Splitting the Field (Explanation help required)

General Questions
#1

Here’s the Problem

At first it seems reasonable that this problem possibly have solution like this, but it does not even pass the sample case :sweat_smile:

Please share your insights related to this problem

My Implementation 
int n; cin >> n;
  vector<array<long long, 2>> va(n);
  for (int i = 0; i < n; i++) cin >> va[i][0] >> va[i][1];
  sort(all(va));

  vector<long long> prfs(n + 1, 0), suf(n + 1, 0);
  long long a = va[0][0], b = va[0][1], c = va[0][0], d = va[0][1];
  for (int i = 0; i < n; i++){
    a = min(a, va[i][0]);
    c = max(c, va[i][0]);
    b = min(b, va[i][1]);
    d = max(d, va[i][1]);
    prfs[i] =  (c - a) * (d - b);
  }
 a = va[n - 1][0], b = va[n - 1][1], c = va[n - 1][0], d = va[n - 1][1];
  for (int i = n - 1; i >= 0; --i){
    a = min(a, va[i][0]);
    c = max(c, va[i][0]);
    b = min(b, va[i][1]);
    d = max(d, va[i][1]);
    suf[i] = (c - a) * (d - b);
  }
  long long ans = 1e18;
  for (int i = 0; i < n - 1; i++){
    ans = min(prfs[i] + suf[i + 1], ans);
  }
  cout << ans;

Edit 1 : Official analysis solution of this problem is beyond my understanding yet. Could someone explain me in easy way… thank-you.

#2

If it doesn’t pass even the sample case, then it should be pretty easy to debug on your own, no?

#3

No, that’s not actually what I mean. There is no debug issue. I just wanna know the thought process, could you explain me the solution of this problem which is given in the official analysis.

#4

This problem uses sweep line, basically you sort the points by x and create an imaginary vertical line that “sweeps” through the coordinate plane.

#5

You’ll also need to use prefix sums to calculate the min/max y reached in range.