{"id":568,"date":"2007-03-05T11:40:00","date_gmt":"2007-03-05T03:40:00","guid":{"rendered":"http:\/\/note.systw.net\/note\/?p=568"},"modified":"2023-11-04T11:42:24","modified_gmt":"2023-11-04T03:42:24","slug":"sort","status":"publish","type":"post","link":"https:\/\/systw.net\/note\/archives\/568","title":{"rendered":"Sort"},"content":{"rendered":"\n

\u5b9a\u7fa9
stable sort<\/strong>(\u7a69\u5b9a\u7684\u6392\u5e8f\u6cd5):
\u82e5\u6709\u76f8\u540c\u8cc7\u6599\uff0c\u5247\u76f8\u5c0d\u4f4d\u7f6e\u4e0d\u6703\u6539\u8b8a

comparison sort<\/strong>:
\u7528\u5169\u5169\u6bd4\u5c0d\u65b9\u5f0f\u505a\u6392\u5e8f\u7684\u65b9\u6cd5
comparison sort\u6700\u5feb\u4e5f\u81f3\u5c11\u8981\u82b1n*log(n)\u7684\u6642\u9593
\u4e00\u4e9bnot a comparison sort\u53ef\u6bd4comparison sort\u5feb
\u5e38\u898b\u7684not a comparison sort\u6709counting sort,radix sort,…<\/p>\n\n\n\n

in-place<\/strong>
\u4e0d\u9700\u7528\u85c9\u7531\u5176\u4ed6\u7a7a\u9593\u4f86\u8655\u7406\u6392\u5e8f

Adaptability<\/strong>
\u82e5\u6578\u5217\u5df2\u7d93\u6709\u90e8\u5206\u6392\u904e\u5e8f\u4e86,\u5247sorting\u7684time complexity\u53ef\u964d\u4f4e<\/p>\n\n\n\n

…………………………………………………<\/p>\n\n\n\n

\u5167\u90e8\u6392\u5e8f\u6cd5<\/strong><\/h2>\n\n\n\n

\u53ef\u5206\u70ba
\u4e00\u822c\u6392\u5e8f\u6cd5
\u9ad8\u7b49\u6392\u5e8f\u6cd5
\u5206\u914d\u6392\u5e8f\u6cd5 <\/p>\n\n\n\n

\u4e00\u822c\u6392\u5e8f\u6cd5<\/strong>
\u5e38\u898b\u7684\u6709:insertion sort,bubble sort,selection sort
\u6642\u9593\u8907\u96dc\u5ea6\u5e73\u5747\u548c\u6700\u5dee\u90fd\u662fO(N^2),\u984d\u5916\u7a7a\u9593\u90fd\u662fO(1)
\u901a\u5e38\u5c07\u8cc7\u6599\u8996\u70ba\u524d(\u5df1\u6392\u597d)\u5f8c(\u9700\u8981\u6392)\u5169\u90e8\u4efd<\/p>\n\n\n\n

…..<\/p>\n\n\n\n

insertion sort(\u63d2\u5165\u6392\u5e8f\u6cd5)<\/strong>:\u9010\u6b65\u6539\u826f\u6cd5
\u5e73\u5747O(N^2),\u6700\u5deeO(N^2),\u984d\u5916\u7a7a\u9593O(1),\u5c6cstable sort
\u6bd4\u8f03\u8207\u4ea4\u63db\u6b21\u6578\uff1a
\u6700\u591a\u9700\u8981\u6bd4\u8f03\u548c\u4ea4\u63db1+2+…+(n-1)=n*(n-1)\/2\u6b21(\u82e5\u8cc7\u6599\u6392\u5217\u548c\u60f3\u8981\u7684\u9806\u5e8f\u5b8c\u5168\u76f8\u53cd)
\u6700\u5c11\u53ea\u9700\u6bd4\u8f03n-1\u6b21\uff0c\u4ea4\u63db0\u6b21(\u82e5\u9806\u5e8f\u5b8c\u5168\u4e00\u6a23),\u8655\u7406\u5df1\u6392\u5e8f\u8cc7\u6599\u6548\u7387\u6700\u4f73
\u5e73\u5747\u60c5\u6cc1\u662f\u6bd4\u8f03\u548c\u4ea4\u63dbn*(n-1)\/4\u6b21<\/p>\n\n\n\n

\u505a\u6cd5\uff1a
\u6bcf\u6b21\u5c07\u5f8c\u90e8\u4efd\u7b2c\u4e00\u500b\u8cc7\u6599\u548c\u524d\u90e8\u4efd\u6700\u5f8c\u8cc7\u6599\u6bd4\u8f03\uff0c\u82e5\u5927\u65bc\u5247\u4ea4\u63db\u4e26\u7e7c\u7e8c\u548c\u4e0b\u500b\u503c\u6bd4\u8f03
\u82e5\u5c0f\u65bc\u5247\u524d\u90e8\u4efd\u8cc7\u6599\u591a1\uff0c\u800c\u5f8c\u90e8\u4efd\u8cc7\u6599\u5c111\uff0c\u5728\u91cd\u8986\u4e0a\u8ff0\u76f4\u5230\u5f8c\u90e8\u4efd\u8cc7\u6599\u70ba0
\u6392\u5e8f\u904e\u7a0b\u5927\u81f4\u5982\u4e0b
step0:37,(1<\/strong>,5,26,12,60)
step1:1,37,(5<\/strong>,26,12,60)
step2:1,5,37,(26<\/strong>,12,60)
step3:1,5,26,37,(12<\/strong>,60)
step4:1,5,12,26,37,(60<\/strong>)
step5:1,5,12,26,37,60<\/p>\n\n\n\n

…..<\/p>\n\n\n\n

selection sort(\u9078\u64c7\u6392\u5e8f\u6cd5)<\/strong>:\u8caa\u5a6a\u6cd5
\u5e73\u5747O(N^2),\u6700\u5deeO(N^2),\u984d\u5916\u7a7a\u9593O(1),
\u6bd4\u8f03\u8207\u4ea4\u63db\u6b21\u6578\uff1a
\u6bd4\u8f03\u6b21\u6578\u56fa\u5b9a\u70ban*(n-1)\/2\u6b21
\u6700\u591a\u9700\u8981\u4ea4\u63dbn-1\u6b21(\u82e5\u8cc7\u6599\u6392\u5217\u548c\u60f3\u8981\u7684\u9806\u5e8f\u5b8c\u5168\u76f8\u53cd)
\u6700\u5c11\u53ea\u9700\u4ea4\u63db0\u6b21(\u82e5\u9806\u5e8f\u5b8c\u5168\u4e00\u6a23)
\u5e73\u5747\u60c5\u6cc1\u53ea\u9700\u4ea4\u63db(n-1)\/2\u6b21<\/p>\n\n\n\n

\u505a\u6cd5\uff1a
\u627e1~n\u4e4b\u9593\u6700\u5c0f\u503c\u548c\u8cc7\u65991\u4ea4\u63db\uff0c\u5728\u627e2~n\u4e4b\u9593\u7684\u6700\u5c0f\u503c\u548c\u8cc7\u65992\u4ea4\u63db….\u5728\u627e(n-1)~n\u9593\u6700\u5c0f\u503c\u548c\u8cc7\u6599(n-1)\u4ea4\u63db
\u6392\u5e8f\u904e\u7a0b\u5927\u81f4\u5982\u4e0b
step0:(37,1<\/strong>,5,26,12,60)
step1:1,(37,5<\/strong>,26,12,60)
step2:1,5,(37,26,12<\/strong>,60)
step3:1,5,12,(37,26<\/strong>,60)
step4:1,5,12,26,(37<\/strong>,60)
step5:1,5,12,26,37,(60<\/strong>)<\/p>\n\n\n\n

…..<\/p>\n\n\n\n

bubble sort(\u6c23\u6ce1\u6392\u5e8f\u6cd5)<\/strong>:\u9010\u6b65\u6539\u826f\u6cd5
\u5e73\u5747O(N^2),\u6700\u5deeO(N^2),\u984d\u5916\u7a7a\u9593O(1),\u5c6cstable sort
\u6bd4\u8f03\u548c\u4ea4\u63db\u548c\u63d2\u5165\u6392\u5e8f\u6cd5\u4e00\u6a23<\/p>\n\n\n\n

\u505a\u6cd5\uff1a
\u6bcf\u6b21\u5c07\u908a\u8cc7\u6599(\u982d\u6216\u5c3e)\u8996\u70bamin\uff0c\u7136\u5f8cmin\u548c\u4e0b\u4e00\u500b\u503c\u6bd4\u8f03\uff0c\u82e5\u5c0f\u65bc\u5c31\u4ea4\u63db\u8cc7\u6599\uff0c\u82e5\u5927\u65bc\u5247\u628a\u4e0b\u4e00\u500b\u503c\u7576min\uff0c
\u91cd\u8986\u4e0a\u8ff0\u6b65\u9a5f\u4e00\u76f4\u5230\u6bd4\u8f03\u5230\u7b2c1\u500b\u8cc7\u6599\uff0c\u7b2c2\u6b21\u5247\u91cd\u8986\u4e0a\u8ff0\u6b65\u9a5f\u6bd4\u8f03\u5230\u7b2c2\u500b\u8cc7\u6599\uff0c\u4e00\u76f4\u5230\u7b2cn-1\u6b21
\u6392\u5e8f\u904e\u7a0b\u5927\u81f4\u5982\u4e0b
step0:(24,26),3,9,45,1,12
step0.1:24,(3,26),9,45,1,12
step0.2:24,3,(9,26),45,1,12
step0.3:24,3,9,(26,45),1,12
step0.4:24,3,9,26,(1,45),12
step1:24,3,9,26,1,(12,45)
step2:3,9,24,1,12,26,45
step3:3,9,1,12,24,26,45<\/p>\n\n\n\n

bubble_sort(int list[],int n){
\u3000int i,j;
\u3000for(i=1;i
\u3000\u3000for(j=1;j
\u3000\u3000\u3000if(list[j]>list[j+1]){swap(list[j],list[j+1])}
\u3000\u3000}
\u3000}
}<\/p>\n\n\n\n

…………………..<\/p>\n\n\n\n

\u9ad8\u7b49\u6392\u5e8f\u6cd5<\/strong>
\u5167\u90e8\u6392\u5e8f\u6cd5\u4e2d\u6700\u4f73\u6f14\u7b97\u6cd5(N 2\u5e95log N)
\u5e38\u898b\u7684\u6709:\u5feb\u901f\u6392\u5e8f\u6cd5\uff0c\u4e8c\u9805\u5408\u4f75\u6392\u5e8f\u6cd5\uff0c\u5806\u7a4d\u6392\u5e8f\u6cd5
\u5176\u4ed6\u6709:radix sort(\u57fa\u5e95\u6392\u5e8f\u6cd5)
ps:
mergesort\u8207heapsort\u90fd\u662fasymptotically optimal sorting algorithm
\u4ed6\u5011\u7684\u6700\u597d\u548c\u6700\u5dee\u60c5\u6cc1\u4e0b\uff0c\u6642\u9593\u8907\u96dc\u5ea6\u4e00\u6a23<\/p>\n\n\n\n

…..<\/p>\n\n\n\n

quick sort(\u5feb\u901f\u6392\u5e8f\u6cd5)<\/strong>:
\u6700\u4f73\u5e73\u5734O(n 2\u5e95log n)\u984d\u5916\u7a7a\u9593O(2\u5e95log n)
\u6700\u5deeO(n^2)\u984d\u5916\u7a7a\u9593O(n)
\u8aaa\u660e\uff1a
\u4f7f\u7528partition\u5207\u5272\u6280\u5de7\uff0c\u6839\u64dar\u503c\u5c07\u8cc7\u6599\u5207\u6210\u524d\u5f8c\u5169\u90e8\u4efd\uff0c\u524d\u9762\u6240\u6709\u503c\u5c0f\u65bc\u8cc7\u6599r\uff0c\u5f8c\u9762\u6240\u6709\u503c\u5927\u65bc\u8cc7\u6599r\uff0c\u5728\u905e\u8ff4\u5c0d\u5169\u90e8\u4efd\u9032\u884c\u8655\u7406
\u7531C.A.R hoare\u6240\u767c\u5c55\uff0c\u5e73\u5734\u8907\u96dc\u5ea6\u662f\u6240\u6709\u5167\u90e8\u6392\u5e8f\u6cd5\u4e2d\u6700\u4f73\u7684<\/p>\n\n\n\n

\u505a\u6cd5\uff1a
1\u7b2c1\u500b\u8cc7\u6599r\u5f9e\u5de6\u5f80\u53f3\u627e\u5927\u65bcr\u7684\u8cc7\u6599s,\u5047\u8a2d\u4f4d\u7f6e=i\uff0c\u5728\u5f9e\u53f3\u5f80\u5de6\u627e\u6bd4r\u5c0f\u7684\u8cc7\u6599t,\u5047\u8a2d\u4f4d\u7f6e=j
2\u82e5i
3\u5206\u5225\u5c0d\u8cc7\u6599r\u7684\u524d\u9762\u90e8\u4efd\u8207\u5f8c\u9762\u90e8\u5206\u9032\u884c\u6b65\u9a5f1\uff0c2
\u6392\u5e8f\u904e\u7a0b\u5927\u81f4\u5982\u4e0b
step0:(26,5,37<\/strong>,1,61,11,59,15,48,19<\/strong>)
step0.1:(26,5,19,1,61<\/strong>,11,59,15<\/strong>,48,37)
step0.2:(26<\/strong>,5,19,1,15,11<\/strong>,59<\/strong>,61,48,37)
step1:(11,5,19,1,15),26,(59,61,48,37) \/\/\u4ee526\u70ba\u4f9d\u64da\u9032\u884c\u5207\u5272
step2:(1,5),11,(19,15),26,(59,61,48,37) \/\/\u4ee511\u70ba\u4f9d\u64da\u9032\u884c\u5207\u5272
step3:1,5,11,(19,15),26,(59,61,48,37) \/\/\u4ee51\u70ba\u4f9d\u64da\u9032\u884c\u5207\u5272
step4:1,5,11,15,19,26,(59,61,48,37) \/\/\u4ee519\u70ba\u4f9d\u64da\u9032\u884c\u5207\u5272
step5:1,5,11,15,19,26,(48,37),59,61 \/\/\u4ee559\u70ba\u4f9d\u64da\u9032\u884c\u5207\u5272
step6:1,5,11,15,19,26,37,48,59,61 \/\/\u4ee548\u70ba\u4f9d\u64da\u9032\u884c\u5207\u5272<\/p>\n\n\n\n

\u82e5\u8cc7\u6599\u500b\u6578\u70ban\uff0c\u5247\u5207\u5272\u8907\u96dc\u5ea6\u70baO(n)
worst case:\u5207\u5272\u5f8c\u5169\u90e8\u4efd\u9577\u5ea6\u5dee\u7570\u6700\u5927(\u7576\u8cc7\u6599\u6709\u6392\u5e8f\u6642)\u8907\u96dc\u5ea6\u6700\u5927(\u6bcf\u6b21\u5207\u5272\uff0c\u4e00\u90e8\u4efd\u8cc7\u6599\u500b\u6578\u70ban-1,\u53e6\u4e00\u90e8\u4efd\u8cc7\u6599\u500b\u6578\u70ba0)\uff0c\u4e14\u9700\u8981\u7684\u5806\u758a\u7a7a\u9593\u662fO(N)
\u6700\u5dee\u60c5\u6cc1\u905e\u8ff4\u95dc\u4fc2\u5f0f
t(n)={ t(n-1)+n,n>1 ;1,n=1
t(n)=t(n-1)+n=t(n-2)+(n-1)+n=…=t(1)+2+3+…+(n-1)+n=1+2+…+n=n*(n+1)\/2=O(n^2)
best case:\u82e5\u5207\u5272\u5f8c\u5dee\u7570\u6700\u5c0f\uff0c\u8907\u96dc\u5ea6\u8d8a\u5c0f\uff0c\u6bcf\u6b21\u5207\u5272\u5f8c\u5169\u90e8\u4efd\u8cc7\u6599\u500b\u6578\u5927\u7d04\u90fd\u662fn\/2\u500b\uff0c\u4e14\u9700\u8981\u7684\u5806\u758a\u7a7a\u9593\u662fO(2\u5e95log n)
\u6700\u4f73\u60c5\u6cc1\u905e\u8ff4\u95dc\u4fc2\u5f0f t(n)=2t(n\/2)+n=…=O(n log2(n))<\/p>\n\n\n\n

void quick_sort(int list[],int first,int last){
\u3000int left,right,key;
\u3000if(first < last){
\u3000\u3000left=first;right=last+1;key=list[first];
\u3000\u3000do{
\u3000\u3000\u3000do{left++;}while(list[left] < key); \/\/\u5f9e\u5de6\u5f80\u53f3\u627e\u6bd4\u8cc7\u6599key\u5927\u7684\u8cc7\u6599s,\u82e5\u628alist\u8dd1\u5b8c\u90fd\u6c92\u6709\u5c31\u5230\u4e0b\u4e00\u884c
\u3000\u3000\u3000do{right–;}while(list[right] > key); \/\/\u5f9e\u53f3\u5f80\u5de6\u627e\u6bd4\u8cc7\u6599key\u5c0f\u7684\u8cc7\u6599t\uff0c\u82e5\u628alist\u8dd1\u5b8c\u90fd\u6c92\u6709\u5c31\u5230\u4e0b\u4e00\u884c
\u3000\u3000\u3000if(left < right)swap(list[left],list[right]); \/\/(\u6c92\u6383\u63cf\u5b8c),\u5247\u5c07\u8cc7\u6599s\u548c\u8cc7\u6599t\u4ea4\u63db
\u3000\u3000}while(left < right);
\u3000\u3000swap(list[first],list[right]); \/\/(\u5df1\u6383\u63cf\u5b8c)\u5c07\u8cc7\u6599key\u8207\u8cc7\u6599t\u4ea4\u63db(\u6b64\u6642\u8cc7\u6599key\u5927\u65bc\u524d\u9762\u8cc7\u6599)
\u3000\u3000quick_sort(list,first,right-1);
\u3000\u3000quick_sort(list,right+1,last);
\u3000}
}<\/p>\n\n\n\n

…..<\/p>\n\n\n\n

merge sort(\u5408\u4f75\u6392\u5e8f\u6cd5):<\/strong>
\u5e73\u5734\u6700\u4f73\u6700\u5deeO(n 2\u5e95log n),\u984d\u5916\u7a7a\u9593O(N),\u5c6cstable sort
\u505a\u6cd5\uff1a\u5c07\u4e32\u5217\u8996\u70ban\u500b\u9577\u5ea61\u7684\u5df1\u6392\u5e8f\u4e32\u5217\uff0c\u7531\u7b2c\u4e00\u500b\u958b\u59cb\u9032\u884c\u5169\u5169\u5408\u4f75\uff0c\u7522\u751f\u500b\u6578ceil(n\/2)\u9577\u5ea6\u70ba2\u7684\u5df1\u6392\u5e8f\u4e32\u5217\uff0c\u53cd\u8986\u4e0a\u8ff0\u6b65\u9a5f\u4e00\u76f4\u5230\u500b\u6578\u70ba1\u9577\u5ea6\u70ban
\u6392\u5e8f\u904e\u7a0b\u5927\u81f4\u5982\u4e0b
step0:(26),(5),(37),(2),(61),(10),(59),(16)
step1:(5,26),(2,37),(10,61),(16,59)
step2:(2,5,26,37),(10,16,59,61)
step3:(2,5,10,16,26,37,59,61)<\/p>\n\n\n\n

\u82e5\u6709n\u500b\u8cc7\u6599\uff0c\u5247\u6bcf\u968e\u6bb5\u7684\u5408\u4f75\u8907\u96dc\u5ea6\u7b49\u7d1a\u56fa\u5b9aO(n),\u800c\u7e3d\u5171\u9700\u89812\u5e95log n\u500b\u968e\u6bb5
\u905e\u8ff4\u95dc\u4fc2\u5f0f\uff1at(n)={2t(n\/2)+n,n>1 ; 1,n=1
t(n)=2t(n\/2)+n=2[2t(n\/4)+n\/2]+n=4t(n\/4)+2n=…=(2^k)t(n\/(2^k))+k*n=2^k*t(1)+k*n=n+n*log2(n),\u9019\u88e1\u5047\u8a2d2^k=n
\u6f14\u7b97\u6cd5\uff1a
void merge_sort(){ \/\/\u5408\u4f75\u6392\u5e8f
}
void merge(){ \/\/\u5408\u4f75\u7684\u526f\u7a0b\u5f0f
}<\/p>\n\n\n\n

…..<\/p>\n\n\n\n

heap sort(\u5806\u7a4d\u6392\u5e8f\u6cd5):<\/strong>
\u5e73\u5734\u6700\u5deeO(n 2\u5e95log n),\u984d\u5916\u7a7a\u9593O(1)
\u505a\u6cd5\uff1a
1\u5c07\u6392\u5e8f\u8cc7\u6599\u8996\u70ba\u4e8c\u5143\u6a39\u4e26\u8b8a\u6210max heap
2\u5728\u628a\u6a39\u6839\u548c\u6700\u5f8c\u7bc0\u9ede\u4ea4\u63db
3\u8abf\u6574max heap(\u7701\u7565\u88ab\u63db\u5230\u6700\u5f8c\u7684\u90a3\u4e9b\u7bc0\u9ede)\u8907\u96dc\u5ea6\u70baO(2\u5e95log n)
4\u91cd\u8986\u6b65\u9a5f2,3(\u6703\u91cd\u8986n-1\u6b21)
\u4e0d\u7ba1\u8cc7\u6599\u662f\u5426\u6392\u5e8f\uff0c\u8655\u7406\u6b21\u6578\u56fa\u5b9a<\/p>\n\n\n\n

\u6f14\u7b97\u6cd5
void adjust(int list[],int position,int last){ \/\/\u7522\u751fheap tree
\u3000int child;int large;
\u3000while(last>=2*position){
\u3000\u3000large=list[2*position];
\u3000\u3000child=2*position;
\u3000\u3000if(last>2*position){if(list[child+1]>larger)larger=list[++child]}
\u3000\u3000if(list[child]>list[position]){swap(list[child],list[position]);position=child;}
\u3000\u3000else{break;}
\u3000}
}
viod heapsort(int list[],int n){
\u3000int i,j;
\u3000int temp;
\u3000for(i=n\/2;i>0;i–){ \/\/\u5c07\u6392\u5e8f\u8cc7\u6599\u8996\u70ba\u4e8c\u5143\u6a39\u4e26\u8b8a\u6210heap tree
\u3000\u3000adjust(list,i,n);
\u3000}
\u3000for(i=n-1;i>0;i–){ \/\/\u91cd\u8986n\u6b21\u6b65\u9a5f2
\u3000\u3000temp=list[1];
\u3000\u3000list[1]=list[i+1];
\u3000\u3000list[i+1]=temp;
\u3000\u3000adjust(list,1,i); \/\/\u91cd\u8986n\u6b21\u6b65\u9a5f3
\u3000}
}<\/p>\n\n\n\n


………………………………………………………………………………………..<\/p>\n\n\n\n

\u5206\u914d\u6392\u5e8f\u6cd5<\/strong>
\u4e5f\u7a31bin sort(\u5bb9\u5668\u6392\u5e8f\u6cd5)
\u6839\u64da\u6bcf\u500b\u95dc\u9375\u503c\u7684\u7bc4\u570d\uff0c\u8a2d\u7acb\u76f8\u540c\u500b\u6578\u7684\u5bb9\u5668\uff0c\u518d\u6839\u64da\u8cc7\u6599\u7684\u503c\uff0c\u628a\u8cc7\u6599\u5206\u914d\u5230\u5c0d\u61c9\u7684\u5bb9\u5668\uff0c\u5373\u53ef\u5f97\u5230\u6392\u5e8f\u7d50\u679c
the most significant digit first,msd\u4e3b\u8981\u95dc\u9375\u503c\u512a\u5148\uff1a\u5404\u5bb9\u5668\u8cc7\u6599\u7368\u7acb\u5730\u8996\u70ba\u4e00\u7d44\uff0c\u5404\u7d44\u9808\u55ae\u7368\u9032\u884c\u6392\u5e8f
the least significant digit first,lsd\u6b21\u8981\u95dc\u9375\u503c\u512a\u5148\uff1a\u6240\u6709\u5bb9\u5668\u8cc7\u6599\u8996\u70ba\u4e00\u7d44\uff0c\u5c0d\u6240\u6709\u8cc7\u6599\u9032\u884c\u6392\u5e8f
\u505a\u6cd5\uff1a\u5982\u679c\u8981\u5c0d\u57fa\u5e95\u70bab,\u7531d\u500b\u6578\u5b57\u7d44\u6210\u7684n\u500b\u6574\u6578\u9032\u884c\u5206\u914d\u6392\u5e8f\uff0c\u5247\u9700d\u500b\u968e\u6bb5\uff0c\u5404\u968e\u6bb5\u8981b\u500b\u5bb9\u5668\uff0c\u5c07n\u500b\u6574\u6578\u5206\u914d\u5230\u5c0d\u61c9\u7684\u5bb9\u5668\u4e2d
\u56e0\u6b64\u6f14\u7b97\u6cd5\u8907\u96dc\u5ea6\u7b49\u7d1a\u662fO(d*(n+b))<\/p>\n\n\n\n


…………………………………………………………………………………………
………………………………………………………………………………………… <\/p>\n\n\n\n


external sort(\u5916\u90e8\u6392\u5e8f\u6cd5)<\/strong><\/h2>\n\n\n\n


\u56e0\u8cc7\u6599\u500b\u6578\u592a\u591a\u7121\u6cd5\u5168\u653e\u5165\u4e3b\u8a18\u61b6\u9ad4,\u6240\u4ee5\u5b58\u653e\u5728\u8f14\u52a9\u8a18\u61b6\u9ad4\u5728\u505a\u6392\u5e8f
\u5e38\u898b\u7684\u6392\u5e8f\u6cd5\u6709:
\u78c1\u789f\u6392\u5e8f\u6cd5
\u78c1\u5e36\u6392\u5e8f\u6cd5<\/p>\n\n\n\n

\u78c1\u789f\u6392\u5e8f\u6cd5<\/strong>
\u5206\u6bb5\u6392\u5e8f\uff1a\u628a\u8f14\u52a9\u8a18\u61b6\u9ad4\u4e2d\u8981\u6392\u5e8f\u7684\u8cc7\u6599\u5206\u6279\u8f38\u5165\u5230\u4e3b\u8a18\u61b6\u9ad4\u4e2d\uff0c\u518d\u7528\u4efb\u4e00\u5167\u90e8\u6392\u5e8f\u6cd5\u5c07\u5df1\u6392\u5e8f\u7684\u8cc7\u6599\u6bb5\u8f38\u51fa\u5230\u8f14\u52a9\u8a18\u61b6\u9ad4
\u5206\u6bb5\u5408\u4f75\uff1a\u5c0d\u8f14\u52a9\u8a18\u61b6\u9ad4\u4e2d\u6392\u5e8f\u597d\u7684\u8cc7\u6599\u5408\u4f75\uff0c\u53ef\u5c07\u4e3b\u8a18\u61b6\u5206\u6210\u5169\u500b\u8f38\u5165\u7de9\u885d\u5340(\u53d6\u5169\u500b\u8cc7\u6599\u6bb5)\u548c\u4e00\u500b\u8f38\u51fa\u7de9\u885d\u5340(\u5408\u4f75\u7d50\u679c)\uff0c\u4e14\u6703\u6709\u591a\u6b21\u8f38\u5165\u8207\u8f38\u51fa
\u82e5\u6709nx\u7b46\u5df1\u6392\u5e8f\u597d\u7684\u8cc7\u6599\u6bb5\uff0c\u5247\u9700\u8981ceil(log2(nx))\u500b\u968e\u6bb5
\u82e5\u7528\u4e8c\u9805\u5408\u4f75\uff0c\u8f38\u51fa\u5165\u6b21\u6578\u591a\uff0c\u6bd4\u8f03\u6b21\u6578\u5c11\uff0c\u53ea\u9700\u7d93\u904e\u4e00\u6b21\u6bd4\u8f03\u5373\u53ef\u5b8c\u6210\u4e00\u500b\u5408\u4f75\u904b\u4f5c\uff0c\u6574\u500b\u5408\u4f75\u9700\u8981\u6bd4\u8f031*n*log2(n)
\u82e5\u7528m\u9805\u5408\u4f75\uff0c\u8f38\u51fa\u5165\u6b21\u6578\u5c11\uff0c\u6bd4\u8f03\u6b21\u6578\u591a\uff0c\u5247\u9700m-1\u6b21\u6bd4\u8f03\u5b8c\u6210\u4e00\u500b\u5408\u4f75\u52d5\u4f5c\uff0c\u6574\u500b\u5408\u4f75\u9700\u8981\u6bd4\u8f03(m-1)*n*logm(n)<\/p>\n\n\n\n

\u9078\u64c7\u6a39\u7d50\u69cb
\u5404\u975e\u7aef\u672b\u7bc0\u9ede\u7684\u503c\u7b49\u65bc\u5de6\u53f3\u5152\u5b50\u6700\u5c0f\u7684\u503c
\u9700ceil(log2(m))\u6b21\u6bd4\u8f03\u5b8c\u6210\u4e00\u500b\u5408\u4f75\u52d5\u4f5c\uff0c\u6574\u500b\u5408\u4f75\u9700\u8981\u6bd4\u8f03n*log2(n)
loser tree(\u8f38\u5bb6\u6a39):\u5404\u975e\u7aef\u672b\u7bc0\u5728\u591a\u7d00\u9304\u5de6\u53f3\u5152\u5b50\u7684\u6700\u5927\u503c<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5b9a\u7fa9stable sort(\u7a69\u5b9a\u7684\u6392\u5e8f\u6cd5):\u82e5\u6709\u76f8\u540c\u8cc7\u6599\uff0c\u5247 …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[15],"tags":[],"class_list":["post-568","post","type-post","status-publish","format-standard","hentry","category-algorithm"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/posts\/568","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/comments?post=568"}],"version-history":[{"count":0,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/posts\/568\/revisions"}],"wp:attachment":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/media?parent=568"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/categories?post=568"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/tags?post=568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}