[算法]打印N个数组的整体最大Top K

题目：

有N个长度不一的数组，所有的数组都是有序的，请从大到小打印这N个数组整体最大的前K个数。

例如：

输入含有N行元素的二维数组代表N个一维数组。

219,405,538,845,971

148,558

52,99,348,691

再输入整数K=5，则打印：

Top 5:971,845,961,558,538。

要求：

1.如果所有数组的元素个数小于K，则从小到大打印所有的数。

2.时间复杂度为O(KlogN)。

解答：

利用堆结构和堆排序完成。

import java.util.Arrays;


public class Problem_20_PrintMaxTopK {


	public static class HeapNode {

		public int value;

		public int arrNum;

		public int index;


		public HeapNode(int value, int arrNum, int index) {

			this.value = value;

			this.arrNum = arrNum;

			this.index = index;

		}

	}


	public static void printTopK(int[][] matrix, int topK) {

		int heapSize = matrix.length;

		HeapNode[] heap = new HeapNode[heapSize];

		for (int i = 0; i != heapSize; i++) {

			int index = matrix[i].length - 1;

			heap[i] = new HeapNode(matrix[i][index], i, index);

			heapInsert(heap, i);

		}

		System.out.println("TOP " + topK + " : ");

		for (int i = 0; i != topK; i++) {

			if (heapSize == 0) {

				break;

			}

			System.out.print(heap[0].value + " ");

			if (heap[0].index != 0) {

				heap[0].value = matrix[heap[0].arrNum][--heap[0].index];

			} else {

				swap(heap, 0, --heapSize);

			}

			heapify(heap, 0, heapSize);

		}

	}


	public static void heapInsert(HeapNode[] heap, int index) {

		while (index != 0) {

			int parent = (index - 1) / 2;

			if (heap[parent].value < heap[index].value) {

				swap(heap, parent, index);

				index = parent;

			} else {

				break;

			}

		}

	}


	public static void heapify(HeapNode[] heap, int index, int heapSize) {

		int left = index * 2 + 1;

		int right = index * 2 + 2;

		int largest = index;

		while (left < heapSize) {

			if (heap[left].value > heap[index].value) {

				largest = left;

			}

			if (right < heapSize && heap[right].value > heap[largest].value) {

				largest = right;

			}

			if (largest != index) {

				swap(heap, largest, index);

			} else {

				break;

			}

			index = largest;

			left = index * 2 + 1;

			right = index * 2 + 2;

		}

	}


	public static void swap(HeapNode[] heap, int index1, int index2) {

		HeapNode tmp = heap[index1];

		heap[index1] = heap[index2];

		heap[index2] = tmp;

	}


	public static int[][] generateRandomMatrix(int maxRow, int maxCol,

			int maxValue) {

		if (maxRow < 0 || maxCol < 0) {

			return null;

		}

		int[][] matrix = new int[(int) (Math.random() * maxRow) + 1][];

		for (int i = 0; i != matrix.length; i++) {

			matrix[i] = new int[(int) (Math.random() * maxCol) + 1];

			for (int j = 0; j != matrix[i].length; j++) {

				matrix[i][j] = (int) (Math.random() * maxValue);

			}

			Arrays.sort(matrix[i]);

		}

		return matrix;

	}


	public static void printMatrix(int[][] matrix) {

		for (int i = 0; i != matrix.length; i++) {

			for (int j = 0; j != matrix[i].length; j++) {

				System.out.print(matrix[i][j] + " ");

			}

			System.out.println();

		}

	}


	public static void main(String[] args) {

		int[][] matrix = generateRandomMatrix(5, 10, 1000);

		printMatrix(matrix);

		System.out.println("===========================");

		printTopK(matrix, 100);

	}


}