Big-O & Complexity Basics

DSARoadmap/Big-O & Complexity Basics/README.md

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+# Big-O & Complexity Basics
+
+## 1. Why Big-O Matters
+
+Big-O isn't about exact time taken, it's about **how code scales when the input size grows**. We want to be able to say:
+
+- **"This function gets slower linearly as data grows"** → `O(n)`
+- **"This function's time stays the same regardless of input"** → `O(1)`
+
+## 2. Common Big-O Notations
+
+Here's the quick reference:
+
+| Notation | Name | Example Scenario |
+|----------|------|------------------|
+| `O(1)` | Constant | Accessing an array element by index |
+| `O(log n)` | Logarithmic | Binary search |
+| `O(n)` | Linear | Looping through an array once |
+| `O(n log n)` | Linearithmic | Merge sort |
+| `O(n²)` | Quadratic | Nested loops over the same array |
+| `O(2ⁿ)` | Exponential | Solving Tower of Hanoi |
+| `O(n!)` | Factorial | Permutations of a set |
+
+## 3. How to Identify Big-O from Code
+
+### Example 1 — O(1)
+
+```javascript
+const getFirst = (arr) => arr[0];
+```
+
+**Analysis:** Accessing the first element doesn't depend on array size → **`O(1)`**.
+
+### Example 2 — O(n)
+
+```javascript
+const printItems = (arr) => {
+  for (let i = 0; i < arr.length; i++) {
+    console.log(arr[i]);
+  }
+};
+```
+
+**Analysis:** One loop → grows linearly with size → **`O(n)`**.
+
+### Example 3 — O(n²)
+
+```javascript
+const printPairs = (arr) => {
+  for (let i = 0; i < arr.length; i++) {
+    for (let j = 0; j < arr.length; j++) {
+      console.log(arr[i], arr[j]);
+    }
+  }
+};
+```
+
+**Analysis:** Two nested loops → **`O(n²)`**.
+
+## 4. Space Complexity
+
+Same idea but for **memory usage**:
+
+- **`O(1)`**: Uses a fixed amount of extra memory
+- **`O(n)`**: Extra memory grows with input size (like making a copy of the array)
+
+### Example:
+
+```javascript
+const copyArray = (arr) => {
+  let newArr = [...arr]; // takes extra space proportional to n
+  return newArr;
+}; // Space: O(n)
+```
+
+## 5. Practice Problems
+
+I want you to look at code and tell me the Big-O.
+
+### Problem 1:
+
+```javascript
+function sumAll(n) {
+  let sum = 0;
+  for (let i = 1; i <= n; i++) {
+    sum += i;
+  }
+  return sum;
+}
+```
+
+**Your Answer:** `O(?)`
+
+### Problem 2:
+
+```javascript
+function printArrayTwice(arr) {
+  for (let i = 0; i < arr.length; i++) console.log(arr[i]);
+  for (let j = 0; j < arr.length; j++) console.log(arr[j]);
+}
+```
+
+**Your Answer:** `O(?)`
+
+### Problem 3:
+
+```javascript
+function logTrios(arr) {
+  for (let i = 0; i < arr.length; i++) {
+    for (let j = 0; j < arr.length; j++) {
+      for (let k = 0; k < arr.length; k++) {
+        console.log(arr[i], arr[j], arr[k]);
+      }
+    }
+  }
+}
+```
+
+**Your Answer:** `O(?)`
+
+---
+
+## Quick Tips
+
+- **Drop constants**: `O(2n)` becomes `O(n)`
+- **Drop lower order terms**: `O(n² + n)` becomes `O(n²)`
+- **Nested loops multiply**: Two nested loops = `O(n²)`
+- **Sequential loops add**: Two separate loops = `O(n + n)` = `O(2n)` = `O(n)`

DSARoadmap/README.md

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+## Table of Contents
+
+- [Big-O & Complexity Basics](./Big-O%20&%20Complexity%20Basics/)