归并排序：

1）整体是递归，左边排好序+右边排好序+merge让整体有序

2）让其整体有序的过程里用了排外序方法

3）利用master公式来求解时间复杂度

4）当然可以用非递归实现

代码如下：

package day3;

import java.util.Arrays;

public class Code1_MergeSort {
	
	//递归归并排序
	public static void mergeSort1(int[] arr) {
		if(arr == null || arr.length <2) {
			return ;
		}
		process(arr,0,arr.length-1);
	}
	
	//arr[l..R]上变为有序
	public static void process(int[] arr,int L,int R) {
		if(L == R) {
			return;
		}
		int mid = L+((R-L)>>1);
		process(arr,L,mid);
		process(arr,mid+1,R);
		merge(arr,L,mid,R);
	} 
	public static void merge(int[] arr,int L,int M,int R) {
		int[] help = new int[R-L+1];
		int i = 0;
		int p1 = L;
		int p2 = M+1;
		//控制不越界
		while(p1<=M && p2<=R) {
			//找到小的值放在原来的数组中
			help[i++] = arr[p1] <= arr[p2] ? arr[p1++] :arr[p2++];
		}
		//要么p1越界了，要么p2越界了
		while(p1<=M) {
			help[i++] = arr[p1++];
		}
		
		while(p2 <= R) {
			help[i++] = arr[p2++];
		}
		
		for(i = 0;i< help.length;i++) {
			arr[L+i] = help[i];
		}
	}
	//非递归实现
	public static void mergeSort2(int[] arr) {
		if(arr == null || arr.length < 2) {
			return ;
		}
		int N = arr.length;
		//步长
		int mergeSize = 1;
		while(mergeSize < N) {//log N
			//当前左组的，第一个位置
			int L = 0;
			while(L < N) { //在组数为mergeSize*2下，让每一小组有序
				int M = L + mergeSize-1;
				if(M >= N) {
					break;
				}
				int R = Math.min(M+mergeSize,N-1);
				merge(arr,L,M,R);
				L = R +1;
			}
			if(mergeSize > N/2) {  //防止溢出
				break;
			}
			mergeSize <<= 1;		
		}	
	}
	// for test
		public static int[] generateRandomArray(int maxSize, int maxValue) {
			int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
			for (int i = 0; i < arr.length; i++) {
				arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
			}
			return arr;
		}

		// for test
		public static int[] copyArray(int[] arr) {
			if (arr == null) {
				return null;
			}
			int[] res = new int[arr.length];
			for (int i = 0; i < arr.length; i++) {
				res[i] = arr[i];
			}
			return res;
		}

		// for test
		public static boolean isEqual(int[] arr1, int[] arr2) {
			if ((arr1 == null && arr2 != null) || (arr1 != null && arr2 == null)) {
				return false;
			}
			if (arr1 == null && arr2 == null) {
				return true;
			}
			if (arr1.length != arr2.length) {
				return false;
			}
			for (int i = 0; i < arr1.length; i++) {
				if (arr1[i] != arr2[i]) {
					return false;
				}
			}
			return true;
		}

		// for test
		public static void printArray(int[] arr) {
			if (arr == null) {
				return;
			}
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
		}

		// for test
		public static void main(String[] args) {
			int testTime = 500000;
			int maxSize = 100;
			int maxValue = 100;
			System.out.println("测试开始");
			for (int i = 0; i < testTime; i++) {
				int[] arr1 = generateRandomArray(maxSize, maxValue);
				int[] arr2 = copyArray(arr1);
				mergeSort1(arr1);
				mergeSort2(arr2);
				if (!isEqual(arr1, arr2)) {
					System.out.println("出错了！");
					printArray(arr1);
					printArray(arr2);
					break;
				}
			}
			System.out.println("测试结束");
		}
}