八排序算法

    nO(nlog2n)

   keyword

1.(Straight Insertion Sort)

:

112

void print(int a[], int n ,int i){
	cout<<i <<":";
	for(int j= 0; j<8; j++){
		cout<<a[j] <<" ";
	}
	cout<<endl;
}


void InsertSort(int a[], int n)
{
	for(int i= 1; i<n; i++){
		if(a[i] < a[i-1]){               //ii-1
			int j= i-1;	
			int x = a[i];		 //
			a[i] = a[i-1];           //
			while(x < a[j]){	 //
				a[j+1] = a[j];
				j--;		 //
			}
			a[j+1] = x;		 //
		}
		print(a,n,i);			//
	}
	
}

int main(){
	int a[8] = {3,1,5,7,2,4,9,6};
	InsertSort(a,8);
	print(a,8,8);
}

On^2.

2-

 2. Shell`s Sort

1959 D.L.Shell

1. t1t2tkti>tjtk=1
2. kk
3. tim 1

d = {n/2 ,n/4, n/8 .....1} n

dn/2,nd.d/21

void print(int a[], int n ,int i){
	cout<<i <<":";
	for(int j= 0; j<8; j++){
		cout<<a[j] <<" ";
	}
	cout<<endl;
}
/**
 * 
 *
 * @param int dk dk=1
 *
 */

void ShellInsertSort(int a[], int n, int dk)
{
	for(int i= dk; i<n; ++i){
		if(a[i] < a[i-dk]){			//ii-1
			int j = i-dk;	
			int x = a[i];			//
			a[i] = a[i-dk];			//
			while(x < a[j]){		//
				a[j+dk] = a[j];
				j -= dk;			 //
			}
			a[j+dk] = x;			//
		}
		print(a, n,i );
	}
	
}

/**
 * dn/2,n
 *
 */
void shellSort(int a[], int n){

	int dk = n/2;
	while( dk >= 1  ){
		ShellInsertSort(a, n, dk);
		dk = dk/2;
	}
}
int main(){
	int a[8] = {3,1,5,7,2,4,9,6};
	//ShellInsertSort(a,8,1); //
	shellSort(a,8);			  //
	print(a,8,8);
}

3. Simple Selection Sort

12n-1n

n

n-1

.....

i i n-i+1 i

void print(int a[], int n ,int i){
	cout<<""<<i+1 <<" : ";
	for(int j= 0; j<8; j++){
		cout<<a[j] <<"  ";
	}
	cout<<endl;
}
/**
 * 值
 *
 * @return int 值
 */
int SelectMinKey(int a[], int n, int i)
{
	int k = i;
	for(int j=i+1 ;j< n; ++j) {
		if(a[k] > a[j]) k = j;
	}
	return k;
}

/**
 * 
 *
 */
void selectSort(int a[], int n){
	int key, tmp;
	for(int i = 0; i< n; ++i) {
		key = SelectMinKey(a, n,i);           //
		if(key != i){
			tmp = a[i];  a[i] = a[key]; a[key] = tmp; //i
		}
		print(a,  n , i);
	}
}
int main(){
	int a[8] = {3,1,5,7,2,4,9,6};
	cout<<"值";
	for(int j= 0; j<8; j++){
		cout<<a[j] <<"  ";
	}
	cout<<endl<<endl;
	selectSort(a, 8);
	print(a,8,8);
}

,n[n/2]

void SelectSort(int r[],int n) {
	int i ,j , min ,max, tmp;
	for (i=1 ;i <= n/2;i++) {  
		// n/2 
		min = i; max = i ; //keyword
		for (j= i+1; j<= n-i; j++) {
			if (r[j] > r[max]) { 
				max = j ; continue ; 
			}  
			if (r[j]< r[min]) { 
				min = j ; 
			}   
	  }  
	  //
	  tmp = r[i-1]; r[i-1] = r[min]; r[min] = tmp;
	  tmp = r[n-i]; r[n-i] = r[max]; r[max] = tmp; 

	} 
}

4. Heap Sort

nk1,k2,...,kn),

值()值值()

a96, 83,27,38,11,09)

  (b)  1236248547305391

nn ()(n-1)n ()n

1. n
2. n-1

n-1

1m m-1

2

3 2.

4 2.

5

n

1n

2

3

4938659776132749
                             

void print(int a[], int n){
	for(int j= 0; j<n; j++){
		cout<<a[j] <<"  ";
	}
	cout<<endl;
}



/**
 * H[sm]H[s] 
 * H[s],.s, 
 *
 * @param H
 * @param s
 * @param length
 *
 */
void HeapAdjust(int H[],int s, int length)
{
	int tmp  = H[s];
	int child = 2*s+1; //(i+1 )
    while (child < length) {
		if(child+1 <length && H[child]<H[child+1]) { // ()
			++child ;
		}
		if(H[s]<H[child]) {  // 
			H[s] = H[child]; // 
			s = child;		 // s ,
			child = 2*s+1;
		}  else {			 // 
			 break;
		}
		H[s] = tmp;			// 
	}
	print(H,length);
}


/**
 * 
 * H[0..length-1]
 * 
 */
void BuildingHeap(int H[], int length)
{ 
	// i=  (length -1) / 2
	for (int i = (length -1) / 2 ; i >= 0; --i)
		HeapAdjust(H,i,length);
}
/**
 * 
 */
void HeapSort(int H[],int length)
{
    //
	BuildingHeap(H, length);
	//
	for (int i = length - 1; i > 0; --i)
	{
		//H[0]
		int temp = H[i]; H[i] = H[0]; H[0] = temp;
		//
		HeapAdjust(H,0,i);
  }
} 

int main(){
	int H[10] = {3,1,5,7,2,4,9,6,10,8};
	cout<<"值";
	print(H,10);
	HeapSort(H,10);
	//selectSort(a, 8);
	cout<<"";
	print(H,10);

}

:

k2(k-1)k  

4n O(nlogn )

5. Bubble Sort

void bubbleSort(int a[], int n){
	for(int i =0 ; i< n-1; ++i) {
		for(int j = 0; j < n-i-1; ++j) {
			if(a[j] > a[j+1])
			{
				int tmp = a[j] ; a[j] = a[j+1] ;  a[j+1] = tmp;
			}
		}
	}
}

exchange

1pos,pos,pos

:

void Bubble_1 ( int r[], int n) {
	int i= n -1;  //,
	while ( i> 0) { 
		int pos= 0; //,
		for (int j= 0; j< i; j++)
			if (r[j]> r[j+1]) {
				pos= j; // 
				int tmp = r[j]; r[j]=r[j+1];r[j+1]=tmp;
			} 
		i= pos; //
	 } 
}  

2值值,值() ,

:

void Bubble_2 ( int r[], int n){
	int low = 0; 
	int high= n -1; //值
	int tmp,j;
	while (low < high) {
		for (j= low; j< high; ++j) //,
			if (r[j]> r[j+1]) {
				tmp = r[j]; r[j]=r[j+1];r[j+1]=tmp;
			} 
		--high;					//high值, 
		for ( j=high; j>low; --j) //,
			if (r[j]<r[j-1]) {
				tmp = r[j]; r[j]=r[j-1];r[j-1]=tmp;
			}
		++low;					//low值,
	} 
} 

6. Quick Sort

1,,

2值值 值值

3

4

a

b

void print(int a[], int n){
	for(int j= 0; j<n; j++){
		cout<<a[j] <<"  ";
	}
	cout<<endl;
}

void swap(int *a, int *b)
{
	int tmp = *a;
	*a = *b;
	*b = tmp;
}

int partition(int a[], int low, int high)
{
	int privotKey = a[low];								//
	while(low < high){								    //
		while(low < high  && a[high] >= privotKey) --high;  //high low+1 
		swap(&a[low], &a[high]);
		while(low < high  && a[low] <= privotKey ) ++low;
		swap(&a[low], &a[high]);
	}
	print(a,10);
	return low;
}


void quickSort(int a[], int low, int high){
	if(low < high){
		int privotLoc = partition(a,  low,  high);  //
		quickSort(a,  low,  privotLoc -1);			//
		quickSort(a,   privotLoc + 1, high);		//
	}
}

int main(){
	int a[10] = {3,1,5,7,2,4,9,6,10,8};
	cout<<"值";
	print(a,10);
	quickSort(a,0,9);
	cout<<"";
	print(a,10);

}

O(nlog2n)

,k,k值 8 ,

void print(int a[], int n){
	for(int j= 0; j<n; j++){
		cout<<a[j] <<"  ";
	}
	cout<<endl;
}

void swap(int *a, int *b)
{
	int tmp = *a;
	*a = *b;
	*b = tmp;
}

int partition(int a[], int low, int high)
{
	int privotKey = a[low];					//
	while(low < high){					//
		while(low < high  && a[high] >= privotKey) --high; //high low+1 
		swap(&a[low], &a[high]);
		while(low < high  && a[low] <= privotKey ) ++low;
		swap(&a[low], &a[high]);
	}
	print(a,10);
	return low;
}


void qsort_improve(int r[ ],int low,int high, int k){
	if( high -low > k ) { //k, k
		int pivot = partition(r, low, high); // Partition
		qsort_improve(r, low, pivot - 1,k);
		qsort_improve(r, pivot + 1, high,k);
	} 
} 
void quickSort(int r[], int n, int k){
	qsort_improve(r,0,n,k);//Qsort

	//
	for(int i=1; i<=n;i ++){
		int tmp = r[i]; 
		int j=i-1;
		while(tmp < r[j]){
			r[j+1]=r[j]; j=j-1; 
		}
		r[j+1] = tmp;
	} 

} 



int main(){
	int a[10] = {3,1,5,7,2,4,9,6,10,8};
	cout<<"值";
	print(a,10);
	quickSort(a,9,4);
	cout<<"";
	print(a,10);

}

7. Merge Sort

Merge

r[in]r[im]r[m+1n]n-i +1n-m

1. j=m+1k=ii=i; //
2. i>m j>n //
3. //r[i]r[j]rf
   r[i]<r[j]rf[k]=r[i] i++ k++
   rf[k]=r[j] j++ k++
4. //rf
   i<=mr[im]rf[kn] //
   j<=n ,  r[jn] rf[kn] //

//r[im]r[m +1 n]rf[in]
void Merge(ElemType *r,ElemType *rf, int i, int m, int n)
{
	int j,k;
	for(j=m+1,k=i; i<=m && j <=n ; ++k){
		if(r[j] < r[i]) rf[k] = r[j++];
		else rf[k] = r[i++];
	}
	while(i <= m)  rf[k++] = r[i++];
	while(j <= n)  rf[k++] = r[j++];
}

1 n 1 n/21 2n

void print(int a[], int n){
	for(int j= 0; j<n; j++){
		cout<<a[j] <<"  ";
	}
	cout<<endl;
}

//r[im]r[m +1 n]rf[in]
void Merge(ElemType *r,ElemType *rf, int i, int m, int n)
{
	int j,k;
	for(j=m+1,k=i; i<=m && j <=n ; ++k){
		if(r[j] < r[i]) rf[k] = r[j++];
		else rf[k] = r[i++];
	}
	while(i <= m)  rf[k++] = r[i++];
	while(j <= n)  rf[k++] = r[j++];
	print(rf,n+1);
}

void MergeSort(ElemType *r, ElemType *rf, int lenght)
{ 
	int len = 1;
	ElemType *q = r ;
	ElemType *tmp ;
	while(len < lenght) {
		int s = len;
		len = 2 * s ;
		int i = 0;
		while(i+ len <lenght){
			Merge(q, rf,  i, i+ s-1, i+ len-1 ); //
			i = i+ len;
		}
		if(i + s < lenght){
			Merge(q, rf,  i, i+ s -1, lenght -1); //
		}
		tmp = q; q = rf; rf = tmp; //q,rfq rf
	}
}


int main(){
	int a[10] = {3,1,5,7,2,4,9,6,10,8};
	int b[10];
	MergeSort(a, b, 10);
	print(b,10);
	cout<<"";
	print(a,10);

}

void MSort(ElemType *r, ElemType *rf,int s, int t)
{ 
	ElemType *rf2;
	if(s==t) r[s] = rf[s];
	else
	{ 
		int m=(s+t)/2;			/**p */
		MSort(r, rf2, s, m);		/*p[sm]p2[sm]*/
		MSort(r, rf2, m+1, t);		/*p[m+1t]p2[m+1t]*/
		Merge(rf2, rf, s, m+1,t);	/*p2[sm]p2[m+1t]p1[st]*/
	}
}
void MergeSort_recursive(ElemType *r, ElemType *rf, int n)
{   /**p */
	MSort(r, rf,0, n-1);
}

8. /(Radix Sort)

值n O(n log n)
          

 [1..1000]nA[1..n]  

 10B[1][1..10]B[2]   (10..20]B[i](   (i-1)*10,   i*10]i   =   1,2,..100  100  

  A[1..n]A[i]B[j]  100 

  nmn/m  

  O(n   +   m   *   n/m*log(n/m))   =   O(n   +   nlogn   -   nlogm)  

  mnO(n)  

  n    

        On2O(nlogn)On

        1值0m-1mm

        2

keywordO(n)

:

52 值
< < <  
值 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9 < 10 < J < Q < K < A

值

值值

14 值4
213 值13 (2 3 ...A )值13 4 ()23 4 值4

n d {k1k2kd}{k1k2kd}r[i]r[j](1ijn)

k1 kd      

(Most Significant Digit first)MSD

1k1 k1

2k2 kd

3值MSD

(Least Significant Digit first)LSD

1) kd kd-1k1

2) , 值LSD

LSD

keywordkeywordkeywordkeyword-值4值13值4值13   

:

Void RadixSort(Node L[],length,maxradix)
{
   int m,n,k,lsp;
   k=1;m=1;
   int temp[10][length-1];
   Empty(temp); //
   while(k<maxradix) //keyword
   {
     for(int i=0;i<length;i++) //
    {
       if(L[i]<m)
          Temp[0][n]=L[i];
       else
          Lsp=(L[i]/m)%10; //keyword
       Temp[lsp][n]=L[i];
       n++;
   }
   CollectElement(L,Temp); //
   n=0;
   m=m*10;
  k++;
 }
}

                             O(n)

nO(nlog2n)

(1)(O(n²))
:
 (2)(O(nlog2n))

 (3)O(n¹⁺)),01

      
(4)(O(n))

On

On2

:keyword  
    

1n

2keyword

3keyword

4

n.

1nO(nlog2n)

   keyword
        

2  n =

3n

5

6

1keyword
2keyword
3