should be able to change the shape of the array dynamically.
should be able to add/delete element fast
should be able to insert/delete a element in the middle.
since we need to make this as efficient as possible. Let’s try what would we have done if we had to invent it for ourself.
First, we take the functionality of it and try to simplify it as much as possible.
Here, let’s take only the ‘adding dynamically’ part.
Adding Dynamically
say we have an fixed array of 4 elements. Then, how can we make it such that we can add an element to it.
Here, we know that we need to describe on a fixed space required for our task before hand to utilize a memory (refer to how memory works).
Alternative #1: Make an array of 5 element then copy all the data to the new array.
Here, using this we can make an dynamic array. However, it is very expensive to do this for huge amount of data.
For example, for an 1M length array, we need to perform around 90 billion copies.
Here lets assume we are continuously adding element to the array. So, for 5th element we need 5 copying operation. For the 6th element, we need to first create a new array of size 6 and copy the 6 elements. So here our total operations is 5+6. For the 7th element, it is 5+6+7. In big O notation it is $O(N^2)$.
Alternative #2: Making a new array of size of the fixed array + 8 (say).
Here, it will reduce a lot of copying operations, however it is still of $O(N^2)$ complexity.
Alternative #3: Making the new array the double size of the array.
Here, the number of copying operation needed for an array of size N is always N. So it’s complexity is $O(N)$.
This is very cool problem, so if you are math savvy then take out a piece of paper and do the math, it is quite fun to think about this problem. Find how this is $O(N)$.
This is how programming languages define dynamic arrays.
For deletion, say if the filled element is less that the half of the size then we reduce the size of array by half. Here, this means our memory usage has also been optimized.
Similarly, with this way we can also easily perform insertions and deletion from the middle or front of the array with high speed .
When it comes to language learning, focusing on phrases and sentences rather than isolated words can make a significant difference. While memorizing vocabulary lists might seem like a straightforward approach, it often leaves learners struggling to use those words in real-life situations. Words alone rarely convey complete meaning; context is crucial. By learning phrases and sentences, you naturally absorb grammar, word order, and common expressions, making your speech sound more natural and fluent.
For example, knowing the word “book” is helpful, but learning the phrase “I’d like to book a table” is far more practical. Phrases provide ready-made building blocks for conversation, reducing the mental effort needed to construct sentences from scratch. This approach also helps with pronunciation and intonation, as you practice speaking in chunks rather than isolated syllables.
Moreover, sentences and phrases expose you to cultural nuances and idiomatic expressions that single words cannot convey. This leads to better comprehension when listening or reading, and more confidence when speaking. In summary, prioritizing phrases and sentences accelerates your ability to communicate effectively, making language learning more enjoyable and efficient.
Below are some of the anki decks that can be used:
Deutsch:
German Sentences
Part 1 - A1 and A2: https://ankiweb.net/shared/info/785874566
Part 2 - B1 : https://ankiweb.net/shared/info/17323417
Part 3 - B2-C1 : https://ankiweb.net/shared/info/944971572
German 7000 Intermediate/Advanced Sentences w/ Audio
Part 1 : https://ankiweb.net/shared/info/1125602705
| Compound Noun | Meaning | | ————— | —————- | | Krankenhaus | hospital | | Zahnarzt | dentist | | Augenarzt | eye doctor | | Kopfschmerzen | headache | | Rückenschmerzen | back pain | | Körperpflege | body care | | Krankenkasse | health insurance | | Herzschlag | heartbeat | | Blutdruck | blood pressure | | Hausarzt | family doctor | | Notaufnahme | emergency room | | Krankenwagen | ambulance |
🎓 School & Learning (Schule und Lernen)
| Compound Noun | Meaning | | —————– | ——————- | | Schulbuch | school book | | Lehrerzimmer | teacher’s room | | Sprachschule | language school | | Hausaufgabe | homework | | Klassenarbeit | class test | | Stundenplan | schedule/timetable | | Schultasche | school bag | | Schulweg | way to school | | Schülerausweis | student ID card | | Schulzeit | school time | | Unterrichtsstunde | lesson | | Schulanfang | beginning of school |
