[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"public-settings":3,"content:materi:notasi-big-o-kompleksitas-waktu":11,"public-catalog":200},{"features.tutoring.enabled":4,"sections.subjects.enabled":5,"sections.pricing.enabled":5,"sections.teachers.enabled":5,"sections.testimonials.enabled":4,"sections.faqs.enabled":5,"bankSoal.enabled":5,"site.maintenance":4,"whatsapp.number":6,"brand.name":7,"brand.tagline":8,"contact.email":9,"contact.address":10},false,true,"6285156084435","MyFismat","Platform belajar Matematika, Fisika, dan Pemrograman untuk SD, SMP, SMA, dan Kuliah","support@myfismat.com","Indonesia",{"id":12,"type":13,"slug":14,"title":15,"excerpt":16,"coverUrl":17,"status":18,"publishedAt":19,"featured":5,"subjectId":20,"blocks":21,"seoTitle":17,"seoDescription":17,"readingMinutes":98,"order":99,"createdAt":100,"updatedAt":100,"subject":101,"levels":105,"topics":110,"tags":114,"author":17,"resolved":115,"related":124},"demo-v2-m-pemrograman-kuliah-1","MATERIAL","notasi-big-o-kompleksitas-waktu","Notasi Big O dan Kompleksitas Waktu Algoritma","Pahami notasi Big O dan kompleksitas waktu algoritma: O(1), O(log n), O(n), O(n²), cara menghitungnya dari kode Python, dan contoh soalnya.",null,"PUBLISHED","2026-10-08T23:58:23.821Z","cmuzbyhdt000671r91cdnnt22",[22,27,34,38,42,46,52,56,60,64,68,74,78,82,88,92],{"id":23,"data":24,"type":26},"s1-1",{"markdown":25},"**Notasi Big O** adalah cara menyatakan **kompleksitas waktu** algoritma, yaitu seberapa cepat banyak langkah bertambah ketika ukuran masukan $n$ membesar. Misalnya, pencarian linear berkompleksitas $O(n)$, sedangkan binary search $O(\\log n)$. Big O tidak mengukur detik, melainkan pola pertumbuhan, dan biasanya dipakai untuk kasus terburuk.","text",{"id":28,"data":29,"type":33},"s1-2",{"title":30,"variant":31,"markdown":32},"Definisi notasi Big O","info","$$f(n) = O(g(n)) \\iff \\exists\\, c > 0,\\ n_0 \\text{ sehingga } f(n) \\le c \\cdot g(n) \\text{ untuk semua } n \\ge n_0$$\n\nArtinya, untuk $n$ yang cukup besar, banyak langkah $f(n)$ tidak tumbuh lebih cepat daripada kelipatan konstan $g(n)$. Big O adalah **batas atas** pertumbuhan.","callout",{"id":35,"data":36,"type":26},"s2-1",{"markdown":37},"## Apa Itu Kompleksitas Waktu?\nWaktu eksekusi dalam detik bergantung pada komputer, bahasa, dan beban sistem. Agar perbandingan adil, kita menghitung **banyak operasi dasar**, misalnya perbandingan atau penjumlahan, sebagai fungsi dari ukuran masukan $n$. Hasilnya disebut **kompleksitas waktu**. Analisis serupa untuk pemakaian memori disebut **kompleksitas ruang**.\n\nYang penting bukan angka pastinya, tetapi **bagaimana angka itu tumbuh**. Algoritma $O(n)$ yang datanya dilipatduakan kira-kira membutuhkan dua kali langkah; algoritma $O(n^2)$ membutuhkan empat kali langkah.",{"id":39,"data":40,"type":26},"s3-1",{"markdown":41},"## Kelas Kompleksitas yang Paling Sering Muncul\n| Notasi | Nama | Contoh | $n = 10$ | $n = 1.000$ |\n|---|---|---|---|---|\n| $O(1)$ | konstan | akses `data[i]` | 1 | 1 |\n| $O(\\log n)$ | logaritmik | binary search | ≈ 3 | ≈ 10 |\n| $O(n)$ | linear | pencarian linear, `sum(data)` | 10 | 1.000 |\n| $O(n \\log n)$ | linearitmik | `sorted(data)`, merge sort | ≈ 33 | ≈ 10.000 |\n| $O(n^2)$ | kuadratik | dua loop bersarang | 100 | 1.000.000 |\n| $O(2^n)$ | eksponensial | mencoba semua himpunan bagian | 1.024 | ≈ $10^{301}$ |\n\nKolom angka menunjukkan perkiraan banyak langkah. Perhatikan bagaimana $O(n^2)$ dan $O(2^n)$ meledak ketika $n$ membesar.",{"id":43,"data":44,"type":26},"s4-1",{"markdown":45},"## Cara Menghitung Big O dari Kode Python\n1. Tentukan apa itu $n$, misalnya panjang list.\n2. Satu perulangan sepanjang $n$ menyumbang $O(n)$.\n3. Perulangan **bersarang** dikalikan: $n \\times n = O(n^2)$.\n4. Bagian kode yang **berurutan** dijumlahkan: $O(n) + O(n) = O(2n)$.\n5. Sederhanakan hasilnya.",{"id":47,"data":48,"type":33},"s4-2",{"title":49,"variant":50,"markdown":51},"Dua aturan penyederhanaan","tip","- **Buang konstanta:** $O(2n) = O(n)$ dan $O(500) = O(1)$.\n- **Ambil suku dominan:** $3n^2 + 5n + 2 = O(n^2)$, karena untuk $n$ besar suku $n^2$ jauh mengalahkan suku lainnya.",{"id":53,"data":54,"type":26},"s5-1",{"markdown":55},"## Contoh Soal Big O dan Pembahasan\n### Contoh 1: O(1) dan O(n)\n~~~python\ndef pertama(data):\n    return data[0]\n\ndef jumlah(data):\n    total = 0\n    for x in data:\n        total += x\n    return total\n~~~\n\n`pertama` hanya melakukan satu akses, berapa pun panjang list, sehingga $O(1)$. `jumlah` mengunjungi setiap elemen sekali, sehingga $O(n)$.\n\n### Contoh 2: O(n²) dengan loop bersarang\n~~~python\ndef ada_duplikat_lambat(data):\n    n = len(data)\n    for i in range(n):\n        for j in range(i + 1, n):\n            if data[i] == data[j]:\n                return True\n    return False\n~~~\n\nPada kasus terburuk (tidak ada duplikat), banyak perbandingan adalah $\\frac{n(n-1)}{2} = \\frac{1}{2}n^2 - \\frac{1}{2}n$, sehingga kompleksitasnya $O(n^2)$.\n\n### Contoh 3: Memperbaiki menjadi O(n) dengan set\n~~~python\ndef ada_duplikat_cepat(data):\n    terlihat = set()\n    for x in data:\n        if x in terlihat:\n            return True\n        terlihat.add(x)\n    return False\n~~~\n\nPemeriksaan `x in terlihat` pada set rata-rata $O(1)$, sehingga seluruh fungsi rata-rata $O(n)$. Harganya adalah memori tambahan $O(n)$ untuk set: kita menukar ruang dengan waktu.\n\n### Contoh 4: Membuktikan pertumbuhan secara empiris\n~~~python\ndef hitung_perbandingan(n):\n    langkah = 0\n    for i in range(n):\n        for j in range(i + 1, n):\n            langkah += 1\n    return langkah\n\nfor n in [10, 100, 1000]:\n    print(n, hitung_perbandingan(n))\n~~~\n\nKeluarannya `10 45`, `100 4950`, dan `1000 499500`. Saat $n$ dikali 10, banyak langkah kira-kira dikali 100, ciri khas $O(n^2)$.",{"id":57,"data":58,"type":26},"s6-1",{"markdown":59},"## Kasus Terbaik, Rata-rata, dan Terburuk\nPencarian linear yang menemukan target di elemen pertama hanya butuh 1 langkah (kasus terbaik), tetapi kasus terburuknya $n$ langkah. Karena itu kita biasa menyebut pencarian linear $O(n)$. Dalam analisis algoritma juga dikenal notasi $\\Omega$ (*Big Omega*, batas bawah) dan $\\Theta$ (*Big Theta*, batas atas sekaligus bawah).",{"id":61,"data":62,"type":26},"s7-1",{"markdown":63},"## Biaya Operasi Struktur Data Python\n| Operasi | Kompleksitas |\n|---|---|\n| `data[i]` pada list | $O(1)$ |\n| `data.append(x)` | $O(1)$ diamortisasi |\n| `data.insert(0, x)` | $O(n)$ |\n| `x in data` pada list | $O(n)$ |\n| `x in s` pada set, `d[k]` pada dict | $O(1)$ rata-rata |\n| `sorted(data)` | $O(n \\log n)$ |",{"id":65,"data":66,"type":26},"s8-1",{"markdown":67},"## Kesalahan yang Sering Terjadi",{"id":69,"data":70,"type":33},"s8-2",{"title":71,"variant":72,"markdown":73},"Salah kaprah tentang Big O","warning","- **Menganggap Big O sebagai detik.** $O(n)$ tidak berarti \"n milidetik\"; ia hanya menggambarkan pola pertumbuhan.\n- **Lupa loop tersembunyi.** `if x in daftar` di dalam `for` terlihat satu loop, padahal `in` pada list juga $O(n)$, sehingga totalnya $O(n^2)$.\n- **Menganggap set selalu $O(1)$.** Itu biaya rata-rata; membangun set sendiri butuh $O(n)$ dan kasus terburuknya bisa lebih buruk.\n- **Mengabaikan ukuran data.** Untuk data kecil, kode $O(n^2)$ yang sederhana bisa lebih tepat daripada kode rumit yang sedikit lebih efisien.",{"id":75,"data":76,"type":26},"s9-1",{"markdown":77},"## Ringkasan\n- Big O menyatakan batas atas pertumbuhan banyak langkah terhadap ukuran masukan $n$.\n- Urutan umum: $O(1) \u003C O(\\log n) \u003C O(n) \u003C O(n \\log n) \u003C O(n^2) \u003C O(2^n)$.\n- Loop bersarang dikalikan, kode berurutan dijumlahkan, lalu buang konstanta dan suku kecil.\n- Pilihan struktur data, seperti set dibanding list, dapat menurunkan kompleksitas.",{"id":79,"data":80,"type":26},"s10-1",{"markdown":81},"## Materi Terkait\nContoh nyata $O(n)$ dan $O(\\log n)$ dibahas di [pencarian linear dan biner](\u002Fmateri\u002Fpencarian-linear-dan-biner). Biaya operasi list dan dictionary dijelaskan di [list dan dictionary Python](\u002Fmateri\u002Flist-dan-dictionary-python). Setelah membuat versi kode yang lebih cepat, pastikan hasilnya tetap benar dengan [unit test Python](\u002Fmateri\u002Funit-test-python).",{"id":83,"data":84,"type":83},"code",{"code":85,"caption":86,"language":87},"def ada_duplikat_lambat(data):\n    n = len(data)\n    for i in range(n):\n        for j in range(i + 1, n):\n            if data[i] == data[j]:\n                return True\n    return False\n\n\ndef ada_duplikat_cepat(data):\n    terlihat = set()\n    for x in data:\n        if x in terlihat:\n            return True\n        terlihat.add(x)\n    return False\n\n\ncontoh = [4, 8, 15, 16, 23, 42, 8]\nprint(ada_duplikat_lambat(contoh), ada_duplikat_cepat(contoh))\nprint(ada_duplikat_lambat([1, 2, 3]), ada_duplikat_cepat([1, 2, 3]))","Dua cara mendeteksi duplikat: O(n²) dan O(n) rata-rata","python",{"id":89,"data":90,"type":26},"sources",{"markdown":91},"## Sumber belajar\n\n- [Python Wiki: TimeComplexity](https:\u002F\u002Fwiki.python.org\u002Fmoin\u002FTimeComplexity)\n- [MIT OpenCourseWare 6.0001: Lecture 12, Searching and Sorting](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F6-0001-introduction-to-computer-science-and-programming-in-python-fall-2016\u002Fresources\u002Flecture-12-searching-and-sorting\u002F)\n- [Python Tutorial: Data Structures](https:\u002F\u002Fdocs.python.org\u002F3\u002Ftutorial\u002Fdatastructures.html)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.",{"id":93,"data":94,"type":97},"practice",{"title":95,"questionSetId":96},"Latihan soal Notasi Big O","demo-v2-p-pemrograman-kuliah-1","quiz",5,0,"2026-10-08T23:58:23.823Z",{"id":20,"slug":102,"name":103,"color":104,"icon":83},"pemrograman","Pemrograman","#3B82F6",[106],{"id":107,"slug":108,"name":109},"cmuzbyhdb000371r9qk125qjd","kuliah","Kuliah",[111],{"id":112,"slug":14,"name":113,"subjectId":20},"demo-v2-topic-pemrograman-kuliah-1","Notasi Big O",[],{"assets":116,"videos":117,"questionSets":118},{},{},{"demo-v2-p-pemrograman-kuliah-1":119},{"id":96,"slug":120,"title":121,"mode":122,"description":123,"questionCount":98,"durationMinutes":17},"latihan-soal-notasi-big-o-kompleksitas-waktu","Latihan Soal Notasi Big O","PRACTICE","5 soal Notasi Big O (Pemrograman Kuliah) lengkap dengan pembahasan langkah demi langkah dan alasan pilihan yang keliru.",[125,151,168,184],{"id":126,"type":127,"slug":128,"title":129,"excerpt":130,"coverUrl":17,"status":18,"publishedAt":131,"featured":5,"readingMinutes":132,"order":99,"updatedAt":133,"subject":134,"levels":135,"topics":149,"tags":150,"author":17},"demo-v2-a-pemrograman","ARTICLE","belajar-python-dari-nol","Belajar Python dari Nol: Panduan Lengkap untuk Pemula","Panduan belajar Python dari nol untuk pemula: cara install, program pertama, urutan materi dari algoritma sampai OOP, proyek kecil, dan jadwal 4 minggu.","2026-10-08T23:58:23.902Z",7,"2026-10-08T23:58:23.903Z",{"id":20,"slug":102,"name":103,"color":104,"icon":83},[136,140,144,148],{"id":137,"slug":138,"name":139},"cmv0762210004113f6m6v04vs","sd","SD",{"id":141,"slug":142,"name":143},"cmuzbyhdb000171r9dcbyf0qg","smp","SMP",{"id":145,"slug":146,"name":147},"cmuzbyhdb000271r9up0bfli4","sma","SMA",{"id":107,"slug":108,"name":109},[],[],{"id":152,"type":13,"slug":153,"title":154,"excerpt":155,"coverUrl":17,"status":18,"publishedAt":156,"featured":4,"readingMinutes":157,"order":158,"updatedAt":159,"subject":160,"levels":161,"topics":163,"tags":167,"author":17},"demo-v2-m-pemrograman-kuliah-3","unit-test-python","Unit Test Python dengan unittest + Contoh Lengkap","Pelajari unit test Python dengan modul unittest: assertEqual, assertRaises, nilai batas, dan cara menjalankan tes, lengkap dengan contoh dan versi pytest.","2026-10-08T23:58:23.888Z",4,2,"2026-10-08T23:58:23.890Z",{"id":20,"slug":102,"name":103,"color":104,"icon":83},[162],{"id":107,"slug":108,"name":109},[164],{"id":165,"slug":153,"name":166,"subjectId":20},"demo-v2-topic-pemrograman-kuliah-3","Unit Test Python",[],{"id":169,"type":13,"slug":170,"title":171,"excerpt":172,"coverUrl":17,"status":18,"publishedAt":173,"featured":4,"readingMinutes":157,"order":174,"updatedAt":175,"subject":176,"levels":177,"topics":179,"tags":183,"author":17},"demo-v2-m-pemrograman-kuliah-2","class-dan-object-python","Class dan Object Python: Dasar OOP + Contoh Program","Pelajari class dan object Python untuk OOP: __init__, self, atribut, method, inheritance, dan invarian objek lewat contoh program dompet digital.","2026-10-08T23:58:23.855Z",1,"2026-10-08T23:58:23.856Z",{"id":20,"slug":102,"name":103,"color":104,"icon":83},[178],{"id":107,"slug":108,"name":109},[180],{"id":181,"slug":170,"name":182,"subjectId":20},"demo-v2-topic-pemrograman-kuliah-2","Class dan Object Python",[],{"id":185,"type":13,"slug":186,"title":187,"excerpt":188,"coverUrl":17,"status":18,"publishedAt":189,"featured":4,"readingMinutes":157,"order":190,"updatedAt":191,"subject":192,"levels":193,"topics":195,"tags":199,"author":17},"demo-v2-m-pemrograman-sma-4","try-except-python","Try Except Python dan Cara Membaca File untuk Pemula","Pelajari try except Python untuk menangani error seperti ValueError dan FileNotFoundError, serta cara membaca dan menulis file txt dengan with open.","2026-10-08T23:58:23.781Z",3,"2026-10-08T23:58:23.782Z",{"id":20,"slug":102,"name":103,"color":104,"icon":83},[194],{"id":145,"slug":146,"name":147},[196],{"id":197,"slug":186,"name":198,"subjectId":20},"demo-v2-topic-pemrograman-sma-4","Try Except dan Membaca File",[],{"subjects":201,"levels":221,"topics":232,"tags":2018},[202,210,218],{"id":203,"slug":204,"name":205,"description":206,"icon":207,"color":208,"order":99,"published":5,"createdAt":209,"updatedAt":209},"cmuzbyhdg000471r9l54yc9ia","matematika","Matematika","Aljabar, geometri, kalkulus, statistika, dan cara berpikir matematis.","sigma","#8B5CF6","2026-10-08T09:24:40.948Z",{"id":211,"slug":212,"name":213,"description":214,"icon":215,"color":216,"order":174,"published":5,"createdAt":217,"updatedAt":217},"cmuzbyhdq000571r9nsdk6scx","fisika","Fisika","Gerak, gaya, energi, listrik, gelombang, hingga fisika modern.","atom","#0EA5E9","2026-10-08T09:24:40.958Z",{"id":20,"slug":102,"name":103,"description":219,"icon":83,"color":104,"order":158,"published":5,"createdAt":220,"updatedAt":220},"Logika, algoritma, dan coding dari dasar sampai proyek nyata.","2026-10-08T09:24:40.962Z",[222,225,228,230],{"id":137,"slug":138,"name":139,"description":223,"order":99,"createdAt":224,"updatedAt":224},"Jenjang SD","2026-10-08T23:58:22.441Z",{"id":141,"slug":142,"name":143,"description":226,"order":174,"createdAt":227,"updatedAt":227},"Sekolah Menengah Pertama","2026-10-08T09:24:40.943Z",{"id":145,"slug":146,"name":147,"description":229,"order":158,"createdAt":227,"updatedAt":227},"Sekolah Menengah Atas",{"id":107,"slug":108,"name":109,"description":231,"order":190,"createdAt":227,"updatedAt":227},"Perguruan tinggi \u002F universitas",[233,240,246,252,258,264,269,275,281,287,293,299,305,311,317,323,329,335,341,347,353,359,365,371,377,383,389,395,401,407,413,419,425,431,437,443,449,455,461,467,472,478,484,490,496,502,508,514,520,526,532,538,544,550,556,562,568,574,579,584,589,594,599,604,609,614,619,624,630,635,640,645,650,655,660,665,670,675,680,685,690,695,700,705,710,715,720,725,730,735,740,745,750,755,760,765,770,775,781,786,791,796,801,806,811,816,821,826,831,836,841,846,851,856,861,866,871,876,881,886,891,896,902,907,912,917,922,927,932,937,942,947,952,957,962,967,972,977,982,987,992,998,1003,1008,1013,1018,1023,1028,1033,1038,1043,1048,1053,1058,1063,1068,1073,1078,1083,1088,1093,1098,1103,1108,1114,1119,1124,1129,1134,1139,1144,1149,1154,1159,1164,1169,1174,1179,1184,1189,1194,1199,1204,1209,1214,1219,1224,1229,1234,1239,1242,1248,1253,1258,1263,1268,1273,1278,1283,1288,1292,1297,1302,1307,1312,1317,1322,1327,1332,1337,1342,1347,1352,1357,1362,1367,1372,1377,1382,1387,1392,1397,1402,1407,1412,1417,1422,1427,1432,1437,1442,1447,1452,1457,1461,1466,1471,1476,1481,1486,1491,1497,1502,1507,1512,1517,1522,1527,1532,1537,1542,1547,1552,1557,1562,1568,1573,1579,1584,1590,1595,1601,1606,1612,1617,1623,1629,1635,1640,1646,1651,1657,1660,1666,1671,1677,1682,1687,1692,1698,1703,1709,1714,1720,1725,1731,1735,1741,1746,1752,1757,1763,1768,1774,1779,1785,1790,1796,1801,1807,1812,1819,1826,1833,1839,1845,1851,1857,1863,1869,1871,1877,1883,1889,1895,1901,1904,1910,1916,1922,1928,1934,1940,1946,1952,1958,1965,1971,1977,1983,1989,1991,1997,2003,2010,2012],{"id":234,"subjectId":211,"levelId":145,"parentId":235,"slug":236,"name":237,"description":238,"order":99,"createdAt":239,"updatedAt":239},"cmuzbyhm9007o71r91e76ir5n","cmuzbyhm6007m71r9multkwzz","arus-dan-tegangan-listrik-bolak-balik","Arus dan Tegangan Listrik Bolak Balik","","2026-10-08T09:24:41.265Z",{"id":241,"subjectId":203,"levelId":145,"parentId":242,"slug":243,"name":244,"description":238,"order":99,"createdAt":245,"updatedAt":245},"cmuzbyht500e271r9p86b0fxe","cmuzbyht300e071r93gyvjn0r","barisan","Barisan","2026-10-08T09:24:41.514Z",{"id":247,"subjectId":203,"levelId":145,"parentId":248,"slug":249,"name":250,"description":238,"order":99,"createdAt":251,"updatedAt":251},"cmuzbyhok009w71r9688mekrn","cmuzbyhoi009u71r9i6j09wcn","barisan-dan-deret-barisan-dan-deret-kelas-10","Barisan dan Deret","2026-10-08T09:24:41.348Z",{"id":253,"subjectId":203,"levelId":145,"parentId":254,"slug":255,"name":256,"description":238,"order":99,"createdAt":257,"updatedAt":257},"cmuzbyhpm00aw71r94xosa04y","cmuzbyhpk00au71r9d9ugx39r","bentuk-umum-dan-akar-persamaan-kuadrat","Bentuk Umum dan Akar Persamaan 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Wajib.","2026-10-08T09:24:41.547Z",{"id":415,"subjectId":203,"levelId":145,"parentId":17,"slug":1736,"name":1737,"description":1738,"order":1739,"createdAt":1740,"updatedAt":1740},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":409,"subjectId":211,"levelId":145,"parentId":17,"slug":1742,"name":1743,"description":1744,"order":1739,"createdAt":1745,"updatedAt":1745},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":283,"subjectId":203,"levelId":145,"parentId":17,"slug":1747,"name":1748,"description":1749,"order":1750,"createdAt":1751,"updatedAt":1751},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":235,"subjectId":211,"levelId":145,"parentId":17,"slug":1753,"name":1754,"description":1755,"order":1750,"createdAt":1756,"updatedAt":1756},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":474,"subjectId":211,"levelId":145,"parentId":17,"slug":1758,"name":1759,"description":1760,"order":1761,"createdAt":1762,"updatedAt":1762},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":289,"subjectId":203,"levelId":145,"parentId":17,"slug":1764,"name":1765,"description":1766,"order":1761,"createdAt":1767,"updatedAt":1767},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":498,"subjectId":203,"levelId":145,"parentId":17,"slug":1769,"name":1770,"description":1771,"order":1772,"createdAt":1773,"updatedAt":1773},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":528,"subjectId":211,"levelId":145,"parentId":17,"slug":1775,"name":1776,"description":1777,"order":1772,"createdAt":1778,"updatedAt":1778},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":373,"subjectId":203,"levelId":145,"parentId":17,"slug":1780,"name":1781,"description":1782,"order":1783,"createdAt":1784,"updatedAt":1784},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":516,"subjectId":211,"levelId":145,"parentId":17,"slug":1786,"name":1787,"description":1788,"order":1783,"createdAt":1789,"updatedAt":1789},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":522,"subjectId":211,"levelId":145,"parentId":17,"slug":1791,"name":1792,"description":1793,"order":1794,"createdAt":1795,"updatedAt":1795},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":421,"subjectId":203,"levelId":145,"parentId":17,"slug":1797,"name":1798,"description":1799,"order":1794,"createdAt":1800,"updatedAt":1800},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":313,"subjectId":203,"levelId":145,"parentId":17,"slug":1802,"name":1803,"description":1804,"order":1805,"createdAt":1806,"updatedAt":1806},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":457,"subjectId":211,"levelId":145,"parentId":17,"slug":1808,"name":1809,"description":1810,"order":1805,"createdAt":1811,"updatedAt":1811},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1813,"subjectId":203,"levelId":145,"parentId":17,"slug":1814,"name":1815,"description":1816,"order":1817,"createdAt":1818,"updatedAt":1818},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1820,"subjectId":203,"levelId":145,"parentId":17,"slug":1821,"name":1822,"description":1823,"order":1824,"createdAt":1825,"updatedAt":1825},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1827,"subjectId":203,"levelId":145,"parentId":17,"slug":1828,"name":1829,"description":1830,"order":1831,"createdAt":1832,"updatedAt":1832},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":1834,"subjectId":203,"levelId":107,"parentId":17,"slug":1835,"name":291,"description":1836,"order":1837,"createdAt":1838,"updatedAt":1838},"demo-v2-topic-matematika-kuliah-1","definisi-turunan-limit","Definisi turunan dengan limit f′(x) = lim [f(x+h) − f(x)]\u002Fh, langkah menghitungnya, gradien garis singgung, syarat diferensiabel, dan contoh soal.",100,"2026-10-08T23:58:22.977Z",{"id":1840,"subjectId":203,"levelId":145,"parentId":17,"slug":1841,"name":1842,"description":1843,"order":1837,"createdAt":1844,"updatedAt":1844},"demo-v2-topic-matematika-sma-1","fungsi-kuadrat","Fungsi Kuadrat","Fungsi kuadrat f(x) = ax² + bx + c: pengaruh a, b, c pada grafik, rumus titik puncak, sumbu simetri, diskriminan, dan contoh soal nilai maksimum.","2026-10-08T23:58:22.868Z",{"id":1846,"subjectId":20,"levelId":145,"parentId":17,"slug":1847,"name":1848,"description":1849,"order":1837,"createdAt":1850,"updatedAt":1850},"demo-v2-topic-pemrograman-sma-1","fungsi-python-def-return","Fungsi Python","Pelajari cara membuat fungsi Python dengan def, parameter, nilai default, dan return, plus perbedaan return dan print lewat contoh program yang jelas.","2026-10-08T23:58:23.661Z",{"id":1852,"subjectId":211,"levelId":141,"parentId":17,"slug":1853,"name":1854,"description":1855,"order":1837,"createdAt":1856,"updatedAt":1856},"demo-v2-topic-fisika-smp-1","glb-dan-glbb","GLB dan GLBB","Rumus GLB dan GLBB lengkap: jarak, kecepatan, percepatan, grafik posisi–waktu, perbedaan GLB dan GLBB, plus contoh soal gerak lurus dan pembahasannya.","2026-10-08T23:58:23.189Z",{"id":1858,"subjectId":211,"levelId":107,"parentId":17,"slug":1859,"name":1860,"description":1861,"order":1837,"createdAt":1862,"updatedAt":1862},"demo-v2-topic-fisika-kuliah-1","gerak-harmonik-sederhana","Gerak Harmonik Sederhana","Gerak harmonik sederhana untuk fisika dasar: persamaan x = A cos(ωt + φ), kecepatan, percepatan, periode pegas dan bandul, energi, serta contoh soal.","2026-10-08T23:58:23.364Z",{"id":1864,"subjectId":211,"levelId":145,"parentId":17,"slug":1865,"name":1866,"description":1867,"order":1837,"createdAt":1868,"updatedAt":1868},"demo-v2-topic-fisika-sma-1","hukum-newton-2","Hukum Newton 2","Hukum Newton 2: bunyi, rumus ΣF = m·a, diagram gaya, gaya gesek statis dan kinetis, serta contoh soal mencari percepatan dan massa beserta pembahasan.","2026-10-08T23:58:23.280Z",{"id":112,"subjectId":20,"levelId":107,"parentId":17,"slug":14,"name":113,"description":16,"order":1837,"createdAt":1870,"updatedAt":1870},"2026-10-08T23:58:23.797Z",{"id":1872,"subjectId":20,"levelId":137,"parentId":17,"slug":1873,"name":1874,"description":1875,"order":1837,"createdAt":1876,"updatedAt":1876},"demo-v2-topic-pemrograman-sd-1","pengertian-algoritma","Pengertian Algoritma","Algoritma adalah langkah-langkah urut untuk menyelesaikan masalah. Pelajari pengertian, ciri, dan contoh algoritma sehari-hari untuk siswa SD.","2026-10-08T23:58:23.477Z",{"id":1878,"subjectId":211,"levelId":137,"parentId":17,"slug":1879,"name":1880,"description":1881,"order":1837,"createdAt":1882,"updatedAt":1882},"demo-v2-topic-fisika-sd-1","pengukuran-panjang","Pengukuran Panjang","Belajar pengukuran panjang untuk SD: satuan baku, alat ukur panjang, cara memakai penggaris, dan tangga satuan panjang km sampai mm + contoh soal.","2026-10-08T23:58:23.095Z",{"id":1884,"subjectId":203,"levelId":137,"parentId":17,"slug":1885,"name":1886,"description":1887,"order":1837,"createdAt":1888,"updatedAt":1888},"demo-v2-topic-matematika-sd-1","penjumlahan-pecahan","Penjumlahan Pecahan","Cara penjumlahan pecahan berpenyebut sama dan beda penyebut memakai KPK, pecahan senilai, dan pecahan campuran, lengkap dengan contoh soal SD.","2026-10-08T23:58:22.508Z",{"id":1890,"subjectId":203,"levelId":141,"parentId":17,"slug":1891,"name":1892,"description":1893,"order":1837,"createdAt":1894,"updatedAt":1894},"demo-v2-topic-matematika-smp-1","teorema-pythagoras","Teorema Pythagoras","Teorema Pythagoras a² + b² = c² untuk mencari sisi miring dan sisi siku-siku, tripel Pythagoras, diagonal ruang balok, dan contoh soal kelas 8.","2026-10-08T23:58:22.690Z",{"id":1896,"subjectId":20,"levelId":141,"parentId":17,"slug":1897,"name":1898,"description":1899,"order":1837,"createdAt":1900,"updatedAt":1900},"demo-v2-topic-pemrograman-smp-1","variabel-dan-tipe-data-python","Variabel dan Tipe Data Python","Belajar variabel dan tipe data Python dari nol: int, float, string, boolean, operator, print, dan input, lengkap dengan contoh program dan latihan.","2026-10-08T23:58:23.562Z",{"id":181,"subjectId":20,"levelId":107,"parentId":17,"slug":170,"name":182,"description":172,"order":1902,"createdAt":1903,"updatedAt":1903},101,"2026-10-08T23:58:23.830Z",{"id":1905,"subjectId":203,"levelId":145,"parentId":17,"slug":1906,"name":1907,"description":1908,"order":1902,"createdAt":1909,"updatedAt":1909},"demo-v2-topic-matematika-sma-2","eksponen-dan-logaritma","Eksponen dan Logaritma","Materi eksponen dan logaritma kelas 10: sifat-sifat eksponen, definisi dan sifat logaritma, persamaan eksponen dan logaritma, serta contoh soal.","2026-10-08T23:58:22.902Z",{"id":1911,"subjectId":211,"levelId":137,"parentId":17,"slug":1912,"name":1913,"description":1914,"order":1902,"createdAt":1915,"updatedAt":1915},"demo-v2-topic-fisika-sd-2","macam-macam-gaya","Gaya dan Macam-Macamnya","Gaya adalah tarikan atau dorongan. Pelajari macam-macam gaya (otot, gravitasi, magnet, gesek, pegas), pengaruhnya pada benda, dan contoh soalnya.","2026-10-08T23:58:23.126Z",{"id":1917,"subjectId":203,"levelId":137,"parentId":17,"slug":1918,"name":1919,"description":1920,"order":1902,"createdAt":1921,"updatedAt":1921},"demo-v2-topic-matematika-sd-2","rumus-keliling-dan-luas-bangun-datar","Keliling dan Luas Bangun Datar","Rumus keliling dan luas bangun datar: persegi, persegi panjang, segitiga, jajargenjang, trapesium, dan lingkaran, dengan cara mudah dan contoh soal.","2026-10-08T23:58:22.588Z",{"id":1923,"subjectId":20,"levelId":145,"parentId":17,"slug":1924,"name":1925,"description":1926,"order":1902,"createdAt":1927,"updatedAt":1927},"demo-v2-topic-pemrograman-sma-2","list-dan-dictionary-python","List dan Dictionary Python","Pahami list dan dictionary Python: indeks, append, key-value, get, dan perulangan, plus perbedaan keduanya lewat contoh pengolahan data nilai siswa.","2026-10-08T23:58:23.694Z",{"id":1929,"subjectId":211,"levelId":141,"parentId":17,"slug":1930,"name":1931,"description":1932,"order":1902,"createdAt":1933,"updatedAt":1933},"demo-v2-topic-fisika-smp-2","rumus-massa-jenis","Massa Jenis","Rumus massa jenis ρ = m\u002FV lengkap dengan satuan kg\u002Fm³ dan g\u002Fcm³, tabel massa jenis air, besi, dan minyak, cara menghitung, serta contoh soal pembahasan.","2026-10-08T23:58:23.217Z",{"id":1935,"subjectId":20,"levelId":141,"parentId":17,"slug":1936,"name":1937,"description":1938,"order":1902,"createdAt":1939,"updatedAt":1939},"demo-v2-topic-pemrograman-smp-2","percabangan-python-if-else","Percabangan Python","Pelajari percabangan Python dengan if, elif, dan else: operator perbandingan, operator logika, dan contoh program nilai rapor lengkap dengan outputnya.","2026-10-08T23:58:23.592Z",{"id":1941,"subjectId":20,"levelId":137,"parentId":17,"slug":1942,"name":1943,"description":1944,"order":1902,"createdAt":1945,"updatedAt":1945},"demo-v2-topic-pemrograman-sd-2","percabangan-dalam-algoritma","Percabangan dalam Algoritma","Percabangan dalam algoritma memilih tindakan berdasarkan syarat jika-maka. Pelajari pengertian, contoh sehari-hari, dan simbol flowchart-nya.","2026-10-08T23:58:23.503Z",{"id":1947,"subjectId":203,"levelId":141,"parentId":17,"slug":1948,"name":1949,"description":1950,"order":1902,"createdAt":1951,"updatedAt":1951},"demo-v2-topic-matematika-smp-2","persamaan-garis-lurus","Persamaan Garis Lurus","Persamaan garis lurus y = mx + c, rumus gradien dari dua titik, garis sejajar dan tegak lurus, cara menggambar grafik, serta contoh soal kelas 8.","2026-10-08T23:58:22.730Z",{"id":1953,"subjectId":211,"levelId":107,"parentId":17,"slug":1954,"name":1955,"description":1956,"order":1902,"createdAt":1957,"updatedAt":1957},"demo-v2-topic-fisika-kuliah-2","usaha-oleh-gaya-berubah","Usaha Gaya Berubah","Usaha oleh gaya berubah dengan integral W = ∫F dx, rumus usaha W = F·s sebagai dot product, usaha pegas, dan teorema usaha–energi, plus contoh soal.","2026-10-08T23:58:23.394Z",{"id":1959,"subjectId":203,"levelId":145,"parentId":17,"slug":1960,"name":1961,"description":1962,"order":1963,"createdAt":1964,"updatedAt":1964},"demo-v2-topic-matematika-sma-3","rumus-peluang","Peluang Kejadian","Rumus peluang P(A) = n(A)\u002Fn(S), ruang sampel, peluang komplemen, frekuensi harapan, kejadian saling lepas dan saling bebas, plus contoh soal dadu dan koin.",102,"2026-10-08T23:58:22.934Z",{"id":1966,"subjectId":20,"levelId":145,"parentId":17,"slug":1967,"name":1968,"description":1969,"order":1963,"createdAt":1970,"updatedAt":1970},"demo-v2-topic-pemrograman-sma-3","pencarian-linear-dan-biner","Pencarian Linear dan Biner","Pelajari pencarian linear dan pencarian biner (binary search): cara kerja, syarat data terurut, kode Python, dan perbandingan jumlah langkahnya.","2026-10-08T23:58:23.724Z",{"id":1972,"subjectId":20,"levelId":141,"parentId":17,"slug":1973,"name":1974,"description":1975,"order":1963,"createdAt":1976,"updatedAt":1976},"demo-v2-topic-pemrograman-smp-3","perulangan-python-for-while","Perulangan Python","Pelajari perulangan Python dengan for, range(), dan while, lengkap dengan contoh program menghitung total, break, continue, dan latihan soal.","2026-10-08T23:58:23.624Z",{"id":1978,"subjectId":20,"levelId":137,"parentId":17,"slug":1979,"name":1980,"description":1981,"order":1963,"createdAt":1982,"updatedAt":1982},"demo-v2-topic-pemrograman-sd-3","perulangan-dalam-algoritma","Perulangan dalam Algoritma","Perulangan dalam algoritma mengulang langkah yang sama beberapa kali. Pelajari pengertian, contoh perulangan sehari-hari, dan cara menghitung hasilnya.","2026-10-08T23:58:23.529Z",{"id":1984,"subjectId":203,"levelId":141,"parentId":17,"slug":1985,"name":1986,"description":1987,"order":1963,"createdAt":1988,"updatedAt":1988},"demo-v2-topic-matematika-smp-3","rumus-prisma-dan-limas","Prisma dan Limas","Rumus volume prisma dan limas, luas permukaan, sifat sisi-rusuk-titik sudut, jaring-jaring, limas 3D interaktif, dan contoh soal bangun ruang sisi datar.","2026-10-08T23:58:22.780Z",{"id":165,"subjectId":20,"levelId":107,"parentId":17,"slug":153,"name":166,"description":155,"order":1963,"createdAt":1990,"updatedAt":1990},"2026-10-08T23:58:23.864Z",{"id":1992,"subjectId":203,"levelId":107,"parentId":17,"slug":1993,"name":1994,"description":1995,"order":1963,"createdAt":1996,"updatedAt":1996},"demo-v2-topic-matematika-kuliah-3","vektor-3-dimensi-dot-product","Vektor 3D dan Dot Product","Vektor 3 dimensi: komponen, panjang vektor, vektor satuan, dot product atau perkalian titik, sudut antara dua vektor, proyeksi, dan contoh soal.","2026-10-08T23:58:23.045Z",{"id":1998,"subjectId":203,"levelId":137,"parentId":17,"slug":1999,"name":2000,"description":2001,"order":1963,"createdAt":2002,"updatedAt":2002},"demo-v2-topic-matematika-sd-3","rumus-volume-kubus","Volume dan Luas Permukaan Kubus","Rumus volume kubus V = s³ dan luas permukaan kubus L = 6s², sifat kubus, jaring-jaring, kubus 3D interaktif, dan contoh soal bertingkat.","2026-10-08T23:58:22.619Z",{"id":2004,"subjectId":203,"levelId":141,"parentId":17,"slug":2005,"name":2006,"description":2007,"order":2008,"createdAt":2009,"updatedAt":2009},"demo-v2-topic-matematika-smp-4","rumus-tabung-dan-kerucut","Tabung dan Kerucut","Rumus volume tabung dan kerucut, luas permukaan, garis pelukis, jaring-jaring berupa persegi panjang dan juring, kerucut 3D interaktif, dan contoh soal.",103,"2026-10-08T23:58:22.828Z",{"id":197,"subjectId":20,"levelId":145,"parentId":17,"slug":186,"name":198,"description":188,"order":2008,"createdAt":2011,"updatedAt":2011},"2026-10-08T23:58:23.755Z",{"id":2013,"subjectId":203,"levelId":137,"parentId":17,"slug":2014,"name":2015,"description":2016,"order":2008,"createdAt":2017,"updatedAt":2017},"demo-v2-topic-matematika-sd-4","rumus-volume-balok","Volume dan Luas Permukaan Balok","Rumus volume balok V = p × l × t dan luas permukaan balok L = 2(pl + pt + lt), sifat balok, jaring-jaring, balok 3D interaktif, dan contoh soal.","2026-10-08T23:58:22.651Z",[]]