递归（二）

分治算法：

递归的二分查找就是分治算法的一个例子。把一个大问题分成两个相对更小的问题，并且去解决每一个小问题。对每一个小问题也是同样的解决方法：再把每个小问题分成更小的问题，并且解决它们。这个过程一直持续下去。
分治算法常常是一个方法，而这个方法含有两个对自身的调用，分别对应于问题的两个部分。

归并排序：

public class DArray {

    private int[] array;

    private int maxLength;

    public DArray(int size) {
        array = new int[size];
        maxLength = 0;
    }

    public void insert(int d) {
        array[maxLength++] = d;
    }

    public void mergeSort() {
        int[] workSpace = new int[maxLength];
        recMergeSort(workSpace, 0, maxLength - 1);
    }

    private void recMergeSort(int[] workSpace, int lower, int upper) {
        if (lower == upper) {
            return;
        }
        int mid = (lower + upper) / 2;
        recMergeSort(workSpace, lower, mid);
        recMergeSort(workSpace, mid + 1, upper);
        merge(workSpace, lower, mid + 1, upper);
    }

    private void merge(int[] workSpace, int lowerPatr, int highPatr, int upper) {
        int j = 0;
        int lower = lowerPatr;
        int mid = highPatr - 1;
        int n = upper - lower + 1;

        while (lowerPatr <= mid && highPatr <= upper) {
            if (array[lowerPatr] < array[highPatr])
                workSpace[j++] = array[lowerPatr++];
            else
                workSpace[j++] = array[highPatr++];
        }

        while (lowerPatr <= mid) {
            workSpace[j++] = array[lowerPatr++];
        }
        while (highPatr <= upper) {
            workSpace[j++] = array[highPatr++];
        }

        for (int k = 0; k < n; k++) {
            array[lower + k] = workSpace[k];
        }

    }

    public void display() {
        for (int i = 0; i < maxLength; i++) {
            System.out.println("NO." + (i + 1) + " --> " + array[i]);
        }
    }

}

    public static void main(String[] args) {
        DArray array = new DArray(12);
        array.insert(61);
        array.insert(5);
        array.insert(15);
        array.insert(45);
        array.insert(25);
        array.insert(99);
        array.insert(3);
        array.insert(37);
        array.insert(84);
        array.insert(16);
        array.insert(7);
        
        array.mergeSort();
        array.display();
    }

打印结果：
NO.1 --> 3
NO.2 --> 5
NO.3 --> 7
NO.4 --> 15
NO.5 --> 16
NO.6 --> 25
NO.7 --> 37
NO.8 --> 45
NO.9 --> 61
NO.10 --> 84
NO.11 --> 99