Blog
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Some problems are naturally two-dimensional: printing grids, building tables, scanning pairs \((i,j)\), summing over regions like \(1 \le j \le i \le N\). A nested loop is just a loop inside another loop—perfect for “for each row, for each column” patterns. The key mental model: Once you see nested loops as row × column, the… Continue reading.
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Sometimes you don’t want to count; you want to act on each element of a known set. The range-based for loop expresses exactly that: It reads naturally: “for each element in this range.” This is great for finite sums/products, evaluating a function at a handful of sample points, or scanning a short list of special… Continue reading.
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Loops repeat work, but sometimes you can decide earlier than your loop’s end whether more work is needed. Two simple tools help: These are especially handy in mathematical code where a condition tells you you’re done (first divisor found, threshold reached) or where some cases are irrelevant (skip evens, skip multiples of 3). We’ll use… Continue reading.
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Once the basic for pattern clicks (i = 0; i < N; i = i + 1), the next hurdle is realizing you can tune both the step and the check to match the problem. Many tasks aren’t “count by ones”; they skip elements, grow geometrically, or stop when a mathematical condition becomes false. This… Continue reading.
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Sooner or later you need to do the same action many times—check several candidates, accumulate a sum over steps, run a procedure for a fixed number of iterations. Writing the same line ten times won’t scale. A loop solves this by repeating a block of code automatically. The classic C++ for loop is the simplest… Continue reading.
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Most programs need to communicate: show results to a user and read values to decide what to do next. C++ provides two standard streams for console programs: They’re part of the <iostream> library and give you a uniform way to send values out and bring values in. The same ideas later extend to files and… Continue reading.
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Real programs respond to situations: a value might be inside a valid range, a file might exist, a counter might have reached a limit. To react, code must branch—follow one path when a requirement holds and a different path when it doesn’t. The simplest way to create such a branch in C++ is the if… Continue reading.
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In the previous post of this thread, I explored the nature of forces. In this post, I will go into more detail on how forces act on physical objects. The central law is Newton’s third law. Action-Reaction Pairs (Newton’s Third Law) Newton’s third law provides a profound insight into how forces actually arise: every force… Continue reading.
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In our previous discussions, we explored Newton’s laws of motion and saw how reference frames shape our description of motion. At the heart of Newtonian mechanics is the concept of a force—a physical influence capable of changing an object’s state of motion, causing acceleration. Forces provide the fundamental way objects interact with one another. Whenever… Continue reading.
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This post continues the exploration of predicate logic, highlighting its expressiveness compared to propositional logic, discussing its limitations, and outlining applications in various fields. Advanced Expressiveness Compared to Propositional Logic Propositional logic treats whole sentences as indivisible. Predicate logic can talk about individuals and relations between them, and it can express generality and existence. Here… Continue reading.
