【左神算法】基础班第一课(二)——归并解决逆序数

问题：小和或者逆序数问题

求数组中，左数小于右数的和。

输入[1 2 3 4 5]

输出20

2的位置 res += 1  res=1

3的位置 res += 1 + 2 res = 4

4的位置res += 1 + 2 + 3 res = 10

5的位置res += 1 + 2 + 3 + 4  res = 20

归并代码

#include 
#include 
#include 
#include 
#include 

using namespace std;

void g(vector &v, int size)
{
    int n = rand() % size + 1;
    for (int i = 0; i < n; i++)
    {
        v.push_back(rand() % 100000007);
    }
}

int rightfunc(vector a)
{
    int res = 0;
    for (int i = 0; i < a.size(); i++)
    {
        for (int j = 0; j < i; j++)
        {
            if (a[i] > a[j])
            {
                res += a[j];
            }
        }
    }
    return res;
}

int Merge(vector &a, int l1, int r1, int l2, int r2)
{
    vector b;
    int res = 0;
    int pos1 = l1, pos2 = l2;
    
    while (pos1 <= r1 && pos2 <= r2)
    {
        if (a[pos1] < a[pos2])
        {
            res += a[pos1] * (r2 - pos2 + 1);
            b.push_back(a[pos1++]);
        }
        else if (a[pos1] > a[pos2])
        {
            b.push_back(a[pos2++]);
        }
        else
        {
            b.push_back(a[pos1]);
            ++pos1;
            ++pos2;
        }
    }
    
    while (pos1 <= r1)
    {
        b.push_back(a[pos1++]);
    }
    while (pos2 <= r2)
    {
        b.push_back(a[pos2++]);
    }
    
    for (int i = 0; i < b.size(); i++)
    {
        a[i + l1] = b[i];
    }
    
    return res;
}

int f(vector& a, int k, int n)
{
    int res = 0;
    if (n > 1)
    {
        int mid = n / 2;
        res += f(a, k, mid);
        res += f(a, k + mid, n - mid);
        
        res += Merge(a, k, k + mid - 1, k + mid, k + n - 1);
        
    }
    return res;
}

void test()
{
    int N = 50;
    while(N--)
    {
        vector a, b;
        g(a, 1000);

        int res1 = rightfunc(a);
        int res2 = f(a, 0, (int)a.size());

        if (res1 == res2)
        {
            cout << N << endl;
        }
        else
        {
            cout << "error" << endl;
        }
    }
    cout << "OK" << endl;
}

int main()
{
    //test();
    vector a;
    int N, x;
    cin >> N;
    for (int i = 0; i < N; i++)
    {
        cin >> x;
        a.push_back(x);
    }

    int res = f(a, 0, (int)a.size());

    cout << res << endl;
    return 0;
}