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| 1 | +package com.baeldung.algorithms.kthsmallest; |
| 2 | + |
| 3 | +import java.util.Arrays; |
| 4 | +import java.util.NoSuchElementException; |
| 5 | + |
| 6 | +import static java.lang.Math.max; |
| 7 | +import static java.lang.Math.min; |
| 8 | + |
| 9 | +public class KthSmallest { |
| 10 | + |
| 11 | + public static int findKthSmallestElement(int k, int[] list1, int[] list2) throws NoSuchElementException, IllegalArgumentException { |
| 12 | + |
| 13 | + checkInput(k, list1, list2); |
| 14 | + |
| 15 | + // we are looking for the minimum value |
| 16 | + if(k == 1) { |
| 17 | + return min(list1[0], list2[0]); |
| 18 | + } |
| 19 | + |
| 20 | + // we are looking for the maximum value |
| 21 | + if(list1.length + list2.length == k) { |
| 22 | + return max(list1[list1.length-1], list2[list2.length-1]); |
| 23 | + } |
| 24 | + |
| 25 | + // swap lists if needed to make sure we take at least one element from list1 |
| 26 | + if(k <= list2.length && list2[k-1] < list1[0]) { |
| 27 | + int[] list1_ = list1; |
| 28 | + list1 = list2; |
| 29 | + list2 = list1_; |
| 30 | + } |
| 31 | + |
| 32 | + // correct left boundary if k is bigger than the size of list2 |
| 33 | + int left = k < list2.length ? 0 : k - list2.length - 1; |
| 34 | + |
| 35 | + // the inital right boundary cannot exceed the list1 |
| 36 | + int right = min(k-1, list1.length - 1); |
| 37 | + |
| 38 | + int nElementsList1, nElementsList2; |
| 39 | + |
| 40 | + // binary search |
| 41 | + do { |
| 42 | + nElementsList1 = ((left + right) / 2) + 1; |
| 43 | + nElementsList2 = k - nElementsList1; |
| 44 | + |
| 45 | + if(nElementsList2 > 0) { |
| 46 | + if (list1[nElementsList1 - 1] > list2[nElementsList2 - 1]) { |
| 47 | + right = nElementsList1 - 2; |
| 48 | + } else { |
| 49 | + left = nElementsList1; |
| 50 | + } |
| 51 | + } |
| 52 | + } while(!kthSmallesElementFound(list1, list2, nElementsList1, nElementsList2)); |
| 53 | + |
| 54 | + return nElementsList2 == 0 ? list1[nElementsList1-1] : max(list1[nElementsList1-1], list2[nElementsList2-1]); |
| 55 | + } |
| 56 | + |
| 57 | + private static boolean kthSmallesElementFound(int[] list1, int[] list2, int nElementsList1, int nElementsList2) { |
| 58 | + |
| 59 | + // we do not take any element from the second list |
| 60 | + if(nElementsList2 < 1) { |
| 61 | + return true; |
| 62 | + } |
| 63 | + |
| 64 | + if(list1[nElementsList1-1] == list2[nElementsList2-1]) { |
| 65 | + return true; |
| 66 | + } |
| 67 | + |
| 68 | + if(nElementsList1 == list1.length) { |
| 69 | + return list1[nElementsList1-1] <= list2[nElementsList2]; |
| 70 | + } |
| 71 | + |
| 72 | + if(nElementsList2 == list2.length) { |
| 73 | + return list2[nElementsList2-1] <= list1[nElementsList1]; |
| 74 | + } |
| 75 | + |
| 76 | + return list1[nElementsList1-1] <= list2[nElementsList2] && list2[nElementsList2-1] <= list1[nElementsList1]; |
| 77 | + } |
| 78 | + |
| 79 | + |
| 80 | + private static void checkInput(int k, int[] list1, int[] list2) throws NoSuchElementException, IllegalArgumentException { |
| 81 | + |
| 82 | + if(list1 == null || list2 == null || k < 1) { |
| 83 | + throw new IllegalArgumentException(); |
| 84 | + } |
| 85 | + |
| 86 | + if(list1.length == 0 || list2.length == 0) { |
| 87 | + throw new IllegalArgumentException(); |
| 88 | + } |
| 89 | + |
| 90 | + if(k > list1.length + list2.length) { |
| 91 | + throw new NoSuchElementException(); |
| 92 | + } |
| 93 | + } |
| 94 | + |
| 95 | + public static int getKthElementSorted(int[] list1, int[] list2, int k) { |
| 96 | + |
| 97 | + int length1 = list1.length, length2 = list2.length; |
| 98 | + int[] combinedArray = new int[length1 + length2]; |
| 99 | + System.arraycopy(list1, 0, combinedArray, 0, list1.length); |
| 100 | + System.arraycopy(list2, 0, combinedArray, list1.length, list2.length); |
| 101 | + Arrays.sort(combinedArray); |
| 102 | + |
| 103 | + return combinedArray[k-1]; |
| 104 | + } |
| 105 | + |
| 106 | + public static int getKthElementMerge(int[] list1, int[] list2, int k) { |
| 107 | + |
| 108 | + int i1 = 0, i2 = 0; |
| 109 | + |
| 110 | + while(i1 < list1.length && i2 < list2.length && (i1 + i2) < k) { |
| 111 | + if(list1[i1] < list2[i2]) { |
| 112 | + i1++; |
| 113 | + } else { |
| 114 | + i2++; |
| 115 | + } |
| 116 | + } |
| 117 | + |
| 118 | + if((i1 + i2) < k) { |
| 119 | + return i1 < list1.length ? list1[k - i2 - 1] : list2[k - i1 - 1]; |
| 120 | + } else if(i1 > 0 && i2 > 0) { |
| 121 | + return Math.max(list1[i1-1], list2[i2-1]); |
| 122 | + } else { |
| 123 | + return i1 == 0 ? list2[i2-1] : list1[i1-1]; |
| 124 | + } |
| 125 | + } |
| 126 | +} |
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