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[Sort] QuickSort
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‎notes/README.md

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1. [그래프(Graph)](./Graph/Graph.md)
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2. [서로소 집합(Disjoint Set)과 Union-Find 알고리즘](./Graph/DisjointSet.md)
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3. [DAG(Directed Acyclic Graph)와 위상정렬(Topological Sort)](./Graph/TopologicalSort.md)
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## 📖 Sort
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1. [퀵정렬(QuickSort)](../src/Sort/QuickSort)

‎src/Sort/QuickSort/Main.java

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package Sort.QuickSort;
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import java.util.Arrays;
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import java.util.Random;
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public class Main {
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public static void main(String[] args) {
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Random random = new Random();
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int n = 100000000;
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int[] arr = new int[n];
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for (int i = 0; i < n; i++) {
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arr[i] = random.nextInt(n);
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}
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System.out.println("n : " + n);
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System.out.println("====== choice of pivot 2.1 ======");
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long start = System.currentTimeMillis();
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QuickSort qs1 = new QuickSort(arr, n);
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long end = System.currentTimeMillis();
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System.out.println( "실행 시간 : " + ( end - start )/1000.0 + "초");
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System.out.println("====== choice of pivot 2.2 ======");
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start = System.currentTimeMillis();
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QuickSort2 qs2 = new QuickSort2(arr, n);
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end = System.currentTimeMillis();
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System.out.println( "실행 시간 : " + ( end - start )/1000.0 + "초");
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System.out.println("====== choice of pivot 2.3 ======");
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start = System.currentTimeMillis();
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QuickSort3 qs3 = new QuickSort3(arr, n);
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end = System.currentTimeMillis();
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System.out.println( "실행 시간 : " + ( end - start )/1000.0 + "초");
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}
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}
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// The first element is the pivot
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class QuickSort {
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int[] S;
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int comparison_count = 0;
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int exchange_count = 0;
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public QuickSort(int[] arr, int n) {
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this.S = new int[n];
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System.arraycopy(arr, 0, this.S, 0, n);
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// System.out.println(Arrays.toString(this.S));
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sort(0, n-1);
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// System.out.println(Arrays.toString(this.S));
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System.out.println("Comparison : " + this.comparison_count);
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System.out.println("Exchange : " + this.exchange_count);
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}
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void sort (int low, int high) {
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if (low < high) {
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int pivotPoint = partition(low, high);
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sort(low, pivotPoint-1);
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sort(pivotPoint+1, high);
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}
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}
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int partition(int low, int high) {
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int pivot = this.S[low];
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int j = low;
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for (int i = low+1; i <= high; i++) {
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if (this.S[i] < pivot) {
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this.comparison_count ++;
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j++;
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swap(i, j);
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}
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}
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swap(low, j);
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return j;
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}
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void swap(int a, int b) {
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this.exchange_count ++;
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int temp = this.S[a];
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this.S[a] = this.S[b];
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this.S[b] = temp;
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}
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}
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// A randomly chosen element between low and high is the pivot.
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class QuickSort2 {
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int[] S;
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int comparison_count = 0;
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int exchange_count = 0;
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public QuickSort2(int[] arr, int n) {
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this.S = new int[n];
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System.arraycopy(arr, 0, this.S, 0, n);
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// System.out.println(Arrays.toString(this.S));
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sort2(0, n-1);
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// System.out.println(Arrays.toString(this.S));
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System.out.println("Comparison : " + this.comparison_count);
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System.out.println("Exchange : " + this.exchange_count);
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}
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void sort2 (int low, int high) {
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if (low < high) {
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int pivotPoint = partition2(low, high);
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sort2(low, pivotPoint-1);
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sort2(pivotPoint+1, high);
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}
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}
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int partition2(int low, int high) {
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Random random = new Random();
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int num = random.nextInt(2);
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int pivot;
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if (num == 0) {
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pivot = this.S[low];
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} else {
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pivot = this.S[high];
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swap(low, high);
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}
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int j = low;
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for (int i = low+1; i <= high; i++) {
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if (this.S[i] < pivot) {
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this.comparison_count ++;
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j++;
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swap(i, j);
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}
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}
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swap(low, j);
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return j;
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}
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void swap(int a, int b) {
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this.exchange_count ++;
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int temp = this.S[a];
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this.S[a] = this.S[b];
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this.S[b] = temp;
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}
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}
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// The pivot is chosen as the median number, as suggested by Robert Sedgewick,
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// among the first, the last, and the mid elements between low and high.
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class QuickSort3 {
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int[] S;
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int comparison_count = 0;
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int exchange_count = 0;
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public QuickSort3(int[] arr, int n) {
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this.S = new int[n];
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System.arraycopy(arr, 0, this.S, 0, n);
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// System.out.println(Arrays.toString(this.S));
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sort3(0, n-1);
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// System.out.println(Arrays.toString(this.S));
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System.out.println("Comparison : " + this.comparison_count);
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System.out.println("Exchange : " + this.exchange_count);
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}
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void sort3 (int low, int high) {
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if (low < high) {
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int pivotPoint = partition3(low, high);
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sort3(low, pivotPoint-1);
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sort3(pivotPoint+1, high);
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}
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}
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int partition3(int low, int high) {
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int mid = (low + high) / 2;
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int num = getMedian(low, mid, high);
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int pivot;
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if (num == low) {
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pivot = this.S[low];
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} else if (num == mid) {
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pivot = this.S[mid];
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swap(low, mid);
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} else {
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pivot = this.S[high];
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swap(low, high);
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}
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int j = low;
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for (int i = low+1; i <= high; i++) {
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if (this.S[i] < pivot) {
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this.comparison_count ++;
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j++;
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swap(i, j);
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}
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}
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swap(low, j);
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return j;
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}
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int getMedian(int a, int b, int c) {
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if (this.S[a] >= this.S[b]) {
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if (this.S[b] >= this.S[c]) return b;
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else if (this.S[a] <= this.S[c]) return a;
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else return c;
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} else if (this.S[a] > this.S[c]) {
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return a;
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} else if (this.S[b] > this.S[c]) {
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return c;
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} else {
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return b;
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}
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}
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void swap(int a, int b) {
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this.exchange_count ++;
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int temp = this.S[a];
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this.S[a] = this.S[b];
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this.S[b] = temp;
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}
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}

‎src/Sort/QuickSort/README.md

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# Sort - QuickSort
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## QuickSort란
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QuickSort는 pivot을 설정하여 그 값을 기준으로 정렬한다.
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추가 메모리 공간을 최대한 활용하지 않은 것이 특징이다.
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재귀 함수를 활용하기에 엄밀하게 이야기하면 In-place sort 라고 할 수 없지만, 그에 가깝다고 할 수 있다.
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Worst-case Time Complexity는 O(n^2)이지만, Worst-case가 매우 극단적인 경우임을 감안한다면
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Average-case Time Complexity를 계산하는 것이 훨씬 유의미할 것이고, 이는 O(nlgn)이다.
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Merge sort와 같은 수준의 Time Complexity를 가지며 Space Complexity 측면에서도 좋은 성능을 가지니
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QuickSort는 참 좋은 알고리즘 !!
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## pivot 선택 방법
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QuickSort에서 pivot을 설정하는 방법은 다음과 같은 3가지가 있다.
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1. 첫 번째 element(`low`)가 pivot이다.
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2. `low`, `high` 값 중 무작위로 선택한 값이 pivot이다.
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3. `low`, `high`, `mid` 값 중 중간값(median value)이 pivot이다. (Robert Sedgewick에 의해 제안됨)
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3가지 방법 각각에 대하여 `QuickSort`, `QuickSort2`, `QuickSort3` class로 구현해보았다.
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그리고 Comparison, Exchange 연산 횟수와 실행 시간을 비교해 본 결과 다음과 같은 그래프를 도출할 수 있었다.
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Comparison
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![image](https://user-images.githubusercontent.com/22045163/95844387-d5932800-0d83-11eb-9f90-cbe70f2f6e31.png)
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Exchange
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![image](https://user-images.githubusercontent.com/22045163/95844415-dcba3600-0d83-11eb-8372-04c6078a8b8e.png)
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Time
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![image](https://user-images.githubusercontent.com/22045163/95844441-e348ad80-0d83-11eb-92b7-3f3391413918.png)
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3번째 pivot 선택 방법이 가장 좋은 성능을 가짐을 알 수 있다. (Median of Three)

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