一个比快速算法更快的排序算法: flashsort

现在最快的排序算法是快速排序算法,它的时间复杂度达到O(n log n).但是还有一种排序算法,就是FlashSort排序算法.它的时间复杂度达到O(n),超过了前者.FlashSort排序是基于分类的算法,它的实现思想很简单,是利用构造出来的索引来排序.举一个简单的例子,比如有一百个整数,你很容易就能把它们放在数组的正确位置上,根本不需要作任何比较. flashsort 主页： http://www.neubert.net/FSOIntro.html 附C实现代码： [code type="c"] /***** FLASH.C ,FLOAT-, recursive subroutine version Translation of Neubert's algorithm into C by Michael Sahota *****/ /* Subroutine Flash(a,n,m,ctr) - Sorts array a with n elements by use of the index vector l of dimension m (with m about 0.1 n). - The routine runs fastest with a uniform distribution of elements. - The vector l is declare dynamically using the calloc function. - The variable ctr counts the number of times that flashsort is called. - THRESHOLD is a very important constant. It is the minimum number of elements required in a subclass before recursion is used. */ #include #include #include const int THRESHOLD = 75; const CLASS_SIZE = 75; /* minimum value for m */ void flashsort(float a[],int n,int m,int *ctr) { /* declare variables */ int *l,nmin,nmax,i,j,k,nmove,nx,mx; float c1,c2,flash,hold; /* allocate space for the l vector */ l=(int*)calloc(m,sizeof(int)); /***** CLASS FORMATION ****/ nmin=nmax=0; for (i=0 ; i < n ; i++) if (a[i] < a[nmin]) nmin = i; else if (a[i] > a[nmax]) nmax = i; if ( (a[nmax]==a[nmin]) && (ctr==0) ) { printf("All the numbers are identical, the list is sorted "); return; } c1=(m-1.0)/(a[nmax]-a[nmin]) ; c2=a[nmin]; l[0]=-1; /* since the base of the "a" (data) array is 0 */ for (k=1; k < m ; k++) l[k]=0; for (i=0; i < n ; i++) { k=floor(c1*(a[i]-c2) ); l[k]+=1; } for (k=1; k < m ; k++) l[k]+=l[k-1]; hold=a[nmax]; a[nmax]=a[0]; a[0]=hold; /**** PERMUTATION *****/ nmove=0; j=0; k=m-1; while ( nmove < n ) { while ( j > l[k] ) { j++; k=floor(c1*(a[j]-c2) ) ; } flash=a[ j ] ; while ( j <= l[k] ) { k=floor(c1*(flash-c2)); hold=a[ l[k] ]; a[ l[k] ] = flash; l[k]--; flash=hold; nmove++; } } /**** Choice of RECURSION or STRAIGHT INSERTION *****/ for (k=0;k<(m-1);k++) if ( (nx = l[k+1]-l[k]) > THRESHOLD ) /* then use recursion */ { flashsort(&a[l[k]+1],nx,CLASS_SIZE,ctr); (*ctr)++; } else /* use insertion sort */ for (i=l[k+1]-1; i > l[k] ; i--) if (a[i] > a[i+1]) { hold=a[i]; j=i; while (hold > a[j+1] ) a[j++]=a[j+1] ; a[j]=hold; } free(l); /* need to free the memory we grabbed for the l vector */ } [/code]