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| 1 | +import java.util.ArrayList; |
| 2 | +import java.util.Arrays; |
| 3 | +import java.util.Queue; |
| 4 | +import java.util.LinkedList; |
| 5 | + |
| 6 | +/** |
| 7 | + * merge K sorted arrays into one. total: N |
| 8 | + * min heap: O(NlgK) |
| 9 | + */ |
| 10 | +public class MergeSortedArray { |
| 11 | + |
| 12 | + private static class ArrayNode { |
| 13 | + public Integer value; |
| 14 | + public int arrayIndex; |
| 15 | + |
| 16 | + public ArrayNode(Integer v, int index) { |
| 17 | + value = v; |
| 18 | + arrayIndex = index; |
| 19 | + } |
| 20 | + public String toString(){ |
| 21 | + return String.valueOf(value); |
| 22 | + } |
| 23 | + } // end of ArrayNode |
| 24 | + |
| 25 | + private static class MinHeapArrayNode { |
| 26 | + private ArrayList<ArrayNode> heap; |
| 27 | + |
| 28 | + public MinHeapArrayNode() { |
| 29 | + heap = new ArrayList<ArrayNode>(); |
| 30 | + // 1 is the min one. |
| 31 | + // it is easy to calculate left, right and parent |
| 32 | + heap.add(null); |
| 33 | + |
| 34 | + } |
| 35 | + |
| 36 | + public void insert(ArrayNode node) { |
| 37 | + heap.add(node); |
| 38 | + shiftUp(heap.size() - 1); |
| 39 | + } |
| 40 | + |
| 41 | + public ArrayNode removeMin() { |
| 42 | + if (isEmpty()) |
| 43 | + throw new RuntimeException("heap is empty"); |
| 44 | + ArrayNode min = heap.get(1); |
| 45 | + heap.remove(min); |
| 46 | + |
| 47 | + if(heap.size() != 1){ |
| 48 | + shiftDown(1); |
| 49 | + } |
| 50 | + return min; |
| 51 | + } |
| 52 | + |
| 53 | + private void shiftUp(int k) { |
| 54 | + //k/2 parent |
| 55 | + while (k > 1 && greater(k / 2, k)) { |
| 56 | + swap(k / 2, k); |
| 57 | + k = k / 2; |
| 58 | + } |
| 59 | + } |
| 60 | + |
| 61 | + private void shiftDown(int k) { |
| 62 | + while (2 * k <= heap.size() - 1) { |
| 63 | + int i = 2 * k; //left |
| 64 | + int j = i + 1; //right |
| 65 | + if (i < heap.size() - 1 && greater(j, i)) { |
| 66 | + i++; |
| 67 | + } |
| 68 | + if (greater(i, k)) break; |
| 69 | + swap(i, k); |
| 70 | + k = i; |
| 71 | + } |
| 72 | + } |
| 73 | + |
| 74 | + private boolean greater(int i, int j) { |
| 75 | + |
| 76 | + if (i > 0 && j < heap.size()) { |
| 77 | + return heap.get(i).value > heap.get(j).value; |
| 78 | + } |
| 79 | + return false; |
| 80 | + } |
| 81 | + |
| 82 | + private void swap(int i, int j) { |
| 83 | + ArrayNode tmp = heap.get(i); |
| 84 | + heap.set(i, heap.get(j)); |
| 85 | + heap.set(j, tmp); |
| 86 | + } |
| 87 | + |
| 88 | + private boolean isEmpty() { |
| 89 | + return heap.size() == 1; |
| 90 | + } |
| 91 | + |
| 92 | + |
| 93 | + } // end of MinHeapArrayNode |
| 94 | + |
| 95 | + public static void main(String[] args) { |
| 96 | + Integer[][] arrays = new Integer[][]{ |
| 97 | + {1, 5, 9}, |
| 98 | + {4, 8, 10}, |
| 99 | + {6, 11} |
| 100 | + }; |
| 101 | + |
| 102 | + ArrayList<Integer> result = mergeSortedArray(arrays); |
| 103 | + System.out.println(result.toString()); |
| 104 | + } |
| 105 | + |
| 106 | + public static ArrayList<Integer> mergeSortedArray(Integer[][] arrays) { |
| 107 | + ArrayList<Integer> result = new ArrayList<Integer>(); |
| 108 | + ArrayList<Queue<Integer>> lists = new ArrayList<Queue<Integer>>(); |
| 109 | + |
| 110 | + for (int i = 0; i < arrays.length; i++) { |
| 111 | + ArrayList<Integer> tmpArray = new ArrayList<Integer>(Arrays.asList(arrays[i])); |
| 112 | + Queue<Integer> tmpQueue = new LinkedList<Integer>(tmpArray); |
| 113 | + lists.add(tmpQueue); |
| 114 | + } |
| 115 | + |
| 116 | + MinHeapArrayNode heap = new MinHeapArrayNode(); |
| 117 | + |
| 118 | + // initialize minheap |
| 119 | + for (int i = 0; i < lists.size(); i++) { |
| 120 | + heap.insert(new ArrayNode(lists.get(i).poll(), i)); |
| 121 | + } |
| 122 | + |
| 123 | + boolean done = false; |
| 124 | + while (!done) { |
| 125 | + |
| 126 | + ArrayNode minNode = heap.removeMin(); |
| 127 | + result.add(minNode.value); |
| 128 | + int nextIndex = minNode.arrayIndex; |
| 129 | + |
| 130 | + Queue<Integer> nextQueue = lists.get(nextIndex); |
| 131 | + while (nextQueue.size() == 0) { |
| 132 | + nextIndex = (nextIndex < lists.size() - 1) ? nextIndex + 1 : 0; |
| 133 | + nextQueue = lists.get(nextIndex); |
| 134 | + if (nextIndex == minNode.arrayIndex) { |
| 135 | + done = true; |
| 136 | + break; |
| 137 | + } |
| 138 | + } |
| 139 | + |
| 140 | + if(!done) |
| 141 | + heap.insert(new ArrayNode(nextQueue.poll(), minNode.arrayIndex)); |
| 142 | + |
| 143 | + } |
| 144 | + while(!heap.isEmpty()) |
| 145 | + result.add(heap.removeMin().value); |
| 146 | + |
| 147 | + return result; |
| 148 | + } |
| 149 | +} |
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