[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":10},"actionData","errors","root",{"_129":130,"_131":132},"routes/public/layout",{"_68":69},"routes/public/primary/notes",{"_11":12,"_13":14},"note",{"_17":44,"_19":44,"_20":59,"_22":60,"_24":61,"_26":27,"_28":62,"_30":63,"_32":63,"_33":64,"_35":65,"_37":66,"_13":67},"backlinks",[15,16],{"_17":41,"_19":41,"_20":47,"_22":48,"_24":49,"_26":27,"_28":50,"_30":51,"_32":51,"_33":52,"_35":53,"_37":54,"_13":55},{"_17":18,"_19":18,"_20":21,"_22":23,"_24":25,"_26":27,"_28":29,"_30":31,"_32":31,"_33":34,"_35":36,"_37":38,"_13":39},"id","computer-science/algorithm/practical-knowledges/insertion-sort/loop-invariant","slug","title","Loop Invariant","path","Computer Science/Algorithm/Practical Knowledges/Insertion Sort/Loop Invariant","canonicalPath","/notes/computer-science/algorithm/practical-knowledges/insertion-sort/loop-invariant","folder","Computer Science","tags",[],"createdAt","2026-07-26T03:12:21.698Z","modifiedAt","excerpt","Loop Invariant adalah [[Subarray]] yang elemennya sudah diurutkan, contohnya seperti subarray di sisi kiri pada Insertion Sort (diwakili tangan kiri dalam ilustrasinya). Loop Invariants membantu kita memahami bagaimana s","html","

Loop Invariant adalah Subarray yang elemennya sudah diurutkan, contohnya seperti subarray di sisi kiri pada Insertion Sort (diwakili tangan kiri dalam ilustrasinya).

Loop Invariants membantu kita memahami bagaimana suatu algoritma dapat memiliki kondisi Correct Algorithm. Saat kita memakai Loop Invariants, ada 3 hal yang perlu diperhatikan:

Pembuktian loop invariant adalah bentuk dari Induksi Matematika.

","outgoing",[44,45,40,42,43,46],[40,41,42,43],"computer-science/algorithm/practical-knowledges/insertion-sort/initialization","computer-science/algorithm/practical-knowledges/insertion-sort/insertion-sort","computer-science/algorithm/practical-knowledges/insertion-sort/maintenance","computer-science/algorithm/practical-knowledges/insertion-sort/termination","computer-science/algorithm/practical-knowledges/insertion-sort/subarray","computer-science/algorithm/theoretical-knowledges/correct-algorithm","computer-science/algorithm/practical-knowledges/insertion-sort/induksi-matematika","Insertion Sort","Computer Science/Algorithm/Practical Knowledges/Insertion Sort/Insertion Sort","/notes/computer-science/algorithm/practical-knowledges/insertion-sort/insertion-sort",[],"2026-07-26T03:12:21.697Z","Insertion sort adalah algoritma sorting (pengurutan) yang paling efisien untuk elemen dalam jumlah kecil. Cara kerjanya mirip seperti mengurutkan kartu dengan tangan kita. Bayangkan ada sebuah tumpukan kartu di meja, kem","

Insertion sort adalah algoritma sorting (pengurutan) yang paling efisien untuk elemen dalam jumlah kecil.

Cara kerjanya mirip seperti mengurutkan kartu dengan tangan kita. Bayangkan ada sebuah tumpukan kartu di meja, kemudian kita mengambil satu kartu untuk dipegang di tangan kiri, lalu kita mengambil kartu baru dengan tangan kanan kemudian menempatkannya di tangan kiri pada posisi yang tepat sesuai kartu yang telah ada.

Diketahui sebuah Sorting Problem sebagai berikut:

Input: Sebuah deretan angka sebanyak n
Output: Sebuah Permutasi dari deret angka input

Berikut solusinya dengan insertion sort dalam Pseudocode:

// Index pertama adalah 1\n\nInsertionSort(A, n)\n\tfor i = 2 to n\n\t\tkey = A[i]\n\t\tj = i - 1\n\t\n\t\t// Memasukkan A[i] ke subarray yang sudah \n\t\t// urut A[1: i - 1]\n\t\twhile j > 0 and A[j] > key\n\t\t\tA[j + 1] = A[j]\n\t\t\tj = j - 1\n\t\tA[j + 1] = key\n

Fungsi tersebut menerima dua input yaitu array berisi deret angka yang ingin diurutkan dengan parameter A dan panjang dari array tersebut dengan parameter n.

Index i adalah kartu yang saat ini sedang diproses. Pada awal perulangan, yang mana indexnya i, Subarray sebelah kiri yang berisi elemen A[1:i-1] mewakili tangan kiri yang memegang kartu yang sudah terurut. Subarray sebelah kanan yang berisi elemen A[i+1:n] mewakili tumpukan kartu yang masih ada di meja. Notasi A[1:i-1] disebut Loop Invariant.

Berikut jika ditulis dalam Typescript:

function insertionSort(numbers: number[]): void {\n  for (let i = 1; i < numbers.length; i++) {\n    const key = numbers[i];\n    let j = i - 1;\n\n    while (j >= 0 && numbers[j] > key) {\n      numbers[j + 1] = numbers[j];\n      j = j - 1;\n    }\n    numbers[j + 1] = key;\n  }\n\n  console.log(\"Sorted array:\", numbers);\n}\n

",[57,58,44,18],[56],"computer-science/algorithm/algorithm","computer-science/algorithm/practical-knowledges/insertion-sort/sorting-problem","general/terms/permutasi","Subarray","Computer Science/Algorithm/Practical Knowledges/Insertion Sort/Subarray","/notes/computer-science/algorithm/practical-knowledges/insertion-sort/subarray",[],"2026-07-26T03:12:21.700Z","Bagian bersebelahan yang dipisahkan oleh Key pada array yang sedang dalam proses sorting.","

Bagian bersebelahan yang dipisahkan oleh Key pada array yang sedang dalam proses sorting.

",[],[41,18],"profile",{"_17":70,"_71":68,"_72":73,"_74":75,"_76":77,"_78":79,"_30":80,"_81":82},"6954a19b11e7fe6da253c845","type","identity",{"_119":120,"_121":122,"_123":124,"_125":126},"contact",{"_111":112,"_113":114},"seo",{"_20":95,"_96":97,"_98":99,"_100":101,"_102":103,"_104":105},"bio",{"_83":84,"_85":86,"_87":88,"_89":90,"_91":92,"_93":94},"2025-12-31T04:07:55.862Z","updatedAt","2026-07-28T08:55:52.260Z","p1","Maulana Hafidz Ismail is an engineer who believes technology isn't just about efficiency. It's about resistance.","p2","While the world optimizes for profit, he builds to question the system itself: in education, work, and how we define value.","p3","His background blends engineering precision with entrepreneurial instinct. He has worked across software development, database systems, and AI, always driven by one goal: to make tools that actually serve people, not the hierarchy itself.","closing","This site is his lab. He writes journals to document a process, articles to share thought, and papers to formalize the things he learns.","tagline","Some ideas fail, some evolve, all of them teach.","callToAction","If you're building, rebelling, or just thinking about how to make things better, you're already part of the conversation.","Maulana Hafidz","description","Technical articles, engineering notes, system design explorations, and project documentation by Maulana Hafidz Ismail, an Engineer documenting real software systems.","shortDescription","Maulana Hafidz Ismail is an Engineer and Entrepreneur in training. Redefining fairness in education, work, and governance.","url","https://maulanahafidz.com","image","https://maulanahafidz.com/og-image.jpg","keywords",[106,107,108,109,110],"Meta Engineer","Entrepreneur","Software Engineer","AI Developer","System Designer","email","contact@maulanahafidz.com","socials",{"_115":116,"_117":118},"github","https://github.com/imhefizh/","linkedin","https://www.linkedin.com/in/maulana-hafidz-ismail/","fullName","Maulana Hafidz Ismail","shortName","ImHefizh","titles",[127,128],"subtitle","Building systems that question the system.","Software Engineering","Entrepreneurship","nonce","5502a268c335478e8fa051241f167264","language","EN"]

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