big o notation

Author: Prakharnagore000

1. Big O Notation/1.1 bigONotation.js

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+// To analyze the performance of an algorithm, we use Big O Notation
+// Big O Notation can give us a high level understanding of the time or space complexity of an algorithm
+// big o notation is a way to formalize fuzzy counting
+// it allows us to talk formally about how the runtime of an algorithm grows as the inputs grow
+// Example - O(1), O(n), O(n*n)
+
+// Time Complexity
+// it allows us to talk formally about how the runtime of an algorithm grows as the inputs grow
+// Big O Shorthands
+// Arithmetic operations are constant
+// Variable assignment is constant
+// Accessing elements in an array (by index) or object (by key) is constant
+// In a loop, the the complexity is the length of the loop times the complexity of whatever happens inside of the loop
+
+// Big O Chart
+// O(n!)
+// O(2^n)
+// O(n^2)
+// O(n log n)
+// O(n)
+// O(log n) or O(1)
+
+// Space Complexity
+// how much additional memory do we need to allocate in order to run the code in our algorithm?
+// Rules of Thumb
+// Most primitives (booleans, numbers, undefined, null) are constant space
+// Strings require O(n) space (where n is the string length)
+// Reference types are generally O( n), where n is the length (for arrays) or the number of keys (for objects)
+// The time or space complexity (as measured by Big O) depends only on the algorithm, not the hardware used to run the algorithm
+
+// Performance Tracker Tool
+// https://rithmschool.github.io/function-timer-demo/

1. Big O Notation/1.2 addUptoSlower.js

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+function addUpTo(n) {
+ let total = 0;
+ for (let i = 1; i <= n; i++) {
+ total += i;
+ }
+ return total;
+}
+
+var t1 = performance.now();
+addUpTo(1000000000);
+var t2 = performance.now();
+console.log(`Time Elapsed: ${(t2 - t1) / 1000} seconds.`);

1. Big O Notation/1.3 addUptoFaster.js

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+function addUpTo(n) {
+ return (n * (n + 1)) / 2;
+}
+
+var time1 = performance.now();
+addUpTo(1000000000);
+var time2 = performance.now();
+console.log(`Time Elapsed: ${(time2 - time1) / 1000} seconds.`);