归并排序

阿秀自己刷过的算法部分经过整理后是按照不同基础、不同人群分类的，如果你不知道自己该看哪个部分的算法题，可以先看一下这里，戳我直达。

归并排序

将一个大的无序数组有序，我们可以把大的数组分成两个，然后对这两个数组分别进行排序，之后在把这两个数组合并成一个有序的数组。由于两个小的数组都是有序的，所以在合并的时候是很快的。

通过递归的方式将大的数组一直分割，直到数组的大小为 1，此时只有一个元素，那么该数组就是有序的了，之后再把两个数组大小为1的合并成一个大小为2的，再把两个大小为2的合并成4的 … 直到全部小的数组合并起来。

归并排序是建立在归并操作上的一种有效的排序算法。该算法是采用分治法（Divide and Conquer）的一个非常典型的应用。将已有序的子序列合并，得到完全有序的序列；即先使每个子序列有序，再使子序列段间有序。若将两个有序表合并成一个有序表，称为2-路归并。

第二个演示动图

算法思想

1、把长度为n的输入序列分成两个长度为n/2的子序列；

2、对这两个子序列分别采用归并排序；

3、 将两个排序好的子序列合并成一个最终的排序序列。

1、 归并排序（C++-迭代版）

template<typename T>
void merge_sort(T arr[], int len) {
	T* a = arr;
	T* b = new T[len];
	for (int seg = 1; seg < len; seg += seg) {
		for (int start = 0; start < len; start += seg + seg) {
			int low = start, mid = min(start + seg, len), high = min(start + seg + seg, len);
			cout << low << " " << mid << " " << high << endl;
			int k = low;
			int start1 = low, end1 = mid;
			int start2 = mid, end2 = high;
			while (start1 < end1 && start2 < end2)
				b[k++] = a[start1] < a[start2] ? a[start1++] : a[start2++];
			while (start1 < end1)
				b[k++] = a[start1++];
			while (start2 < end2)
				b[k++] = a[start2++];
		}

		swap(a, b); //交换a b 地址
        //T* temp = a;
        //  a = b;
        //  b = temp;

	}

	//if (a != arr) {
	//	for (int i = 0; i < len; i++)
	//		b[i] = a[i];
	//	b = a;
	//}
       
    /*
    十分严谨的一种安排
    每次排序都要交换 a、b 值（数组首地址）
1、if(a != arr)：如果排序结束后，a 值为原来数组 b 首地址，此时 arr 与 b 相同，arr 数组内容不是最终的结果，
2、循环内容：把 a数组内容复制到数组 b（数组arr）
3、b = a ：循环结束后，让 b 指向它原来的数组首地址，以便 delete[]
    
    */
	delete[] b;
}

2、归并排序（C++-递归版）

template<typename T>
void merge_sort_recursive(T arr[], T reg[], int start, int end) {
    if (start >= end)
        return;
    int len = end - start, mid = (len >> 1) + start;
    int start1 = start, end1 = mid;
    int start2 = mid + 1, end2 = end;
    merge_sort_recursive(arr, reg, start1, end1);
    merge_sort_recursive(arr, reg, start2, end2);
    int k = start;
    while (start1 <= end1 && start2 <= end2)
        reg[k++] = arr[start1] < arr[start2] ? arr[start1++] : arr[start2++];
    while (start1 <= end1)
        reg[k++] = arr[start1++];
    while (start2 <= end2)
        reg[k++] = arr[start2++];
    for (k = start; k <= end; k++)
        arr[k] = reg[k];
}

// merge_sort
template<typename T>
void merge_sort(T arr[], const int len) {
    T reg[len];
    merge_sort_recursive(arr, reg, 0, len - 1);
}

3、vector 类型的递归 ，就记这一种

void mergeSortCore(vector<int>& data, vector<int>& dataTemp, int low, int high) {

	if (low >= high) return;
	int len = high - low, mid = low + len / 2;
	int start1 = low, end1 = mid, start2 = mid + 1, end2 = high;
	mergeSortCore(data, dataTemp, start1, end1);
	mergeSortCore(data, dataTemp, start2, end2);
	int index = low;
	while (start1 <= end1 && start2 <= end2) {
		dataTemp[index++] = data[start1] < data[start2] ? data[start1++] : data[start2++];
	}

	while (start1 <= end1) {
		dataTemp[index++] = data[start1++];
	}


	while (start2 <= end2) {
		dataTemp[index++] = data[start2++];
	}

	for (index = low; index <= high; ++index) {
		data[index] = dataTemp[index];
	}
}


void mergeSort(vector<int>& data) {
	int len = data.size();
	vector<int> dataTemp(len, 0);
	mergeSortCore(data, dataTemp, 0, len - 1);
}

节约时间的一种递归归并排序，很好，也记这一种：

void mergeSortCore(vector<int>& nums, vector<int>& copy, int begin, int end) {
	if (begin >= end) return;
	int mid = begin + (end - begin) / 2;
	int low1 = begin, high1 = mid, low2 = mid + 1, high2 = end;
	mergeSortCore(copy, nums, low1, high1);//这里减少了copy向nums的赋值部分，千万注意不要把copy 和 nums赋值反了
	mergeSortCore(copy, nums, low2, high2);

	int copyIndex = low1;
	while (low1 <= high1 && low2 <= high2) {
		copy[copyIndex++] = nums[low1] < nums[low2] ? nums[low1++] : nums[low2++];
	}
	while (low1 <= high1) {
		copy[copyIndex++] = nums[low1++];
	}
	while (low2 <= high2) {
		copy[copyIndex++] = nums[low2++];
	}

	cout << begin << " " << end << endl;
	for (auto a : copy) {
		cout << a << " ";
	}
	cout << endl;

}

void mergeSort(vector<int> nums) {

	for (auto a : nums) {
		cout << a << " ";
	}
	cout << endl;
	
	
	vector<int> copyNums(nums);//这里要借助一个一模一样的数组的
	mergeSortCore(nums, copyNums, 0, nums.size() - 1);
	nums.assign(copyNums.begin(), copyNums.end());//到最后copy数组是排序好的，记得要赋值一下
		
	for (auto a : nums) {
		cout << a << " ";
	}
}

复写

void print(vector<int>& nums) {
	for (auto a : nums)
		cout << a << " ";
	cout << endl;

}

void mergeSort(vector<int>& data, vector<int>&temp,int begin,int end) {
	if (begin >= end) return;
	int low1 = begin, high2 = end, mid = begin + (end - begin) / 2;
	int high1 = mid, low2 = mid + 1;
	print(data);
	mergeSort(temp, data, low1, high1);
	mergeSort(temp, data, low2, high2);
	int index = low1;
	while (low1 <= high1 && low2 <= high2) {
		temp[index++] = data[low1] < data[low2] ? data[low1++] : data[low2++];
	}
	while (low1 <= high1) {
		temp[index++] = data[low1++];
	}

	while (low2 <= high2) {
		temp[index++] = data[low2++];
	}

}

void main(){
    
    
    vector<int> nums = { 5,3,5,6,1,4,9,10,6,2};
	vector<int> temp(nums);
	mergeSort(nums,temp , 0, nums.size() - 1);
    nums.assign(temp.begin(),temp.end());
}

4、vector 类型的迭代

void mergeSort(vector<int>& data) {
	int len = data.size();
	vector<int> dataTemp(len, 0);
	for (int seg = 1; seg < len; seg += seg) {
		for (int start = 0; start < len; start += seg + seg) {

			int low = start, mid = min(start + seg, len), high = min(start + seg + seg, len);
			int index = low, start1 = low, end1 = mid, start2 = mid, end2 = high;
			
			while (start1 < end1 && start2 < end2) {
				dataTemp[index++] = data[start1] < data[start2] ? data[start1++] : data[start2++];
			}

			while (start1 < end1) {
				dataTemp[index++] = data[start1++];
			}


			while (start2 < end2) {
				dataTemp[index++] = data[start2++];
			}

		}
		swap(data, dataTemp);
	}

	for (auto a : data)
		cout << a << " ";	
}