Binary Watch LeetCode solution in C++

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class Solution {
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 public:
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  string convertCombination(int *c, int k) {
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    int hours = 0;
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    int minutes = 0;
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    for (int i = 0; i < k; i++) {
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      int indicatorIdx = c[i];
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      switch (indicatorIdx) {
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        case 0:
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          hours += 8;
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          break;
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        case 1:
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          hours += 4;
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          break;
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        case 2:
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          hours += 2;
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          break;
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        case 3:
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          hours += 1;
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          break;
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        case 4:
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          minutes += 32;
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          break;
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        case 5:
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          minutes += 16;
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          break;
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        case 6:
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          minutes += 8;
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          break;
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        case 7:
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          minutes += 4;
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          break;
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        case 8:
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          minutes += 2;
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          break;
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        case 9:
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          minutes += 1;
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          break;
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      }
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    }
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    if (hours > 11 || minutes > 59) return ""; // invalid time
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    return (to_string(hours) + ":" + to_string(minutes / 10) + to_string(minutes % 10));
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  }
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  vector<string> readBinaryWatch(int turnedOn) {
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    vector<string> result;
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    int k = turnedOn;
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    int c[10];
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    std::iota(begin(c), begin(c) + k, 0);
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    constexpr int N = 10;
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    int count = 0;
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    string str = convertCombination(c, k);
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    if (!str.empty()) result.push_back(str);
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    //        print(c,k,str);
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    while (true) {
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      // go to the next combination
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      int alter_idx = 0; // count from the right digit
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      while (alter_idx < k && c[k - alter_idx - 1] == (N - 1 - alter_idx)) alter_idx++;
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      if (alter_idx == k) break;
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      c[k - alter_idx - 1]++;
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      for (int i = 0; i < alter_idx; i++) c[k - alter_idx + i] = c[k - alter_idx - 1] + 1 + i;
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      str = convertCombination(c, k);
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      if (!str.empty()) result.push_back(str);
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      //            print(c,k,str);
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    }
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    return result;
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  }
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  void print(int *c, int k, string s) {
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    if (s.empty()) return;
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    for (int i = 0; i < k; i++) cout << c[i];
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    cout << " : " << s << endl;
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  }
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};