[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);

}

}