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  1. #include <iostream>
  2. #include <sstream>
  3. #include <vector>
  4. #include <cstdio>
  5. #include <chrono>
  6. #include <cmath>
  7. #include <set>
  8. #include <map>
  9.  
  10. using namespace std;
  11.  
  12. const int INF = 0x3f3f3f3f;
  13.  
  14. struct Timer {
  15. using clock = chrono::high_resolution_clock;
  16. clock::time_point p = clock::now();
  17. template<typename T> string fmt(const char* unit) const {
  18. auto d = chrono::duration_cast<T>(clock::now() - p).count();
  19. return to_string(d) + unit;
  20. }
  21. string NS() const { return fmt<chrono::nanoseconds>("ns"); }
  22. string US() const { return fmt<chrono::microseconds>("us"); }
  23. string MS() const { return fmt<chrono::milliseconds>("ms"); }
  24. };
  25.  
  26. static Timer timer;
  27.  
  28. // Get all ranges [l, r] that provide floor(n/v) = d for all v in [l, r]
  29. // In this case, we actually want to returns d instead
  30. set<int> harmonySeq(int n)
  31. {
  32. set<int> res;
  33. int sqrtn = sqrt(n);
  34. for (int l = 1, r = 1, v = 1; l <= sqrtn; l = r + 1) {
  35. v = n / l;
  36. r = n / v;
  37. res.insert(l + 1);
  38. res.insert(v + 1);
  39. }
  40. res.insert(1);
  41.  
  42. return res;
  43. }
  44.  
  45. int main()
  46. {
  47. if (fopen("SOCIALIZE.inp", "r") != nullptr) {
  48. freopen("SOCIALIZE.inp", "r", stdin);
  49. freopen("SOCIALIZE.out", "w", stdout);
  50. freopen("SOCIALIZE.err", "w", stderr);
  51. }
  52.  
  53. int n;
  54. cin >> n;
  55.  
  56. vector<int> a(n);
  57. for (int& height : a) {
  58. cin >> height;
  59. }
  60.  
  61. if (n == 0)
  62. {
  63. n = 1000;
  64. a.resize(n);
  65. for (int i = 0; i < n; ++i) {
  66. a[i] = i;
  67. }
  68. cerr << timer.MS() << endl;
  69. }
  70.  
  71.  
  72. // changesByDay[day][value] = change in count of [value] on day [day]
  73. map<int /*day*/, map<int /*value*/, int /*changes*/> > changesByDay;
  74.  
  75. set<int> relevantDays;
  76. for (int i = 0; i < n; ++i) {
  77. set<int> changeDays = harmonySeq(a[i]);
  78. relevantDays.insert(changeDays.begin(), changeDays.end());
  79.  
  80. // Insert Event: update new value of a[i] in that day D
  81. for (int day : changeDays) {
  82. int value = a[i] / day;
  83. changesByDay[day][value]++;
  84. }
  85.  
  86. // Remove Event: when will that value of a[i] stop existing
  87. int prevDay = -1;
  88. for (int day : changeDays) {
  89. if (prevDay != -1) {
  90. int prevValue = a[i] / prevDay;
  91. changesByDay[day][prevValue]--;
  92. }
  93. prevDay = day;
  94. }
  95. }
  96. cerr << timer.MS() << endl;
  97.  
  98. // heightFreq is the array of [ Floor(A1 / D), Floor(A2 / D), ..., Floor(AN / D) ]
  99. // On day 1, the array is = [ A1, A2, ..., AN ]
  100. // HeightFreq[value] is the number of times that value appears in H
  101. // By using map, we can group equal value bundle together into iterator(heightFreq).first
  102. // and their size as iterator(heightFreq).second
  103. map<int, int> heightFreq;
  104. for (int height : a) {
  105. heightFreq[height]++;
  106. }
  107.  
  108. // freqCounter count and track the number of iterator(HeightFreq).second
  109. // That value is also group size, and also heightFreq[value]
  110. // freqCounter[size] is the number of times that size appears in heightFreq
  111. // freqCounter[size] = number of value groups of that size
  112. vector<int> freqCounter(n + 1, 0);
  113. for (const auto &group : heightFreq) {
  114. const auto &value = group.first;
  115. const auto &size = group.second;
  116. freqCounter[size]++;
  117. }
  118.  
  119. // res[len] is the min day D where there exists such D that made (iterator(H).second = len)
  120. vector<int> res(n + 1, +INF);
  121. const int firstDay = 1;
  122. for (int size = 1; size <= n; ++size) {
  123. if (freqCounter[size] > 0) {
  124. res[size] = min(res[size], firstDay);
  125. }
  126. }
  127. cerr << "Day #1 -> " << timer.MS() << endl;
  128.  
  129. relevantDays.erase(firstDay); // Already processed day 1
  130. for (int today : relevantDays) {
  131. const auto& todayEvents = changesByDay[today];
  132.  
  133. for (const auto &events : todayEvents) {
  134. const auto &value = events.first;
  135. const auto &delta = events.second;
  136.  
  137. int prevSize = heightFreq[value];
  138. --freqCounter[prevSize];
  139.  
  140. int updatedSize = (heightFreq[value] += delta);
  141. if (updatedSize == 0) {
  142. heightFreq.erase(value);
  143. } else {
  144. freqCounter[updatedSize]++;
  145. }
  146. }
  147.  
  148. for (int size = 1; size <= n; ++size) {
  149. if (freqCounter[size] > 0) {
  150. res[size] = min(res[size], today);
  151. }
  152. }
  153. cerr << "Day #" << today << " -> " << timer.MS() << endl;
  154. }
  155.  
  156. for (int size = 1; size <= n; ++size) {
  157. if (res[size] == INF) {
  158. cout << "-1\n";
  159. } else {
  160. cout << res[size] << "\n";
  161. }
  162. }
  163.  
  164. return 0;
  165. }
Success #stdin #stdout #stderr 0.04s 5288KB
stdin
17
70254 52064 62274 71245 96148 62165 6312 99965 46711 51990 77139 50801 74997 35607 32196 45343 80921 
stdout
1
82
1270
5785
7438
15428
20231
25000
31138
37499
38570
40461
74998
77140
80922
96149
99966
stderr
6ms
Day #1 -> 6ms
Day #2 -> 6ms
Day #3 -> 6ms
Day #4 -> 6ms
Day #5 -> 7ms
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Day #512 -> 28ms
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Day #750 -> 36ms
Day #751 -> 36ms
Day #752 -> 36ms
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Day #789 -> 37ms
Day #790 -> 37ms
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Day #806 -> 37ms
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Day #822 -> 37ms
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Day #830 -> 38ms
Day #831 -> 38ms
Day #833 -> 38ms
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Day #844 -> 38ms
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Day #848 -> 38ms
Day #849 -> 38ms
Day #850 -> 38ms
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Day #866 -> 39ms
Day #867 -> 39ms
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Day #870 -> 39ms
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Day #882 -> 39ms
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Day #889 -> 39ms
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Day #892 -> 39ms
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Day #942 -> 40ms
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Day #944 -> 41ms
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Day #971 -> 41ms
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Day #974 -> 41ms
Day #975 -> 41ms
Day #976 -> 41ms
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Day #981 -> 41ms
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Day #987 -> 41ms
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Day #1015 -> 42ms
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Day #1020 -> 42ms
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Day #1097 -> 43ms
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Day #1270 -> 46ms
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Day #1485 -> 49ms
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Day #5200 -> 70ms
Day #5207 -> 70ms
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Day #5342 -> 70ms
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Day #5656 -> 70ms
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Day #5668 -> 70ms
Day #5770 -> 70ms
Day #5777 -> 70ms
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Day #6228 -> 71ms
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Day #6387 -> 71ms
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Day #6429 -> 71ms
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Day #6477 -> 72ms
Day #6478 -> 72ms
Day #6499 -> 72ms
Day #6509 -> 72ms
Day #6665 -> 72ms
Day #6674 -> 72ms
Day #6744 -> 72ms
Day #6818 -> 72ms
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Day #7013 -> 72ms
Day #7026 -> 72ms
Day #7122 -> 72ms
Day #7125 -> 72ms
Day #7141 -> 72ms
Day #7258 -> 72ms
Day #7357 -> 72ms
Day #7397 -> 72ms
Day #7428 -> 72ms
Day #7438 -> 73ms
Day #7500 -> 73ms
Day #7558 -> 73ms
Day #7690 -> 73ms
Day #7714 -> 73ms
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Day #7785 -> 73ms
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Day #96149 -> 79ms
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