分治算法-归并排序

伪代码：

MERGE(A,p,q,r)

n1 = q-p+1 
n2 = r-q
for i = 1 to n1
    L[i] = A[p+i-1]

for j = 1 to n2
    R[j] = A[q+i]

L[1+n1]=无穷大
R[1+n2]=无穷大

i=1
j=1

for k = p to r
    if L[i]<=R[j]
        A[k] = L[i]
        i++
    else 
        A[k]=R[j]
        j++

Java代码实现：

  private static void mergeSort(Integer[] r, int left, int right){
        if(right<=left)//如果数组大小不大于1，不再递归
            return;
        int mid = (left+right)/2;
        mergeSort(r, left, mid);
        mergeSort(r, mid+1, right);
        merge(r, left, mid, right);
    }

    private static void merge(Integer[] r, int left, int mid, int right){
        int i=left, j=mid+1;

        for(int k=left; k<=right; k++)
            aux[k] = r[k];

        for(int k=left; k<=right; k++)
            if(i>mid)//mid是左侧数列的最后一个位置。这里判断i是否溢出
                r[k] = aux[j++];
            else if(j>right)
                r[k] = aux[i++];
            else if(aux[i]<aux[j])//比较元素的大小
                r[k] = aux[i++];
            else
                r[k] = aux[j++];
    }