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Problem solution · C++

ABC175 B — Making Triangle

ABC175 B — Making Triangle: a C++ solution using sorting and greedy selection. Learn the idea, check the complexity, and read the full code, with credit to michimani AtCoder Solutions.

Technique
Sorting and greedy selection
Source
michimani AtCoder Solutions
Length
47 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Sorting and greedy selection

For ABC175 B — Making Triangle, the implementation first exposes a useful order, then scans that order while making locally justified choices.

  1. Choose the key that reveals the greedy or grouping structure.
  2. Sort the relevant records by that key.
  3. Scan in order, maintaining the invariant that makes each local choice safe.

Code notes

  • 47 lines of C++ from the credited upstream file abc175_b.cpp.
  • The implementation visibly relies on sequence storage.
  • 4 loop blocks detected.

Complexity

Sorting is typically the dominant term unless the subsequent scan uses a more expensive nested operation.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from michimani AtCoder Solutions by michimani and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeABC175 B — Making Triangle · C++C++
Use this to learn the idea, then write your own version.
#include <algorithm>#include <iostream>#include <vector> using namespace std; int main() {    unsigned int n;    cin >> n;     vector<long> L(n, 0);    for (auto& l : L) {        cin >> l;    }     unsigned int ans = 0;    vector<vector<vector<bool>>> checked(        n, vector<vector<bool>>(n, vector<bool>(n, false)));    for (unsigned int i = 0; i < n; i++) {        for (unsigned int j = 0; j < n; j++) {            for (unsigned int k = 0; k < n; k++) {                if (L[i] == L[j] || L[j] == L[k] || L[k] == L[i]) {                    continue;                }                 vector<unsigned int> c = {i, j, k};                sort(c.begin(), c.end());                if (i == k || j == k || checked[c[0]][c[1]][c[2]]) {                    continue;                }                checked[c[0]][c[1]][c[2]] = true;                 if ((L[c[0]] > L[c[1]] && L[c[0]] > L[c[2]] &&                     L[c[0]] < L[c[1]] + L[c[2]]) ||                    (L[c[1]] > L[c[2]] && L[c[1]] > L[c[0]] &&                     L[c[1]] < L[c[2]] + L[c[0]]) ||                    (L[c[2]] > L[c[0]] && L[c[2]] > L[c[1]] &&                     L[c[2]] < L[c[0]] + L[c[1]])) {                    ans++;                }            }        }    }     cout << ans << endl;    return 0;}

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