#include <iostream> #include <sstream> #include <vector> #include <cstdio> #include <chrono> #include <cmath> #include <set> #include <map> using namespace std; const int INF = 0x3f3f3f3f; struct Timer { using clock = chrono::high_resolution_clock; clock::time_point p = clock::now(); template<typename T> string fmt(const char* unit) const { auto d = chrono::duration_cast<T>(clock::now() - p).count(); return to_string(d) + unit; } string NS() const { return fmt<chrono::nanoseconds>("ns"); } string US() const { return fmt<chrono::microseconds>("us"); } string MS() const { return fmt<chrono::milliseconds>("ms"); } }; static Timer timer; // Get all ranges [l, r] that provide floor(n/v) = d for all v in [l, r] // In this case, we actually want to returns d instead set<int> harmonySeq(int n) { set<int> res; int sqrtn = sqrt(n); for (int l = 1, r = 1, v = 1; l <= sqrtn; l = r + 1) { v = n / l; r = n / v; res.insert(l + 1); res.insert(v + 1); } res.insert(1); return res; } int main() { if (fopen("SOCIALIZE.inp", "r") != nullptr) { freopen("SOCIALIZE.inp", "r", stdin); freopen("SOCIALIZE.out", "w", stdout); freopen("SOCIALIZE.err", "w", stderr); } int n; cin >> n; vector<int> a(n); for (int& height : a) { cin >> height; } if (n == 0) { n = 1000; a.resize(n); for (int i = 0; i < n; ++i) { a[i] = i; } cerr << timer.MS() << endl; } // changesByDay[day][value] = change in count of [value] on day [day] map<int /*day*/, map<int /*value*/, int /*changes*/> > changesByDay; set<int> relevantDays; for (int i = 0; i < n; ++i) { set<int> changeDays = harmonySeq(a[i]); relevantDays.insert(changeDays.begin(), changeDays.end()); // Insert Event: update new value of a[i] in that day D for (int day : changeDays) { int value = a[i] / day; changesByDay[day][value]++; } // Remove Event: when will that value of a[i] stop existing int prevDay = -1; for (int day : changeDays) { if (prevDay != -1) { int prevValue = a[i] / prevDay; changesByDay[day][prevValue]--; } prevDay = day; } } cerr << timer.MS() << endl; // heightFreq is the array of [ Floor(A1 / D), Floor(A2 / D), ..., Floor(AN / D) ] // On day 1, the array is = [ A1, A2, ..., AN ] // HeightFreq[value] is the number of times that value appears in H // By using map, we can group equal value bundle together into iterator(heightFreq).first // and their size as iterator(heightFreq).second map<int, int> heightFreq; for (int height : a) { heightFreq[height]++; } // freqCounter count and track the number of iterator(HeightFreq).second // That value is also group size, and also heightFreq[value] // freqCounter[size] is the number of times that size appears in heightFreq // freqCounter[size] = number of value groups of that size vector<int> freqCounter(n + 1, 0); for (const auto &group : heightFreq) { const auto &value = group.first; const auto &size = group.second; freqCounter[size]++; } // res[len] is the min day D where there exists such D that made (iterator(H).second = len) vector<int> res(n + 1, +INF); const int firstDay = 1; for (int size = 1; size <= n; ++size) { if (freqCounter[size] > 0) { res[size] = min(res[size], firstDay); } } cerr << "Day #1 -> " << timer.MS() << endl; relevantDays.erase(firstDay); // Already processed day 1 for (int today : relevantDays) { const auto& todayEvents = changesByDay[today]; for (const auto &events : todayEvents) { const auto &value = events.first; const auto &delta = events.second; int prevSize = heightFreq[value]; --freqCounter[prevSize]; int updatedSize = (heightFreq[value] += delta); if (updatedSize == 0) { heightFreq.erase(value); } else { freqCounter[updatedSize]++; } } for (int size = 1; size <= n; ++size) { if (freqCounter[size] > 0) { res[size] = min(res[size], today); } } cerr << "Day #" << today << " -> " << timer.MS() << endl; } for (int size = 1; size <= n; ++size) { if (res[size] == INF) { cout << "-1\n"; } else { cout << res[size] << "\n"; } } return 0; }
17 70254 52064 62274 71245 96148 62165 6312 99965 46711 51990 77139 50801 74997 35607 32196 45343 80921
1 82 1270 5785 7438 15428 20231 25000 31138 37499 38570 40461 74998 77140 80922 96149 99966
6ms Day #1 -> 6ms Day #2 -> 6ms Day #3 -> 6ms Day #4 -> 6ms Day #5 -> 7ms Day #6 -> 7ms Day #7 -> 7ms Day #8 -> 7ms Day #9 -> 7ms Day #10 -> 7ms Day #11 -> 7ms Day #12 -> 7ms Day #13 -> 7ms Day #14 -> 7ms Day #15 -> 7ms Day #16 -> 7ms Day #17 -> 7ms Day #18 -> 7ms Day #19 -> 7ms Day #20 -> 7ms Day #21 -> 7ms Day #22 -> 7ms Day #23 -> 7ms Day #24 -> 7ms Day #25 -> 8ms Day #26 -> 8ms Day #27 -> 8ms Day #28 -> 8ms Day #29 -> 8ms Day #30 -> 8ms Day #31 -> 8ms Day #32 -> 8ms Day #33 -> 8ms Day #34 -> 8ms Day #35 -> 8ms Day #36 -> 8ms Day #37 -> 8ms Day #38 -> 8ms Day #39 -> 8ms Day #40 -> 8ms Day #41 -> 8ms Day #42 -> 8ms Day #43 -> 8ms Day #44 -> 8ms Day #45 -> 9ms Day #46 -> 9ms Day #47 -> 9ms Day #48 -> 9ms Day #49 -> 9ms Day #50 -> 9ms Day #51 -> 9ms Day #52 -> 9ms Day #53 -> 9ms Day #54 -> 9ms Day #55 -> 9ms Day #56 -> 9ms Day #57 -> 9ms Day #58 -> 9ms Day #59 -> 9ms Day #60 -> 9ms Day #61 -> 9ms Day #62 -> 9ms Day #63 -> 9ms Day #64 -> 10ms Day #65 -> 10ms Day #66 -> 10ms Day #67 -> 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46ms Day #1270 -> 46ms Day #1271 -> 46ms Day #1272 -> 46ms Day #1273 -> 46ms Day #1278 -> 46ms Day #1282 -> 46ms Day #1285 -> 46ms Day #1286 -> 46ms Day #1288 -> 46ms Day #1294 -> 46ms Day #1296 -> 46ms Day #1298 -> 46ms Day #1299 -> 46ms Day #1300 -> 46ms Day #1302 -> 46ms Day #1303 -> 47ms Day #1306 -> 47ms Day #1308 -> 47ms Day #1316 -> 47ms Day #1318 -> 47ms Day #1319 -> 47ms Day #1320 -> 47ms Day #1323 -> 47ms Day #1325 -> 47ms Day #1326 -> 47ms Day #1327 -> 47ms Day #1330 -> 47ms Day #1333 -> 47ms Day #1334 -> 47ms Day #1335 -> 47ms Day #1336 -> 47ms Day #1337 -> 47ms Day #1340 -> 47ms Day #1342 -> 47ms Day #1345 -> 47ms Day #1349 -> 47ms Day #1351 -> 47ms Day #1352 -> 47ms Day #1354 -> 47ms Day #1355 -> 47ms Day #1364 -> 47ms Day #1369 -> 47ms Day #1370 -> 47ms Day #1371 -> 47ms Day #1372 -> 47ms Day #1374 -> 47ms Day #1375 -> 48ms Day #1378 -> 48ms Day #1382 -> 48ms Day #1384 -> 48ms Day #1389 -> 48ms Day #1394 -> 48ms Day #1396 -> 48ms Day #1397 -> 48ms Day #1400 -> 48ms Day #1403 -> 48ms Day #1406 -> 48ms Day #1408 -> 48ms Day #1412 -> 48ms Day #1413 -> 48ms Day #1414 -> 48ms Day #1416 -> 48ms Day #1417 -> 48ms Day #1420 -> 48ms Day #1425 -> 48ms Day #1429 -> 48ms Day #1434 -> 48ms Day #1436 -> 48ms Day #1443 -> 48ms Day #1445 -> 48ms Day #1446 -> 48ms Day #1447 -> 48ms Day #1449 -> 48ms Day #1452 -> 48ms Day #1454 -> 48ms Day #1456 -> 48ms Day #1457 -> 48ms Day #1460 -> 48ms Day #1463 -> 49ms Day #1464 -> 49ms Day #1471 -> 49ms Day #1472 -> 49ms Day #1480 -> 49ms Day #1481 -> 49ms Day #1483 -> 49ms Day #1484 -> 49ms Day #1485 -> 49ms Day #1486 -> 49ms Day #1488 -> 49ms Day #1493 -> 49ms Day #1495 -> 49ms Day #1499 -> 49ms Day #1500 -> 49ms Day #1503 -> 49ms Day #1507 -> 49ms Day #1512 -> 49ms Day #1513 -> 49ms Day #1515 -> 49ms Day #1516 -> 49ms Day #1517 -> 49ms Day #1519 -> 49ms Day #1527 -> 49ms Day #1528 -> 49ms Day #1530 -> 49ms Day #1531 -> 49ms Day #1532 -> 49ms Day #1534 -> 50ms Day #1538 -> 50ms Day #1540 -> 50ms Day #1543 -> 50ms Day #1549 -> 50ms Day #1551 -> 50ms Day #1555 -> 50ms Day #1557 -> 50ms Day #1558 -> 50ms Day #1562 -> 50ms Day #1563 -> 50ms Day #1564 -> 50ms Day #1575 -> 50ms Day #1576 -> 50ms Day #1577 -> 50ms Day #1578 -> 50ms Day #1579 -> 50ms Day #1584 -> 50ms Day #1587 -> 50ms Day #1588 -> 50ms Day #1594 -> 50ms Day #1596 -> 50ms Day #1597 -> 50ms Day #1603 -> 51ms Day #1608 -> 51ms Day #1610 -> 51ms Day #1611 -> 51ms Day #1613 -> 51ms Day #1619 -> 51ms Day #1620 -> 51ms Day #1625 -> 51ms Day #1628 -> 51ms Day #1630 -> 51ms Day #1631 -> 51ms Day #1634 -> 51ms Day #1636 -> 51ms Day #1639 -> 51ms Day #1642 -> 51ms Day #1652 -> 51ms Day #1657 -> 51ms Day #1658 -> 51ms Day #1667 -> 51ms Day #1669 -> 51ms Day #1673 -> 51ms Day #1677 -> 51ms Day #1678 -> 51ms Day #1680 -> 51ms Day #1681 -> 51ms Day #1684 -> 51ms Day #1686 -> 51ms Day #1687 -> 51ms Day #1694 -> 51ms Day #1695 -> 51ms Day #1696 -> 51ms Day #1697 -> 52ms Day #1705 -> 52ms Day #1714 -> 52ms Day #1715 -> 52ms Day #1717 -> 52ms Day #1722 -> 52ms Day #1724 -> 52ms Day #1727 -> 52ms Day #1730 -> 52ms Day #1731 -> 52ms Day #1734 -> 52ms Day #1736 -> 52ms Day #1738 -> 52ms Day #1744 -> 52ms Day #1745 -> 52ms Day #1749 -> 52ms Day #1752 -> 52ms Day #1754 -> 52ms Day #1757 -> 52ms Day #1760 -> 52ms Day #1777 -> 52ms Day #1780 -> 52ms Day #1781 -> 52ms Day #1782 -> 52ms Day #1786 -> 52ms Day #1789 -> 53ms Day #1793 -> 53ms Day #1794 -> 53ms Day #1796 -> 53ms Day #1797 -> 53ms Day #1799 -> 53ms Day #1802 -> 53ms Day #1814 -> 53ms Day #1815 -> 53ms Day #1818 -> 53ms Day #1827 -> 53ms Day #1829 -> 53ms Day #1830 -> 53ms Day #1832 -> 53ms Day #1837 -> 53ms Day #1840 -> 53ms Day #1849 -> 53ms Day #1850 -> 53ms Day #1852 -> 53ms Day #1857 -> 53ms Day #1860 -> 53ms Day #1869 -> 54ms Day #1875 -> 54ms Day #1882 -> 54ms Day #1884 -> 54ms Day #1886 -> 54ms Day #1887 -> 54ms Day #1888 -> 54ms Day #1890 -> 54ms Day #1894 -> 54ms Day #1899 -> 54ms Day #1923 -> 54ms Day #1924 -> 54ms Day #1926 -> 54ms Day #1927 -> 54ms Day #1929 -> 54ms Day #1943 -> 54ms Day #1947 -> 54ms Day #1952 -> 54ms Day #1954 -> 54ms Day #1961 -> 54ms Day #1963 -> 55ms Day #1972 -> 55ms Day #1974 -> 55ms Day #1978 -> 55ms Day #1979 -> 55ms Day #1980 -> 55ms Day #2000 -> 55ms Day #2003 -> 55ms Day #2004 -> 55ms Day #2006 -> 55ms Day #2008 -> 55ms Day #2009 -> 55ms Day #2013 -> 55ms Day #2024 -> 55ms Day #2027 -> 55ms Day #2030 -> 55ms Day #2031 -> 55ms Day #2033 -> 55ms Day #2036 -> 55ms Day #2041 -> 55ms Day #2046 -> 56ms Day #2062 -> 56ms Day #2067 -> 56ms Day #2073 -> 56ms Day #2075 -> 56ms Day #2076 -> 56ms Day #2080 -> 56ms Day #2083 -> 56ms Day #2084 -> 56ms Day #2085 -> 56ms Day #2091 -> 56ms Day #2095 -> 56ms Day #2096 -> 56ms Day #2105 -> 56ms Day #2117 -> 56ms Day #2124 -> 56ms Day #2127 -> 56ms Day #2129 -> 56ms Day #2130 -> 56ms Day #2137 -> 56ms Day #2143 -> 56ms Day #2144 -> 57ms Day #2147 -> 57ms Day #2148 -> 57ms Day #2159 -> 57ms Day #2160 -> 57ms Day #2167 -> 57ms Day #2170 -> 57ms Day #2174 -> 57ms Day #2186 -> 57ms Day #2188 -> 57ms Day #2196 -> 57ms Day #2204 -> 57ms Day #2206 -> 57ms Day #2209 -> 57ms Day #2221 -> 57ms Day #2222 -> 57ms Day #2225 -> 57ms Day #2226 -> 57ms Day #2227 -> 57ms Day #2237 -> 57ms Day #2248 -> 58ms Day #2261 -> 58ms Day #2264 -> 58ms Day #2267 -> 58ms Day #2268 -> 58ms Day #2269 -> 58ms Day #2272 -> 58ms Day #2273 -> 58ms Day #2290 -> 58ms Day #2299 -> 58ms Day #2300 -> 58ms Day #2303 -> 58ms Day #2307 -> 58ms Day #2310 -> 58ms Day #2313 -> 58ms Day #2325 -> 58ms Day #2336 -> 58ms Day #2338 -> 58ms Day #2342 -> 58ms Day #2344 -> 58ms Day #2346 -> 58ms Day #2364 -> 59ms Day #2367 -> 59ms Day #2374 -> 59ms Day #2375 -> 59ms Day #2381 -> 59ms Day #2387 -> 59ms Day #2391 -> 59ms Day #2396 -> 59ms Day #2404 -> 59ms Day #2411 -> 59ms Day #2420 -> 59ms Day #2423 -> 59ms Day #2439 -> 59ms Day #2453 -> 59ms Day #2457 -> 59ms Day #2459 -> 59ms Day #2466 -> 59ms Day #2476 -> 59ms Day #2477 -> 59ms Day #2480 -> 59ms Day #2487 -> 60ms Day #2489 -> 60ms Day #2491 -> 60ms Day #2500 -> 60ms Day #2510 -> 60ms Day #2520 -> 60ms Day #2529 -> 60ms Day #2531 -> 60ms Day #2541 -> 60ms Day #2544 -> 60ms Day #2545 -> 60ms Day #2564 -> 60ms Day #2572 -> 60ms Day #2587 -> 60ms Day #2591 -> 60ms Day #2595 -> 60ms Day #2596 -> 60ms Day #2599 -> 60ms Day #2600 -> 60ms Day #2603 -> 60ms Day #2604 -> 61ms Day #2611 -> 61ms Day #2631 -> 61ms Day #2639 -> 61ms Day #2660 -> 61ms Day #2668 -> 61ms Day #2671 -> 61ms Day #2674 -> 61ms Day #2679 -> 61ms Day #2684 -> 61ms Day #2698 -> 61ms Day #2702 -> 61ms Day #2703 -> 61ms Day #2708 -> 61ms Day #2737 -> 61ms Day #2740 -> 61ms Day #2741 -> 61ms Day #2748 -> 61ms Day #2755 -> 61ms Day #2777 -> 61ms Day #2778 -> 61ms Day #2791 -> 62ms Day #2811 -> 62ms Day #2823 -> 62ms Day #2826 -> 62ms Day #2828 -> 62ms Day #2831 -> 62ms Day #2834 -> 62ms Day #2850 -> 62ms Day #2857 -> 62ms Day #2858 -> 62ms Day #2885 -> 62ms Day #2889 -> 62ms Day #2891 -> 62ms Day #2893 -> 62ms Day #2914 -> 62ms Day #2920 -> 62ms Day #2927 -> 62ms Day #2928 -> 62ms Day #2941 -> 62ms Day #2961 -> 62ms Day #2966 -> 63ms Day #2967 -> 63ms Day #2968 -> 63ms Day #2969 -> 63ms Day #2989 -> 63ms Day #2998 -> 63ms Day #3000 -> 63ms Day #3005 -> 63ms Day #3023 -> 63ms Day #3030 -> 63ms Day #3055 -> 63ms Day #3059 -> 63ms Day #3063 -> 63ms Day #3086 -> 63ms Day #3098 -> 63ms Day #3102 -> 63ms Day #3109 -> 63ms Day #3113 -> 63ms Day #3114 -> 63ms Day #3115 -> 63ms Day #3124 -> 64ms Day #3125 -> 64ms Day #3157 -> 64ms Day #3176 -> 64ms Day #3194 -> 64ms Day #3205 -> 64ms Day #3215 -> 64ms Day #3220 -> 64ms Day #3225 -> 64ms Day #3237 -> 64ms Day #3238 -> 64ms Day #3239 -> 64ms Day #3250 -> 64ms Day #3255 -> 64ms Day #3261 -> 64ms Day #3272 -> 64ms Day #3278 -> 64ms Day #3316 -> 64ms Day #3333 -> 64ms Day #3337 -> 64ms Day #3346 -> 64ms Day #3354 -> 65ms Day #3372 -> 65ms Day #3387 -> 65ms Day #3393 -> 65ms Day #3409 -> 65ms Day #3434 -> 65ms Day #3448 -> 65ms Day #3454 -> 65ms Day #3460 -> 65ms Day #3467 -> 65ms Day #3471 -> 65ms Day #3488 -> 65ms Day #3507 -> 65ms Day #3513 -> 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#4412 -> 68ms Day #4441 -> 68ms Day #4449 -> 68ms Day #4451 -> 68ms Day #4453 -> 68ms Day #4496 -> 68ms Day #4535 -> 68ms Day #4538 -> 68ms Day #4544 -> 68ms Day #4579 -> 68ms Day #4600 -> 68ms Day #4619 -> 68ms Day #4672 -> 69ms Day #4684 -> 69ms Day #4688 -> 69ms Day #4727 -> 69ms Day #4734 -> 69ms Day #4750 -> 69ms Day #4761 -> 69ms Day #4782 -> 69ms Day #4791 -> 69ms Day #4808 -> 69ms Day #4822 -> 69ms Day #4999 -> 69ms Day #5000 -> 69ms Day #5019 -> 69ms Day #5039 -> 69ms Day #5058 -> 69ms Day #5061 -> 69ms Day #5081 -> 69ms Day #5087 -> 69ms Day #5089 -> 69ms Day #5143 -> 69ms Day #5181 -> 70ms Day #5190 -> 70ms Day #5191 -> 70ms Day #5200 -> 70ms Day #5207 -> 70ms Day #5262 -> 70ms Day #5342 -> 70ms Day #5357 -> 70ms Day #5367 -> 70ms Day #5395 -> 70ms Day #5405 -> 70ms Day #5481 -> 70ms Day #5510 -> 70ms Day #5554 -> 70ms Day #5645 -> 70ms Day #5652 -> 70ms Day #5656 -> 70ms Day #5662 -> 70ms Day #5668 -> 70ms Day #5770 -> 70ms Day #5777 -> 70ms Day #5781 -> 71ms Day #5785 -> 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#8666 -> 73ms Day #8678 -> 73ms Day #8741 -> 73ms Day #8782 -> 73ms Day #8881 -> 74ms Day #8897 -> 74ms Day #8902 -> 74ms Day #8906 -> 74ms Day #8992 -> 74ms Day #9069 -> 74ms Day #9088 -> 74ms Day #9343 -> 74ms Day #9375 -> 74ms Day #9615 -> 74ms Day #9643 -> 74ms Day #9997 -> 74ms Day #10037 -> 74ms Day #10116 -> 74ms Day #10161 -> 74ms Day #10178 -> 74ms Day #10361 -> 74ms Day #10380 -> 74ms Day #10399 -> 74ms Day #10413 -> 74ms Day #10684 -> 75ms Day #10714 -> 75ms Day #10733 -> 75ms Day #11020 -> 75ms Day #11108 -> 75ms Day #11336 -> 75ms Day #11561 -> 75ms Day #11678 -> 75ms Day #11710 -> 75ms Day #11870 -> 75ms Day #11875 -> 75ms Day #12019 -> 75ms Day #12434 -> 75ms Day #12455 -> 75ms Day #12496 -> 75ms Day #12500 -> 75ms Day #12701 -> 75ms Day #12857 -> 75ms Day #12998 -> 75ms Day #13017 -> 75ms Day #13487 -> 75ms Day #13736 -> 76ms Day #14051 -> 76ms Day #14250 -> 76ms Day #14281 -> 76ms Day #15000 -> 76ms Day #15115 -> 76ms Day #15428 -> 76ms Day #15542 -> 76ms Day #15569 -> 76ms Day #15571 -> 76ms Day #16025 -> 76ms Day #16099 -> 76ms Day #16185 -> 76ms Day #16661 -> 76ms Day #16934 -> 76ms Day #17331 -> 76ms Day #17355 -> 76ms Day #17564 -> 76ms Day #17804 -> 76ms Day #17812 -> 76ms Day #18750 -> 77ms Day #19230 -> 77ms Day #19285 -> 77ms Day #19994 -> 77ms Day #20231 -> 77ms Day #20722 -> 77ms Day #20759 -> 77ms Day #22672 -> 77ms Day #23356 -> 77ms Day #23419 -> 77ms Day #23749 -> 77ms Day #24038 -> 77ms Day #24992 -> 77ms Day #25000 -> 77ms Day #25401 -> 77ms Day #25714 -> 77ms Day #25996 -> 77ms Day #26033 -> 77ms Day #26974 -> 77ms Day #31083 -> 77ms Day #31138 -> 77ms Day #32050 -> 78ms Day #32197 -> 78ms Day #33322 -> 78ms Day #35128 -> 78ms Day #35608 -> 78ms Day #35623 -> 78ms Day #37499 -> 78ms Day #38570 -> 78ms Day #40461 -> 78ms Day #45344 -> 78ms Day #46712 -> 78ms Day #48075 -> 78ms Day #49983 -> 78ms Day #50802 -> 78ms Day #51991 -> 78ms Day #52065 -> 78ms Day #62166 -> 78ms Day #62275 -> 78ms Day #70255 -> 78ms Day #71246 -> 78ms Day #74998 -> 78ms Day #77140 -> 79ms Day #80922 -> 79ms Day #96149 -> 79ms Day #99966 -> 79ms