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| 1 | +package com.thealgorithms.divideandconquer; |
| 2 | + |
| 3 | +/** |
| 4 | + * Deterministic QuickSelect (Median of Medians) algorithm. |
| 5 | + * |
| 6 | + * Finds the kth smallest element in an unsorted array in O(n) worst-case time. |
| 7 | + * |
| 8 | + * Reference: https://en.wikipedia.org/wiki/Median_of_medians |
| 9 | + */ |
| 10 | +public final class DeterministicQuickSelect { |
| 11 | + |
| 12 | + private DeterministicQuickSelect() { |
| 13 | + } |
| 14 | + |
| 15 | + public static int select(int[] arr, int k) { |
| 16 | + if (arr == null) { |
| 17 | + throw new IllegalArgumentException("Input array cannot be null"); |
| 18 | + } |
| 19 | + if (k < 1 || k > arr.length) { |
| 20 | + throw new IllegalArgumentException("k is out of bounds"); |
| 21 | + } |
| 22 | + return quickSelect(arr, 0, arr.length - 1, k - 1); |
| 23 | + } |
| 24 | + |
| 25 | + private static int quickSelect(int[] arr, int left, int right, int k) { |
| 26 | + if (left == right) { |
| 27 | + return arr[left]; |
| 28 | + } |
| 29 | + |
| 30 | + int pivotIndex = medianOfMedians(arr, left, right); |
| 31 | + pivotIndex = partition(arr, left, right, pivotIndex); |
| 32 | + |
| 33 | + if (k == pivotIndex) { |
| 34 | + return arr[k]; |
| 35 | + } else if (k < pivotIndex) { |
| 36 | + return quickSelect(arr, left, pivotIndex - 1, k); |
| 37 | + } else { |
| 38 | + return quickSelect(arr, pivotIndex + 1, right, k); |
| 39 | + } |
| 40 | + } |
| 41 | + |
| 42 | + private static int partition(int[] arr, int left, int right, int pivotIndex) { |
| 43 | + int pivotValue = arr[pivotIndex]; |
| 44 | + swap(arr, pivotIndex, right); |
| 45 | + int storeIndex = left; |
| 46 | + for (int i = left; i < right; i++) { |
| 47 | + if (arr[i] < pivotValue) { |
| 48 | + swap(arr, storeIndex, i); |
| 49 | + storeIndex++; |
| 50 | + } |
| 51 | + } |
| 52 | + swap(arr, right, storeIndex); |
| 53 | + return storeIndex; |
| 54 | + } |
| 55 | + |
| 56 | + private static int medianOfMedians(int[] arr, int left, int right) { |
| 57 | + int n = right - left + 1; |
| 58 | + if (n <= 5) { |
| 59 | + return partition5(arr, left, right); |
| 60 | + } |
| 61 | + |
| 62 | + int numMedians = (int) Math.ceil((double) n / 5); |
| 63 | + int[] medians = new int[numMedians]; |
| 64 | + |
| 65 | + for (int i = 0; i < numMedians; i++) { |
| 66 | + int subLeft = left + i * 5; |
| 67 | + int subRight = Math.min(subLeft + 4, right); |
| 68 | + medians[i] = arr[partition5(arr, subLeft, subRight)]; |
| 69 | + } |
| 70 | + |
| 71 | + return quickSelect(medians, 0, medians.length - 1, medians.length / 2); |
| 72 | + } |
| 73 | + |
| 74 | + private static int partition5(int[] arr, int left, int right) { |
| 75 | + java.util.Arrays.sort(arr, left, right + 1); |
| 76 | + return (left + right) / 2; |
| 77 | + } |
| 78 | + |
| 79 | + private static void swap(int[] arr, int i, int j) { |
| 80 | + int tmp = arr[i]; |
| 81 | + arr[i] = arr[j]; |
| 82 | + arr[j] = tmp; |
| 83 | + } |
| 84 | +} |
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