import java.io.IOException; import java.io.PrintWriter; import java.util.Arrays; import java.util.Random; /** * Generator which creates a test where Java 7 dual-pivot quicksort algorithm runs in O(n^2) time. * * Number of operations is not the best possible: * maximal recursion depth is about n^2 / 5 while best possible result is n^2 / 4. * * It's because Java 7 checks if array is nearly sorted. * If it is, a strange algorithm with something called 'runs' is used. * In our case it is not, but in process of this checking Java 7 swaps some elements. * I didn't figure out how to maintain these swaps yet. Feel free to improve it! * * @author Alexey Dergunov * @since 1.7 */ public class Main implements Runnable { private final Random rnd = new Random(239); private final int INSERTION_SORT_THRESHOLD = 47; // private final int MAX_RUN_LENGTH = 33; // private final int QUICKSORT_THRESHOLD = 286; // private final int MAX_RUN_COUNT = 67; private int MIN_VALUE; private int MAX_VALUE; private final int NO_VALUE = -1; private void hackedSort(int[] a, int[] p, int left, int right, boolean leftmost) { int length = right - left + 1; // Use insertion sort on tiny arrays if (length < INSERTION_SORT_THRESHOLD) { for (int i = right; i >= left; i--) { if (a[i] == NO_VALUE) a[i] = MIN_VALUE++; } randomShuffle(a, left, right); // why not? if (leftmost) { /* * Traditional (without sentinel) insertion sort, * optimized for server VM, is used in case of * the leftmost part. */ for (int i = left, j = i; i < right; j = ++i) { int ai = a[i + 1]; int pi = p[i + 1]; while (ai < a[j]) { a[j + 1] = a[j]; p[j + 1] = p[j]; if (j-- == left) { break; } } a[j + 1] = ai; p[j + 1] = pi; } } else { /* * Skip the longest ascending sequence. */ do { if (left >= right) { return; } } while (a[++left] >= a[left - 1]); /* * Every element from adjoining part plays the role * of sentinel, therefore this allows us to avoid the * left range check on each iteration. Moreover, we use * the more optimized algorithm, so called pair insertion * sort, which is faster (in the context of Quicksort) * than traditional implementation of insertion sort. */ for (int k = left; ++left <= right; k = ++left) { int a1 = a[k], a2 = a[left]; int p1 = p[k], p2 = p[left]; if (a1 < a2) { a2 = a1; a1 = a[left]; p2 = p1; p1 = p[left]; } while (a1 < a[--k]) { a[k + 2] = a[k]; p[k + 2] = p[k]; } ++k; a[k + 1] = a1; p[k + 1] = p1; while (a2 < a[--k]) { a[k + 1] = a[k]; p[k + 1] = p[k]; } a[k + 1] = a2; p[k + 1] = p2; } int last = a[right]; int plast = p[right]; while (last < a[--right]) { a[right + 1] = a[right]; p[right + 1] = p[right]; } a[right + 1] = last; p[right + 1] = plast; } return; } // Inexpensive approximation of length / 7 int seventh = (length >> 3) + (length >> 6) + 1; /* * Sort five evenly spaced elements around (and including) the * center element in the range. These elements will be used for * pivot selection as described below. The choice for spacing * these elements was empirically determined to work well on * a wide variety of inputs. */ int e3 = (left + right) >>> 1; // The midpoint int e2 = e3 - seventh; int e1 = e2 - seventh; int e4 = e3 + seventh; int e5 = e4 + seventh; if (a[e5] == NO_VALUE) a[e5] = MIN_VALUE++; if (a[e4] == NO_VALUE) a[e4] = MIN_VALUE++; if (a[e1] == NO_VALUE) a[e1] = MAX_VALUE--; if (a[e2] == NO_VALUE) a[e2] = MAX_VALUE--; // Sort these elements using insertion sort if (less(a[e2], a[e1])) { int t = a[e2]; a[e2] = a[e1]; a[e1] = t; int s = p[e2]; p[e2] = p[e1]; p[e1] = s; } if (less(a[e3], a[e2])) { int t = a[e3]; a[e3] = a[e2]; a[e2] = t; int s = p[e3]; p[e3] = p[e2]; p[e2] = s; if (less(t, a[e1])) { a[e2] = a[e1]; a[e1] = t; p[e2] = p[e1]; p[e1] = s; } } if (less(a[e4], a[e3])) { int t = a[e4]; a[e4] = a[e3]; a[e3] = t; int s = p[e4]; p[e4] = p[e3]; p[e3] = s; if (less(t, a[e2])) { a[e3] = a[e2]; a[e2] = t; p[e3] = p[e2]; p[e2] = s; if (less(t, a[e1])) { a[e2] = a[e1]; a[e1] = t; p[e2] = p[e1]; p[e1] = s; } } } if (less(a[e5], a[e4])) { int t = a[e5]; a[e5] = a[e4]; a[e4] = t; int s = p[e5]; p[e5] = p[e4]; p[e4] = s; if (less(t, a[e3])) { a[e4] = a[e3]; a[e3] = t; p[e4] = p[e3]; p[e3] = s; if (less(t, a[e2])) { a[e3] = a[e2]; a[e2] = t; p[e3] = p[e2]; p[e2] = s; if (less(t, a[e1])) { a[e2] = a[e1]; a[e1] = t; p[e2] = p[e1]; p[e1] = s; } } } } // Pointers int less = left; // The index of the first element of center part int great = right; // The index before the first element of right part if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) { /* * Use the second and fourth of the five sorted elements as pivots. * These values are inexpensive approximations of the first and * second terciles of the array. Note that pivot1 <= pivot2. */ int pivot1 = a[e2]; int pivot2 = a[e4]; int ppivot1 = p[e2]; int ppivot2 = p[e4]; /* * The first and the last elements to be sorted are moved to the * locations formerly occupied by the pivots. When partitioning * is complete, the pivots are swapped back into their final * positions, and excluded from subsequent sorting. */ a[e2] = a[left]; a[e4] = a[right]; p[e2] = p[left]; p[e4] = p[right]; /* * Skip elements, which are less or greater than pivot values. */ //while (a[++less] < pivot1); //while (a[--great] > pivot2); while (less(a[++less], pivot1)); while (greater(a[--great], pivot2)); /* * Partitioning: * * left part center part right part * +--------------------------------------------------------------+ * | < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 | * +--------------------------------------------------------------+ * ^ ^ ^ * | | | * less k great * * Invariants: * * all in (left, less) < pivot1 * pivot1 <= all in [less, k) <= pivot2 * all in (great, right) > pivot2 * * Pointer k is the first index of ?-part. */ outer: for (int k = less - 1; ++k <= great; ) { int ak = a[k]; int pk = p[k]; //if (ak < pivot1) { // Move a[k] to left part if (less(ak, pivot1)) { // Move a[k] to left part a[k] = a[less]; p[k] = p[less]; /* * Here and below we use "a[i] = b; i++;" instead * of "a[i++] = b;" due to performance issue. */ a[less] = ak; p[less] = pk; ++less; //} else if (ak > pivot2) { // Move a[k] to right part } else if (greater(ak, pivot2)) { // Move a[k] to right part //while (a[great] > pivot2) { while (greater(a[great], pivot2)) { if (great-- == k) { break outer; } } //if (a[great] < pivot1) { // a[great] <= pivot2 if (less(a[great], pivot1)) { // a[great] <= pivot2 a[k] = a[less]; p[k] = p[less]; a[less] = a[great]; p[less] = p[great]; ++less; } else { // pivot1 <= a[great] <= pivot2 a[k] = a[great]; p[k] = p[great]; } /* * Here and below we use "a[i] = b; i--;" instead * of "a[i--] = b;" due to performance issue. */ a[great] = ak; p[great] = pk; --great; } } // Swap pivots into their final positions a[left] = a[less - 1]; a[less - 1] = pivot1; a[right] = a[great + 1]; a[great + 1] = pivot2; p[left] = p[less - 1]; p[less - 1] = ppivot1; p[right] = p[great + 1]; p[great + 1] = ppivot2; // Sort left and right parts recursively, excluding known pivots hackedSort(a, p, left, less - 2, leftmost); hackedSort(a, p, great + 2, right, false); /* * If center part is too large (comprises > 4/7 of the array), * swap internal pivot values to ends. */ if (less < e1 && e5 < great) { /* * Skip elements, which are equal to pivot values. */ while (a[less] == pivot1) { throw new RuntimeException("We should not enter here!"); // ++less; } while (a[great] == pivot2) { throw new RuntimeException("We should not enter here!"); // --great; } /* * Partitioning: * * left part center part right part * +----------------------------------------------------------+ * | == pivot1 | pivot1 < && < pivot2 | ? | == pivot2 | * +----------------------------------------------------------+ * ^ ^ ^ * | | | * less k great * * Invariants: * * all in (*, less) == pivot1 * pivot1 < all in [less, k) < pivot2 * all in (great, *) == pivot2 * * Pointer k is the first index of ?-part. */ outer: for (int k = less - 1; ++k <= great; ) { int ak = a[k]; int pk = p[k]; if (ak == pivot1) { // Move a[k] to left part a[k] = a[less]; p[k] = p[less]; a[less] = ak; p[less] = pk; ++less; } else if (ak == pivot2) { // Move a[k] to right part while (a[great] == pivot2) { if (great-- == k) { break outer; } } if (a[great] == pivot1) { // a[great] < pivot2 a[k] = a[less]; p[k] = p[less]; /* * Even though a[great] equals to pivot1, the * assignment a[less] = pivot1 may be incorrect, * if a[great] and pivot1 are floating-point zeros * of different signs. Therefore in float and * double sorting methods we have to use more * accurate assignment a[less] = a[great]. */ a[less] = pivot1; p[less] = ppivot1; ++less; } else { // pivot1 < a[great] < pivot2 a[k] = a[great]; p[k] = p[great]; } a[great] = ak; p[great] = pk; --great; } } } // Sort center part recursively hackedSort(a, p, less, great, false); } else { // Partitioning with one pivot throw new RuntimeException("We should not enter here!"); // /* // * Use the third of the five sorted elements as pivot. // * This value is inexpensive approximation of the median. // */ // int pivot = a[e3]; // int ppivot = p[e3]; // // /* // * Partitioning degenerates to the traditional 3-way // * (or "Dutch National Flag") schema: // * // * left part center part right part // * +-------------------------------------------------+ // * | < pivot | == pivot | ? | > pivot | // * +-------------------------------------------------+ // * ^ ^ ^ // * | | | // * less k great // * // * Invariants: // * // * all in (left, less) < pivot // * all in [less, k) == pivot // * all in (great, right) > pivot // * // * Pointer k is the first index of ?-part. // */ // for (int k = less; k <= great; ++k) { // if (a[k] == pivot) { // continue; // } // int ak = a[k]; // int pk = p[k]; // if (less(ak, pivot)) { // Move a[k] to left part // a[k] = a[less]; // p[k] = p[less]; // a[less] = ak; // p[less] = pk; // ++less; // } else { // a[k] > pivot - Move a[k] to right part // while (greater(a[great], pivot)) { // --great; // } // if (less(a[great], pivot)) { // a[great] <= pivot // a[k] = a[less]; // p[k] = p[less]; // a[less] = a[great]; // p[less] = p[great]; // ++less; // } else { // a[great] == pivot // /* // * Even though a[great] equals to pivot, the // * assignment a[k] = pivot may be incorrect, // * if a[great] and pivot are floating-point // * zeros of different signs. Therefore in float // * and double sorting methods we have to use // * more accurate assignment a[k] = a[great]. // */ // a[k] = pivot; // p[k] = ppivot; // } // a[great] = ak; // p[great] = pk; // --great; // } // } // // /* // * Sort left and right parts recursively. // * All elements from center part are equal // * and, therefore, already sorted. // */ // hackedSort(a, p, left, less - 1, leftmost, depth + 1); // hackedSort(a, p, great + 1, right, false, depth + 1); } } private void randomShuffle(int[] a, int left, int right) { for (int i = left; i <= right; i++) { int j = left + rnd.nextInt(i - left + 1); swap(a, i, j); } } private void swap(int[] a, int i, int j) { int t = a[i]; a[i] = a[j]; a[j] = t; } private boolean less(int a, int b) { if (a != NO_VALUE && b != NO_VALUE) { return a < b; } if (a == NO_VALUE) { return b > MAX_VALUE; } if (b == NO_VALUE) { return a < MIN_VALUE; } throw new RuntimeException("We should not enter here!"); } private boolean greater(int a, int b) { if (a != NO_VALUE && b != NO_VALUE) { return a > b; } if (a == NO_VALUE) { return b < MIN_VALUE; } if (b == NO_VALUE) { return a > MAX_VALUE; } throw new RuntimeException("We should not enter here!"); } public void run() { int n = 60000; int[] a = new int[n]; int[] p = new int[n]; for (int i = 0; i < n; i++) { a[i] = NO_VALUE; p[i] = i; } MIN_VALUE = 1; MAX_VALUE = n; long t1, t2; t1 = System.currentTimeMillis(); hackedSort(a, p, 0, n-1, true); t2 = System.currentTimeMillis(); System.out.println("Generation time = " + (t2 - t1) + " ms."); checkValues(a, 1, n); checkValues(p, 0, n-1); applyPermutation(a, p); /* try { printArray(a, new PrintWriter("output.txt")); } catch (IOException e) { throw new RuntimeException(e); } */ t1 = System.currentTimeMillis(); Arrays.sort(a.clone()); t2 = System.currentTimeMillis(); System.out.println("Sorting time = " + (t2 - t1) + " ms."); } private void applyPermutation(int[] a, int[] pos) { int n = a.length; int[] tmp = new int[n]; for (int i = 0; i < n; i++) { tmp[pos[i]] = a[i]; } for (int i = 0; i < n; i++) { a[i] = tmp[i]; pos[i] = i; } } private void checkValues(int[] a, int min, int max) { boolean[] b = new boolean[max - min + 1]; for (int x : a) { if (b[x - min]) { throw new RuntimeException(); } b[x - min] = true; } } private void printArray(int[] a, PrintWriter pw) { int n = a.length; pw.println(n); for (int i = 0; i < n; i++) { pw.print(a[i]); if (i == n-1) pw.println(); else pw.print(' '); } pw.close(); } public static void main(String[] args) { new Thread(null, new Main(), "", 128*1024*1024).start(); } }