒椾腑鏈€澶ф暟鐨?浣嶆暟// 鍒嗗埆瀵瑰緟鎺掑簭搴忓垪鐨勪釜浣嶃€佸崄浣嶃€佺櫨浣嶁€︹€﹁繘琛屾《鎺掑簭// 鏈€鍚庤幏寰楁湁搴忓簭鍒?銆愪粎鍙闈炶礋鏁存暟鎺掑簭銆?绋冲畾绠楁硶/**********************End***********************/int maxbit(int data[], int n){ int d = 1; //淇濆瓨鏈€澶х殑浣嶆暟 int p = 10; for (int i = 0; i < n; ++i) { while (data[i] >= p) { p *= 10; ++d; } } return d;}void radixsort(int data[], int n) //鍩烘暟鎺掑簭{ int d = maxbit(data, n); int tmp[100]; int count[10]; //璁℃暟鍣?/span> int i, j, k; int radix = 1; for (i = 1; i <= d; i++) //杩涜d娆℃帓搴?/span> { for (j = 0; j < 10; j++) count[j] = 0; //姣忔鍒嗛厤鍓嶆竻绌鸿鏁板櫒 for (j = 0; j < n; j++) { k = (data[j] / radix) % 10; //缁熻姣忎釜妗朵腑鐨勮褰曟暟 count[k]++; } for (j = 1; j < 10; j++) count[j] = count[j - 1] + count[j]; //灏唗mp涓殑浣嶇疆渚濇鍒嗛厤缁欐瘡涓《 for (j = n - 1; j >= 0; j--) //灏嗘墍鏈夋《涓褰曚緷娆℃敹闆嗗埌tmp涓?/span> { k = (data[j] / radix) % 10; tmp[count[k] - 1] = data[j]; count[k]--; } for (j = 0; j < n; j++) //灏嗕复鏃舵暟缁勭殑鍐呭澶嶅埗鍒癲ata涓?/span> data[j] = tmp[j]; radix = radix * 10; }}

---

馃敆寰€鏈熷垎浜?/span>