Strange Comparison: vector<vector<int>> vs vector<pair<int,int>> ?

Правка en3, от physics0523, 2022-12-17 17:31:08

If we want to use a 2D dynamic array, some C++ user writes following 2D vector:

vector<vector<int>> a(n);

// add y to a[x]
a[x].push_back(y);

// walkthrough a[x]
for(auto &nx : a[x]){
  cout << nx << "\n";
}

But we can do the equivalent thing with handwritten linked list (when we know the total size) by using 1D vector<pair<int,int>>:

pair<int,int> empty={-1,-1};
vector<pair<int,int>> b(n+total_size,empty);
int add_point=n;

// add y to b[x]
if(b[x]!=empty){
  b[add_point]=b[x];
  b[x].second=add_point;
  add_point++;
}
b[x].first=y;

// walkthrough b[x]
int current=x;
while(current!=empty.second && b[currnt]!=empty){
  cout << b[current].first << "\n";
  current=b[current].second;
}

So, what's the benefit for the later implementation? The merit is the generation time of later one is very fast.

vector size = $$$10^5$$$, Total elements = $$$10^6$$$ (this means we need vector<vector<int>>(1e5) and the sum of the size of $$$10^5$$$ vectors is $$$10^6$$$)

generate walkthrough
vector<vector<int>> 49.04 ms 3.12 ms
vector<pair<int,int>> 12.78 ms 19.52 ms

vector size = $$$10^6$$$, Total elements = $$$10^6$$$

generate walkthrough
vector<vector<int>> 138.56 ms 10.92 ms
vector<pair<int,int>> 17.4 ms 7.8 ms

vector size = $$$10^6$$$, Total elements = $$$10^7$$$

generate walkthrough
vector<vector<int>> 1406.84 ms 32.86 ms
vector<pair<int,int>> 120.48 ms 437.28 ms

( on CF judge(C++20 64bit), x10 average, experiment code )

So, when the vector size is large and need small number of walkthrough, the vector<pair<int,int>> implementation have an advantage.
I use this implementation for 303C - Minimum Modular (because the package is old, current TL is 1s). 185222734

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en3 Английский physics0523 2022-12-17 17:31:08 1472 Tiny change: 'average)\n| |' -> 'average)\n\n| |' (published)
en2 Английский physics0523 2022-12-17 17:04:41 81
en1 Английский physics0523 2022-12-17 15:19:02 757 Initial revision (saved to drafts)