【愚公系列】2023年11月数据结构（十三）-嘿

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/ void siftDown(int i) { while (true) { // 纭畾鑺傜偣 i,l,r 涓?兼渶澶х殑鑺傜偣锛岃涓?ma int l =宸︼紙i锛夛紝r = 鍙筹紙i锛夛紝ma = i锛?if (l < size() && maxHeap[l] > maxHeap[ma]) ma = l; if (r < size() && maxHeap[r] > maxHeap[ma]) ma = r;// 濡傛灉鈥滆妭鐐筰鏈?澶р?濇垨鑰呪?滅┛杩囧彾瀛愯妭鐐光?濓紝鍒欑粨鏉熷爢 if (ma == i) break; // 浜ゆ崲涓や釜鑺傜偣 swap(i, ma); // 鍚戜笅寰幆鍫?i = ma ; } } /* 浜ゆ崲鍏冪礌*/ void swap(int i, int p) { (maxHeap[i], maxHeap[p]) = (maxHeap[p], maxHeap[i]); } /* 鎵撳嵃鍫嗭紙浜屽弶鏍戯級 */ public void print() { var queue = new Queue(maxHeap); PrintUtil.PrintHeap(闃熷垪); }} public class my_heap { [Test] public void Test() { /* 鍒濆鍖栧ぇ鍫? / MaxHeap maxHeap = new MaxHeap(new int[] { 9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2 }); Console.WriteLine("\n杈撳叆鍒楄〃骞跺湪涔嬪悗鏋勫缓鍫?); maxHeap.print(); /* 鑾峰彇鍫嗛《鍏冪礌*/ int peek = maxHeap.peek(); Console.WriteLine($"鍫嗛《鍏冪礌鏄瘂peek}"); /* 灏嗗厓绱犳斁鍏ュ爢*/ int val = 7; maxHeap.push(val); Console.WriteLine($"鍏冪礌{val}鏀惧叆鍫嗗悗"); maxHeap.print(); /* 浠庡爢涓彇鍑哄爢椤跺厓绱?/ peek = maxHeap.pop() ;鎺у埗鍙?WriteLine($"椤堕儴鍏冪礌{peek}浠庡爢涓嚭鏉ュ悗"); maxHeap.print(); /* 鑾峰彇鍫嗗ぇ灏?/ int size = maxHeap.size(); Console.WriteLine($"鍫嗗厓绱犱釜鏁颁负{size }"); /* 鍒ゆ柇鍫嗘槸鍚︿负绌?/ bool isEmpty = maxHeap.isEmpty(); Console.WriteLine($"鍫嗘槸鍚︿负绌簕isEmpty}"); }}鍦ㄦ鎻掑叆鍥剧墖璇存槑馃攷4.寤哄爢鎿嶄綔 鍦ㄥ爢鎺掑簭涓紝寤哄爢鏄寚灏嗘棤搴忓簭鍒楀彉鎴愬爢锛堜簩鍙夊爢锛夈?傚缓鍫嗘搷浣滅殑鏃堕棿澶嶆潅搴︽槸O(n)锛岃繖鏄爢鎺掑簭鐨勭涓?姝ャ?傚爢鏄竴妫靛畬鍏ㄤ簩鍙夋爲锛屽叾涓瘡涓妭鐐圭殑鍊奸兘澶т簬鎴栫瓑浜庡叾宸﹀彸瀛愯妭鐐圭殑鍊硷紝绉颁负鏈?澶у爢锛涙垨鑰呮瘡涓妭鐐圭殑鍊煎皬浜庢垨绛変簬鍏跺乏鍙冲瓙鑺傜偣鐨勫?硷紝绉颁负灏忔牴鍫嗭紙min heap锛夈?傛瀯寤哄爢鐨勮繃绋嬪氨鏄牴鎹爢鐨勫睘鎬у皢鏃犲簭搴忓垪璋冩暣涓哄爢鐨勮繃绋嬨?傚湪鏋勫缓鍫嗙殑杩囩▼涓紝浠庢渶鍚庝竴涓潪鍙跺瓙鑺傜偣锛堝彾瀛愯妭鐐圭殑鐖惰妭鐐癸級寮?濮嬶紝渚濇鍚戜笂璋冩暣鍫嗐?傚浜庢瘡涓妭鐐癸紝灏嗗叾澶у皬涓庡乏鍙冲瓙鑺傜偣杩涜姣旇緝锛屽苟浣跨敤鏈?澶?鏈?灏忕殑鑺傜偣浣滀负鐖惰妭鐐广??銆傚鏋滃綋鍓嶈妭鐐硅浜ゆ崲锛屽垯缁х画鍚戜笅璋冩暣璇ヨ妭鐐癸紝閲嶅涓婅堪姝ラ锛岀洿鍒版墍鏈夎妭鐐归兘婊¤冻鍫嗙殑灞炴?с?傚缓鍫嗘搷浣滅殑鏃堕棿澶嶆潅搴︿负O(n)锛屽洜涓哄彧闇?瑕佽皟鏁撮潪鍙跺瓙鑺傜偣锛屽嵆n/2涓妭鐐广?傝繖閲屾彃鍏ュ浘鐗囪鏄庰煍?.Top-K闂鍫嗘槸涓?妫靛畬鍏ㄤ簩鍙夋爲锛屾弧瓒冲爢搴忓睘鎬э細姣忎釜鑺傜偣鐨勫?煎ぇ浜庣瓑浜庯紙鎴栧皬浜庣瓑浜庯級鍏跺乏鍙崇殑鍊煎瓙鑺傜偣銆傚爢鐨凾op-K闂鏄粠鏈帓搴忕殑鏁扮粍涓壘鍒板墠K涓渶澶э紙鎴栨渶灏忥級鍏冪礌銆傝В鍐冲爢鐨凾op-K闂鐨勫熀鏈?濇兂鏄淮鎶や竴涓ぇ灏忎负K鐨勫皬锛堟垨澶э級鏍瑰爢锛岄亶鍘嗘暟缁勬椂锛屽皢鍏冪礌涓庡皬锛堟垨澶э級鏍瑰爢鐨勯《閮ㄥ厓绱犺繘琛屾瘮杈冦?傚鏋滃ぇ浜庯紙鎴栧皬浜庯級鍫嗛《鍏冪礌锛屽垯寮瑰嚭鍫嗛《鍏冪礌骞跺皢璇ュ厓绱犳坊鍔犲埌鍫嗕腑銆傞亶鍘嗗畬鎴愬悗锛屽墠K涓渶澶э紙鎴栨渶灏忥級鍏冪礌淇濆瓨鍦ㄥ爢涓?傚叿浣撳疄鐜板垎涓轰袱绉嶏細 1銆佸爢鎺掑簭娉曪細鍒╃敤鍫嗘帓搴忕殑鎬濇兂锛屾瀯寤轰竴涓皬鐨勬牴鍫嗭紝鐒跺悗灏嗘湭鎺掑簭鐨勫厓绱犳坊鍔犲埌鍫嗕腑锛屽脊鍑哄爢椤跺厓绱狅紝鐩村埌鍫嗗ぇ灏忎负K锛屾渶鍚庣殑鍏冪礌鏄墠K涓渶澶х殑鍏冪礌銆?.蹇?熼?夋嫨娉曪細鍒╃敤蹇?熸帓搴忕殑鎬濇兂瀵规暟缁勮繘琛屽垝鍒嗭紝浣垮乏杈圭殑鏁板瓧灏忎簬鍙宠竟鐨勬暟瀛楋紝鐒跺悗鏍规嵁K 鐨勫ぇ灏忥紝鐩村埌鎵惧埌鍓?K 涓渶澶х殑銆傛暟瀛椼??馃5.1 閬嶅巻閫夋嫨鍦ㄦ鎻掑叆鍥剧墖鎻忚堪馃5.2 鎺掑簭鍦ㄦ鎻掑叆鍥剧墖鎻忚堪馃5.3 鍫嗕唬鐮佽瑷?锛歝# copy/* 鏍规嵁鍫嗘煡鎵炬暟缁勪腑鏈?澶х殑 k 涓厓绱?/using NUnit.Framework;static PriorityQueue topKHeap(int[] nums, int k){ PriorityQueue heap = new PriorityQueue(); // 灏嗘暟缁勭殑鍓?k 涓厓绱犳斁鍏ュ爢涓?for (int i = 0; i < k; i++) { heap.Enqueue(nums[i], nums[i]); } // 浠庣 k 涓厓绱犲紑濮嬶紝淇濇寔鍫嗙殑闀垮害涓?k for (int i = k; i < nums.Length; i++ ) { // 濡傛灉褰撳墠鍏冪礌澶т簬鍫嗛《鍏冪礌锛屼粠鍫嗕腑绉婚櫎椤堕儴鍏冪礌骞跺皢褰撳墠鍏冪礌鏀惧叆鍫嗕腑 if (nums[i] > heap.Peek()) { heap.Dequeue();鍫?Enqueue(nums[i], nums[i]); } } 杩斿洖鍫?}int[] nums = { 1, 7, 6, 3, 2,8,9 };int k = 3;PriorityQueue res = topKHeap (nums, k);Console.WriteLine (鈥滄渶澶х殑鈥?k+鈥濅釜鍏冪礌鏄??;姝ゅ鎻掑叆鍥剧墖鎻忚堪 姝ゅ鎻掑叆鍥剧墖鎻忚堪 馃攷 6.浼樼己鐐?鍫嗘槸涓?涓畬鍏ㄤ簩鍙夋爲缁撴瀯锛屽悓鏃舵弧瓒冲爢搴忓睘鎬э紙Heap property锛夛紝鍗崇埗鑺傜偣鐨勫?兼?绘槸灏忎簬鎴栧ぇ浜庡瓙鑺傜偣鐨勫?笺?傚爢鍦ㄦ暟鎹粨鏋勪笂鏈変互涓嬩紭鐐瑰拰缂虹偣锛?浼樼偣锛氬揩閫熸壘鍒版渶澶у?硷細鍫嗘槸涓?绉嶄紭绉?鐨勬暟鎹粨鏋勶紝鍙互蹇?熸壘鍒版渶澶у?笺?傚湪鏈?灏忓爢涓紝鏍硅妭鐐瑰缁堝瓨鍌ㄦ渶灏忕殑鍏冪礌锛涘湪鏈?澶у爢涓紝鏍硅妭鐐瑰缁堝瓨鍌ㄦ渶澶х殑鍏冪礌銆傝繖浣垮緱鍫嗘垚涓哄疄鐜颁紭鍏堢骇闃熷垪鐨勭悊鎯抽?夋嫨銆傛彃鍏ュ拰鍒犻櫎鍏冪礌鐨勬晥鐜囬珮锛氬湪鍫嗕腑鎻掑叆鍜屽垹闄ゅ厓绱犵殑鏃堕棿澶嶆潅搴﹂?氬父涓篛(log n)銆傝繖鏄洜涓哄爢鏄竴妫靛畬鍏ㄤ簩鍙夋爲锛屾彃鍏ュ拰鍒犻櫎鎿嶄綔鏈?澶氬彧闇?瑕丱(log n)娆℃爲鐨勬瘮杈冨拰浜ゆ崲鍗冲彲瀹屾垚銆傝兘澶熼珮鏁堝鐞嗗姩鎬佹暟鎹泦鍚堬細鍫嗚兘澶熼珮鏁堝鐞嗗姩鎬佹暟鎹泦鍚堬紝鍗冲湪鍏冪礌鏁伴噺涓嶆柇鍙樺寲鏃惰兘澶熷揩閫熸壘鍒版渶浼樺?笺?傜己鐐癸細涓嶆敮鎸佹煡鎵句换鎰忓厓绱狅細铏界劧鍫嗗彲浠ュ揩閫熸壘鍒版渶澶у?硷紝浣嗗鏋滈渶瑕佹煡鎵句换鎰忓厓绱狅紝鍒欓渶瑕侀亶鍘嗘墍鏈夎妭鐐癸紝鏃堕棿澶嶆潅搴︿负O(n)銆備笉鏀寔鍏冪礌鐨勫揩閫熶慨鏀癸細褰撳爢涓煇涓厓绱犵殑鍊煎彂鐢熷彉鍖栨椂锛岄渶瑕侀噸鏂拌皟鏁村爢鏉ョ淮鎸佸爢椤哄簭灞炴?э紝杩欓?氬父闇?瑕丱(n)鐨勬椂闂村鏉傚害銆傛棤娉曚繚璇佺粨鏋勫钩琛★細鍫嗘棤娉曞儚骞宠　浜屽弶鏍戜竴鏍蜂?濊瘉缁撴瀯骞宠　锛岃繖鍙兘浼氬鑷存煇浜涙搷浣滅殑鏈?鍧忔儏鍐垫椂闂村鏉傚害杈冮珮銆備緥濡傦紝鍦ㄦ瀬绔儏鍐典笅锛屽爢鍙兘閫?鍖栦负閾捐〃锛屽鑷存彃鍏ュ拰鍒犻櫎鎿嶄綔鐨勬椂闂村鏉傚害涓?O(n)銆?馃攷7.搴旂敤鍦烘櫙 鍫嗘槸涓?绉嶅熀浜庡畬鍏ㄤ簩鍙夋爲鐨勬暟鎹粨鏋勩?傚湪瀹為檯搴旂敤涓畠鏈夊緢澶氬簲鐢ㄥ満鏅?備互涓嬫槸涓?浜涘父瑙佺殑搴旂敤鍦烘櫙锛?1銆佸爢鎺掑簭锛氬爢鎺掑簭鏄竴绉嶉珮鏁堢殑鎺掑簭绠楁硶锛屽埄鐢?heap 鐨勫睘鎬э紝鍙互瀹炵幇鏃堕棿澶嶆潅搴︿负 O(nlogn) 鐨勬帓搴忋??2.浼樺厛绾ч槦鍒楋細鍙互鍒╃敤鍫嗘潵瀹炵幇浼樺厛绾ч槦鍒楋紝鍙互鍦∣(logn)鏃堕棿鍐呮壘鍒版渶灏忔垨鏈?澶х殑鍏冪礌銆?3銆佹煡鎵総op k闂锛氬鏋滄兂鍦ㄤ竴缁勬暟鎹腑鎵惧埌top k鏈?澶ф垨鑰卼op k鏈?灏忕殑鏁版嵁锛屽彲浠ヤ娇鐢ㄥ爢鏉ュ疄鐜般??4. 姹備腑浣嶆暟锛氬埄鐢ㄥ爢锛屼綘鍙互鍦∣(logn)鏃堕棿鍐呮眰鍑轰竴缁勬暟鎹殑涓綅鏁般??5銆佸浘鎼滅储鐨勬渶鐭矾寰勭畻娉曪細姣斿Dijkstra绠楁硶鍜孭rim绠楁硶锛岄兘闇?瑕佷娇鐢ㄥ爢鏉ュ疄鐜颁紭鍏堢骇闃熷垪銆傛?讳箣锛屽爢鏄竴绉嶉潪甯告湁鐢ㄧ殑鏁版嵁缁撴瀯锛屽彲浠ュ湪寰堝搴旂敤鍦烘櫙涓彂鎸ラ噸瑕佷綔鐢ㄣ?傛垜姝ｅ湪鍙傚姞鑵捐绉戞妧鍒涢?犵壒璁惀绗笁鏈熸湁濂栧緛鏂囨瘮璧涳紝鎴戝皢缁勯槦鑾峰锛?