Merge sort algorithm analysis

Merge sort algorithm analysis

1. Algorithmic thinking

Using the idea of ​​divide and conquer, the original array is divided into two parts each time, and then the sub-arrays are sorted, and finally the sorted arrays are merged to form a new ordered sequence.

1.1 Execution process

2. Implementation steps

2.1 mergeSort() method

public static void mergeSort(int[]arr){
    
    
        if (arr == null || arr.length < 2){
    
    
            return;
        }
        mergeSort(arr,0,arr.length-1);
    }

2.2 Split into several subarrays

 public static void mergeSort(int[] arr, int l, int r) {
    
    
		//如果l和r相等，说明中间只有一个数，数组已经排好序了。
		if (l == r) {
    
    
			return;
		}
		int mid = l + ((r - l) >> 1);//求中点
		//l到mid之间变为有序的
		mergeSort(arr, l, mid);
		//mid+1到r之间变成有序的
		mergeSort(arr, mid + 1, r);
		
		merge(arr, l, mid, r);
	}

2.3 Merge subarrays

public static void merge(int[] arr ,int l ,int m ,int r){
    
    
        //辅助数组长度的大小
		int[] help = new int[r - l + 1];
		int i = 0;//辅助数组指针
		int p1 = l;//左边数组指针
		int p2 = m + 1;//右边数组指针
		while (p1 <= m && p2 <= r) {
    
    
			help[i++] = arr[p1] < arr[p2] ? arr[p1++] : arr[p2++];
		}
//		有一边结束了就输入另一边
		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];
		}
	}

3. Time complexity analysis

Use Master's formula to analyze the time complexity of recursive behavior

The comparison formula is: T(N) = 2 T(N/2) + O(N); *

So the time complexity is O(N * log N);