Split array into negative-diff (A), positive-diff (B), zero-diff (C)

We have ai + aj > bi + bj 
<=> ai - bi > -(aj - bj)
<=> ci > -cj (where ck = diff(ak, bk) = ak - bk for all k E [1, n])
=> Count number of sum ci + cj > 0

Let res = |A| * (|A| - 1) / 2 + |A| * |C|
// sum of them is always >= 0
for i = 0 -> |A| - 1
-- while (j + 1 < |B| && B[j + 1] < A[i]) ++j
// move the pointer until the next element >= current
-- res = res + j
output << res

#include <algorithm>
#include <iostream>
#include <vector>
 
using namespace std;
 
typedef long long ll;
typedef vector<int> vi;
 
int main()
{
    int n;
    cin >> n;
 
    /// Count ai - bi > bj - aj // ci > -cj
    /// 0 3 -2 5 -1
    /// -2 -1
    /// 0 3 5
 
    vi a(n);
    for (int i = 0; i < n; ++i) { int x; cin >> x; a[i]  = x; }
    for (int i = 0; i < n; ++i) { int x; cin >> x; a[i] -= x; }
    
    int zero = 0;
    vi nega, posi;
    for (int i = 0; i < n; ++i)
    {
        if (a[i] < 0)
            nega.push_back(a[i]);
        if (a[i] > 0)
            posi.push_back(a[i]);
        if (a[i] == 0)
            zero++;
    }
    nega.insert(nega.begin(), 0);
    int p = nega.size();
    int q = posi.size();
 
    sort(nega.begin(), nega.end(), greater<int>());
    sort(posi.begin(), posi.end(), less<int>());
 
    /*
    for (int i = 0; i < p; ++i) cout << nega[i] << ' '; cout << endl;
    for (int i = 0; i < q; ++i) cout << posi[i] << ' '; cout << endl;
    cout << endl;
    */
 
    if (posi.empty())
    {
        cout << 0;
        return 0;
    }
 
    if (posi.size() == n)
    {
        cout << 1LL * n * (n + 1) / 2;
        return 0;
    }
    
    ll res = q * (q - 1) / 2 + q * zero;
    for (int t = 0, i = 0, j = 0; i < q; ++i)
    {   
        while (j + 1 < p && -nega[j + 1] < posi[i]) ++j;
        res += j;
    }
    cout << res;
    return 0;
}

#include <algorithm>
#include <iostream>
#include <vector>
 
using namespace std;
 
typedef long long ll;
typedef vector<int> vi;
 
int main()
{
    int n;
    cin >> n;
 
    /// Count ai - bi > bj - aj // ci > -cj
    /// 0 3 -2 5 -1
    /// -2 -1
    /// 0 3 5
 
    vi a(n);
    for (int i = 0; i < n; ++i) { int x; cin >> x; a[i]  = x; }
    for (int i = 0; i < n; ++i) { int x; cin >> x; a[i] -= x; }
    
    int zero = 0;
    vi nega, posi;
    for (int i = 0; i < n; ++i)
    {
        if (a[i] < 0)
            nega.push_back(a[i]);
        if (a[i] > 0)
            posi.push_back(a[i]);
        if (a[i] == 0)
            zero++;
    }
    nega.insert(nega.begin(), 0);
    int p = nega.size();
    int q = posi.size();
 
    sort(nega.begin(), nega.end(), greater<int>());
    sort(posi.begin(), posi.end(), less<int>());
 
    /*
    for (int i = 0; i < p; ++i) cout << nega[i] << ' '; cout << endl;
    for (int i = 0; i < q; ++i) cout << posi[i] << ' '; cout << endl;
    cout << endl;
    */
 
    if (posi.empty())
    {
        cout << 0;
        return 0;
    }
 
    if (posi.size() == n)
    {
        cout << 1LL * n * (n - 1) / 2;
        return 0;
    }
    
    ll res = 1LL * q * (q - 1) / 2 + 1LL * q * zero;
    for (int t = 0, i = 0, j = 0; i < q; ++i)
    {   
        while (j + 1 < p && -nega[j + 1] < posi[i]) ++j;
        res += j;
    }
    cout << res;
    return 0;
}