Quickly find the K-large number in an unordered array?

1. Topic Analysis:

Finding the number of K in an unordered array , the intuitive feeling is to first order and then find the element labeled K-1 , time complexity O (NLGN). Here, we want to explore the existence of time complexity < O (nlgn), and an efficient algorithm that is approximately equal to O (N) .

Do you remember the idea of our quick sequencing? The front and back parts are divided recursively by "partition". In this problem solving strategy, the division function based on the fast row can use the "attack method", continuously from the original interval [0,n-1] to the middle of the search for the number of K , about the direction of the search:

2. Reference code:

1#include <cstdio>2 3 #defineSwap (x, y) {int temp=x;x=y;y=temp;}4 5 using namespacestd;6 7  8 9 Const intmaxn=1e5;Ten  One intA[MAXN]; A  -   -  the intPartint*arr,intPintq) { -  -     inti=p-1; -  +      for(intj=p;j<q;j++)if(arr[j]<A[q]) { -  +i++; A  at swap (arr[i],arr[j]); -  -     } -  -i=i+1; -  in swap (arr[i],arr[q]); -  to     returni; +  - } the  * intFINDK (int*arr,intNintk) { $ Panax Notoginseng     intp=0, q=n-1; -  the      while(p<q) { +  A         //int m=p+ (Q-P)/2; the  +         intf=Part (ARR,P,Q); -  $         //printf ("f=%d\n", f); //For tested $  -         if(f==k) { -  the             returnArr[k]; - Wuyi}Else if(f>k) { the  -q=f-1; Wu  -}Else{ About  $p=f+1; -  -         } -  A     } +  the     returnARR[K];//needed -  $ } the  the intMain () { the  the     intn,k; -  in     /* the  the *input includes 2 integers. n indicates the num of elements, About  the *k means for the kth larger num to be found the  the     */ +  -      while(SCANF ("%d%d", &n,&k) = =2){ the Bayi          for(intI=0; i<n;i++) scanf ("%d",&a[i]); the  the         intANS=FINDK (a,n,k-1); -  -printf"%d\n", ans); the  the     } the  the     return 0; -  the } the  the /*94  the data for the test: the  the 4 298  About 1 5433 2 - 101 4 3102 103 1 5433 2104  the 4 4106 107 1 5433 2108 109 */ the 111  

3. Test results:

Conclusion:

The implementation of this algorithm only applies to the general situation, if k=1 or 2 Smart You should know not to apply the algorithm of this article, simple traversal Save the maximum, so that the specific problem has to be specific analysis ^_^

Quickly find the K-large number in an unordered array?