Sorting detailed explanation: merge sort

Merge sorting (MERGE-SORT) is an effective sorting algorithm based on merge operations. This algorithm is a very typical application of Divide and Conquer. Combine existing ordered subsequences to obtain a completely ordered sequence; that is, first make each subsequence in order, and then make the subsequences in order. If two ordered lists are merged into one ordered list, it is called two-way merge.

Simply put, merge sort is a relatively simple and stable algorithm.
As long as you are a friend who can call recursion, you can definitely type merge sort by hand.

The merge operation (merge), also called the merge algorithm, refers to the method of merging two sequential sequences into one sequential sequence.

Such as 　 has a number sequence {6, 202, 100, 301, 38, 8, 1}

Initial state: 6,202,100,301,38,8,1

After the first merge: {6,202},{100,301},{8,38},{1}, the number of comparisons: 3;

After the second merging: {6,100,202,301}, {1,8,38}, the number of comparisons: 4;

After the third merge: {1,6,8,38,100,202,301}, the number of comparisons: 4;

The total number of comparisons is: 3+4+4=11,;

The reverse number is 14;

The speed is second only to quick sort, and it is a stable sorting algorithm. It is generally used for the sequence of numbers in which the overall is disordered, but the sub-items are relatively orderly.

int n, a[maxn], t[maxn];
LL ans;//Returns the reverse number of records
void Merg_Sort(int x, int y)
{
    if (y - x <= 1)
        return;
    int mid = x + (y - x) / 2;
    Merg_Sort(x, mid);
    Merg_Sort(mid, y);
    int p = x;
    int q = mid;
    int i = x;
    while (p < mid || q < y)
    {
        if (q >= y || (p < mid&&a[p] <= a[q]))
        {
            t[i++] = a[p++];
        }
        else
        {
            if (p < mid)
                ans += (mid - p);
            t[i++] = a[q++];
        }
    }
    for (i = x; i < y; i++)
    {
        a[i] = t[i];
    }
}

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