Introduction to algorithms-Chapter 7-quick sorting

Chapter 7 quick sorting

 

Summary: This chapter describes the fast sorting algorithm, analyzes the complexity of the algorithm, and describes the random version of quick sorting.

 

1.Quick sorting

Partition (A, P, R) converts a [p... R] performs local shuffling and returns Q, where a [p... The elements in q-1] are less than a [Q], a [q + 1 ,... The elements in R] are greater than a [Q].

Recursive sorting of quicksort (A, P, R)

Analysis: Worst Case O (N ^ 2)

Best case o (nlgn)

Average O (N ^ 2)

 

Pseudocode

Partition (A, P, R)

X <-A [R]

I <-P-1

For j <-P to R-1

Do if a [J] <= x

Then I <-I + 1

Exchange a [I] <-> A [J]

Exchange a [I + 1] <-> A [R]

Return I + 1

 

Quicksort (A, P, R)

If P <r

Then q <-partion (A, P, R)

Quicksort (A, P, q-1)

Quicksort (A, q + 1, R)

 

 

# Include <iostream> <br/> using namespace STD; <br/> int partition (int A [], int P, int R) // A [p... r] <br/>{< br/> int I = p-1; <br/> Int J = P; <br/> int temp; <br/> int key = A [R]; <br/> for (j = P; j <r; j ++) <br/>{< br/> if (a [J] <= Key) <br/>{< br/> I ++; <br/> temp = A [I]; <br/> A [I] = A [J]; <br/> A [J] = temp; <br/>}< br/> temp = A [I + 1]; <br/> A [I + 1] = A [R]; <br/> A [R] = temp; <br/> return I + 1; <br/>}< br/> void quicksort (int A [], int P, int R) <br/>{< br/> If (P> = r) <br/> return; <br/> int q = partition (A, P, r); <br/> quicksort (A, P, q-1); <br/> quicksort (A, q + 1, R ); <br/>}< br/> int main () <br/> {<br/> int A [10] = }; <br/> quicksort (A, 0, 9); <br/> for (INT I = 0; I <10; I ++) <br/> cout <A [I] <Endl; <br/>}< br/>

2.Quick Sort random Edition

A random algorithm is introduced. In partition, a [R] is not used as the primary element. Instead, the sub-array a [p... R] randomly selects an element as the principal component.

Analysis: Worst Case O (N ^ 2)

Best case o (nlgn)

Average O (N ^ 2)

 

Pseudocode

Randomized-partition (A, P, R)

I <-random (P, R)

Exchange a [I] <-> A [R]

Return partition (A, P, R)

 

# Include <iostream> <br/> # include <ctime> <br/> using namespace STD; <br/> void Exchange (Int & A, Int & B) <br/>{< br/> int temp = A; <br/> A = B; <br/> B = temp; <br/>}</P> <p> int randomizedpartition (int A [], int P, int R) <br/>{< br/> int I = p-1; <br/> Int J = P; <br/> srand (Time (null); <br/> int K = P + rand () % (r-p + 1); <br/> Exchange (A [K], a [R]); <br/> for (j = P; j <R; j ++) <br/>{< br/> if (a [J] <= A [R]) <br/>{< br/> I ++; <br/> Exchange (A [I], a [J]); <br/>}< br/> Exchange (A [I + 1], A [R]); <br/> return I + 1; <br/>}</P> <p> void randomizedquicksort (int A [], int P, int R) <br/>{< br/> If (P> = r) <br/> return; <br/> int q = randomizedpartition (A, P, r); <br/> randomizedquicksort (A, P, q-1); <br/> randomizedquicksort (A, q + 1, R ); <br/>}< br/> int main () <br/> {<br/> int A [10] = }; <br/> randomizedquicksort (A, 0, 9); <br/> for (INT I = 0; I <10; I ++) <br/> cout <A [I] <Endl; <br/>}</P> <p>