it allow us to talk formally about how the runtime of an algorithm grows as the input grows.
n = number of operation the computer has to do can be: f(n) = n f(n) = n^2 f(n) = 1
f(n) = could be something entirely different !
O(n):
function addUpToSimple(n: number) {
let total = 0;
for (let i = 0; i < n; i++) {
total += i;
}
return total;
}O(1):
function addUpComplex(n: number) {
return (n * (n + 1)) / 2;
}O(n): maybe thinking O(2n) but we see big picture! BigONotation doesn't care about precision only about general trends linear? quadric? constant?
function printUpAndDown(n: number) {
console.log("Going up");
for (let i = 0; i < n; i++) {
console.log(i);
}
console.log("Going down");
for (let j = n - 1; j > 0; j--) {
console.log(j);
}
}O(n^2)
function printAllPairs(n: number) {
for (let i = 0; i < n; i++) {
console.log(i);
for (let j = 0; j < n; j++) {
console.log(j);
}
}
}O(n) : cuz as soon as n grows complexity grows too
function logAtLeastFive(n: number) {
for (let i = 0; i <= Math.max(5, n); i++) {
console.log(i);
}
}O(1)
function logAtMostFive(n: number) {
for (let i = 0; i <= Math.min(5, n); i++) {
console.log(i);
}
}Rules of Thumb
- most primitive booleans numbers undefined null are constant space.
- strings and reference types like objects an arrays require O(n) space n is string length or number of keys
O(1)
function sum(arr: number[]) {
let total = 0;
for (let i = 0; i < arr.length; i++) {
total += arr[i];
}
}O(n)
function double(arr: number[]) {
const newArr = [];
for (let i = 0; i < arr.length; i++) {
array.push(arr[i] * 2);
}
return newArr;
}object:
const person = { name: "John", age: 22, hobbies: ["reading", "sleeping"] };
Object.keys(person); // ["name", "age", "hobbies"] O(n)
Object.values(person); // ["John", 22, Array(2)] O(n)
Object.entries(person); // [Array(2), Array(2), Array(2)] O(n)
person.hasOwnProperty("name"); // true O(1)array: push() and pop() are always faster from unshift() and shift() cuz inserting or removing element from beginning of an array needs reIndexing all elements
O(n^3)
function same(arrOne: number[], arrTwo: number[]): boolean {
if (arrOne.length !== arrTwo.length) {
return false;
}
for (let element of arrOne) {
// for O(n)
if (!arrTwo.includes(element ** 2)) {
// includes cuz iterate over all indexes O(n)
return false;
}
arrTwo.splice(arrTwo.indexOf(element ** 2), 1); // indexOf cuz iterate over all indexes O(n)
}
return true;
}frequencyCounter:
O(n)
function same(arr1: number[], arr2: number[]) {
if (arr1.length !== arr2.length) {
return false;
}
const frequencyCounter1 = {};
const frequencyCounter2 = {};
for (let val of arr1) {
frequencyCounter1[val] = (frequencyCounter1[val] || 0) + 1;
}
for (let val of arr2) {
frequencyCounter2[val] = (frequencyCounter2[val] || 0) + 1;
}
for (let key in frequencyCounter1) {
const sqrtKey = parseInt(key, 10) ** 2;
if (
!(sqrtKey in frequencyCounter2) || // interesting ** in ** check if object contains key
frequencyCounter2[sqrtKey] !== frequencyCounter1[key]
) {
return false;
}
}
return true;
}O(n)
// approach one
function validAnagram(str1: string, str2: string): boolean {
if (str1.length !== str2.length) {
return false;
}
const frequencyCount1 = {};
const frequencyCount2 = {};
for (let value of str1) {
frequencyCount1[value] = (frequencyCount1[value] || 0) + 1;
}
for (let value of str2) {
frequencyCount2[value] = (frequencyCount2[value] || 0) + 1;
}
for (let key in frequencyCount1) {
if (frequencyCount1[key] !== frequencyCount2[key]) {
return false;
}
}
return true;
}
// approach two
function validAnagram(str1: string, str2: string): boolean {
if (str1.length !== str2.length) {
return false;
}
const frequencyCount = {};
for (let i = 0; i < str1.length; i++) {
const currentElement = str1[i];
frequencyCount[currentElement]
? (frequencyCount[currentElement] += 1)
: (frequencyCount[currentElement] = 1);
}
for (let i = 0; i < str2.length; i++) {
const currentElement = str2[i];
if (!frequencyCount[currentElement]) {
return false;
} else {
frequencyCount[currentElement] -= 1;
}
}
return true;
}O(n^2)
function sumZero(arr: number[]) {
for (let i = 0; i < arr.length; i++) {
for (let j = i + 1; j < arr.length; j++) {
if (arr[i] + arr[j] === 0) {
return [arr[i], arr[j]];
}
}
}
}multiple pointers:
O(n)
function sumZero(arr: number[]) {
let left = 0;
let right = arr.length - 1;
while (left < right) {
const sum = arr[left] + arr[right];
if (sum === 0) {
return [arr[left], arr[right]];
} else if (sum > 0) {
right--;
} else {
left++;
}
}
}O(n)
// my approach
function countUniqueValues(arr: number[]): number {
let pointer = 0;
let count = 0;
while (pointer < arr.length) {
if (arr[pointer] === arr[pointer + 1]) {
pointer++;
} else {
count++;
pointer++;
}
}
return count;
}
// steele approach
function countUniqueValues(arr: number[]): number {
if (arr.length === 0) {
return 0;
}
let i = 0;
for (let j = 1; j < arr.length; j++) {
if (arr[i] !== arr[j]) {
i++;
arr[i] = arr[j];
}
}
return i + 1;
}O(n^2)
function maxSubArraySum(arr: number[], n: number): number | null {
if (arr.length < n) {
return null;
}
let max = -Infinity;
for (let i = 0; i < arr.length - n + 1; i++) {
let tmp = 0;
for (let j = 0; j < n; j++) {
tmp += arr[i + j];
}
if (tmp > max) {
max = tmp;
}
}
return max;
}O(n)
sliding window:
function maxSubArraySum(arr: number[], n: number): number | null {
if (arr.length < n) {
return null;
}
let maxSum = 0;
let tmpSum = 0;
for (let i = 0; i < n; i++) {
maxSum += arr[i];
}
for (let i = n; i < arr.length; i++) {
tmpSum = tmpSum - arr[i - n] + arr[i];
maxSum = Math.max(tmpSum, maxSum);
}
return maxSum;
}linearSearch
O(n)
function linearSearch(arr, val): number {
for (let i = 0; i < arr.length; i++) {
if (arr[i] === val) {
return i;
}
}
return -1;
}divide an conquer:
binarySearch
O (Log n)
function binarySearch(sortedArr: number[], value: number): number {
let min = 0;
let max = sortedArr.length - 1;
while (min <= max) {
let middle = Math.floor((min + max) / 2);
if (sortedArr[middle] < value) {
min = middle + 1;
} else if (sortedArr[middle] > value) {
max = middle - 1;
} else {
return middle;
}
}
return -1;
}a process that calls itself
quick note around callStack
function wakeUp() {
// callStack [wakeUp]
takeShower();
eatBreakfast();
console.log("Ready to go ... ");
} // callStack []
function takeShower() {
// callStack [takeShower, wakeUp]
console.log("taking shower");
} // callStack[wakeUp]
function eatBreakfast() {
// callStack [eatBreakfast, wakeUp]
const meal = cookBreakFast();
console.log(`eating ${meal}`);
} // callStack [wakeUp]
function cookBreakFast() {
// callStack [cookBreakFast, eatBreakfast, wakeUp]
const meals = ["Cheese", "Protein Shake", "Coffee"];
return meals[Math.floor(Math.random() * meals.length)]; // callStack [eatBreakFast, wakeUp]
}
wakeUp();two essential part of recursive functions
- base case : end of the line
- different input : recursive should call by different piece of data
function sumRange(num: number) {
if (num === 1) return 1;
return num + sumRange(num - 1);
}
function factorial(num: number) {
if (num === 1) return 1;
return num * factorial(num - 1);
}helper method recursion vs pure recursion
// helper method recursion approach
function collectOdd(arr: number[]) {
const result = [];
function helper(helperArr: number[]) {
if (!helperArr.length) {
return;
}
if (helperArr[0] % 2 !== 0) {
result.push(helperArr[0]);
}
helper(helperArr.slice(1));
}
helper(arr);
return result;
}
// pure recursion approach
function collectOdd(arr: number[]): number[] {
let result = [];
if (!arr.length) {
return result;
}
if (arr[0] % 2 !== 0) {
result.push(arr[0]);
}
result = collectOdd(result.concat(arr.slice(1)));
return result;
}indexOf() includes() find() findIndex() all this methods doing linear search behind the scene
O(n)
function linearSearch(arr: number[], value: number): number {
for (let i = 0; i < arr.length; i++) {
if (arr[i] === value) {
return i;
}
return -1;
}
}O(Log n)
function binarySearch(sortedArr: number[], value: number): number {
let left = 0;
let right = sortedArr.length - 1;
while (left <= right) {
const middle = Math.round((right + left) / 2);
if (sortedArr[middle] > value) {
right = middle - 1;
} else if (sortedArr[middle] < value) {
left = middle + 1;
} else {
return middle;
}
}
return -1;
}O(n^2)
function naiveStringSearch(long: string, pattern: string): number {
let count = 0;
for (let i = 0; i < long.length; i++) {
for (let j = 0; j < pattern.length; j++) {
if (pattern[j] !== long[i + j]) {
break;
}
if (j === pattern.length - 1) {
count++;
}
}
}
return count;
}array.sort(cb?) will turn all values to string then sort it based on it's unicode
["a", "c", "b", "f", "d"].sort(); // (5) ["a", "b", "c", "d", "f"]
[1, 10, 6, 8, 2, 3, 5].sort(); //(7) [1, 10, 2, 3, 5, 6, 8]
/*
also receive callback function by two arguments:
a: previous number
b: next number
*/
// if callback return NEGATIVE number a will placed before b
[1, 10, 6, 8, 2, 3, 5].sort((a, b) => a - b); // (7) [1, 2, 3, 5, 6, 8, 10]
// if callback return POSITIVE number a will placed after b
(7)[(1, 2, 3, 5, 6, 8, 10)].sort((a, b) => b - a); // (7) [10, 8, 6, 5, 3, 2, 1]
// if callback return ZERO a and b will placed at the same position
general: O(n^2) nearlySortedData: O(n)
function bubbleSort(arr: number[]): number[] {
for (let i = 0; i < arr.length; i++) {
let noSwap = true;
for (let j = 0; j < arr.length - i; j++) {
if (arr[j] > arr[j + 1]) {
[arr[j], arr[j + 1]] = [arr[j + 1], arr[j]];
noSwap = false;
}
}
if (noSwap) break;
}
return arr;
}
// or
function bubbleSort(arr: number[]): number[] {
for (let i = arr.length; i > 0; i--) {
let noSwap = true;
for (let j = 0; j < i - 1; j++) {
if (arr[j] > arr[j + 1]) {
[arr[j], arr[j + 1]] = [arr[j + 1], arr[j]];
noSwap = false;
}
}
if (noSwap) break;
}
return arr;
}
O(n^2)
function selectionSort(arr: number[]) {
for (let i = 0; i < arr.length; i++) {
let min = i;
for (let j = i + 1; j < arr.length; j++) {
if (arr[j] < arr[min]) {
min = j;
}
}
if (min !== i) {
[arr[i], arr[min]] = [arr[min], arr[i]];
}
}
return arr;
}
general: O(n^2) nearlySortedData: O(n)
function insertionSort(arr) {
var currentVal;
for (let i = 1; i < arr.length; i++) {
currentVal = arr[i];
for (var j = i - 1; j >= 0 && arr[j] > currentVal; j--) {
arr[j + 1] = arr[j];
}
arr[j + 1] = currentVal;
}
return arr;
}| Algorithm | Time Complexity (Best) | Time Complexity (Average) | Time Complexity (worst) | Space Complexity |
|---|---|---|---|---|
| bubble sort | O(n) | O(n^2) | O(n^2) | O(1) |
| insertion sort | O(n) | O(n^2) | O(n^2) | O(1) |
| selection sort | O(n^2) | O(n^2) | O(n^2) | O(1) |
O(n Log n)
// merge two sorted array
function merge(arr1: number[], arr2: number[]): number[] {
let result = [];
let i = 0;
let j = 0;
while (i < arr1.length && j < arr2.length) {
if (arr1[i] < arr2[j]) {
result.push(arr1[i]);
i++;
} else {
result.push(arr2[j]);
j++;
}
}
while (i < arr1.length) {
result.push(arr1[i]);
i++;
}
while (j < arr2.length) {
result.push(arr2[j]);
j++;
}
return result;
}
function mergeSort(arr: number[]): number[] {
if (arr.length <= 1) return arr;
const middle = Math.floor(arr.length / 2);
const left = mergeSort(arr.slice(0, middle));
const right = mergeSort(arr.slice(middle));
return merge(left, right);
}
in following implementation we always assume first item as pivot
general: O(n Log n) sorted: O(n^2)
// place pivot in the right index and return pivot index
function pivot(arr: number[], start = 0, end = arr.length - 1) {
const pivot = arr[start];
let pivotIndex = start;
for (let i = start + 1; i < end; i++) {
if (arr[i] < pivot) {
pivotIndex++;
[arr[pivotIndex], arr[i]] = [arr[i], arr[pivotIndex]];
}
}
[arr[start], arr[pivotIndex]] = [arr[pivotIndex], arr[start]];
}
function quickSort(arr: number[], start = 0, end = arr.length - 1) {
if (left < right) {
const pivot = pivot(arr, start, end);
// left
quickSort(arr, start, pivotIndex - 1);
// right
quickSort(arr, pivotIndex + 1, end);
}
return arr;
}
O(nk) n: the number of items we sorting k: average length of those numbers
// get the actual number at the given index
function getDigit(num: number, i: number): number {
return Math.floor(Math.abs(num) / Math.pow(10, i)) % 10;
}
// get number length
function digitCount(num: number): number {
if (num === 0) return 1;
return Math.floor(Math.log10(Math.abs(num))) + 1;
}
// return number by most length
function mostDigits(arr: number[]): number {
let maxDigits = 0;
for (let i = 0; i < arr.length; i++) {
maxDigits = Math.max(maxDigits, digitCount(arr[i]));
}
return maxDigits;
}
function radixSort(arr: number[]): number[] {
let maxDigitCount = mostDigits(arr);
for (let k = 0; k < maxDigitCount; k++) {
let digitBuckets = Array.from({ length: 10 }, () => []);
for (let j = 0; j < arr.length; j++) {
digitBuckets[getDigit(arr[j], k)].push(arr[j]);
}
arr = [].concat(...digitBuckets);
}
return arr;
}| Algorithm | Time Complexity (Best) | Time Complexity (Average) | Time Complexity (worst) | Space Complexity |
|---|---|---|---|---|
| merge sort | O(n Log n) | O(n Log n) | O(n Log n) | O(n) |
| quick sort | O(n Log n) | O(n Log n) | O(n^2) | O(Log n) |
| radix sort | O(nk) | O(nk) | O(nk) | O(n + k) |
| DataStructure | Insertion | Removal | Searching | Access |
|---|---|---|---|---|
| Singly Linked List | O(1) | bestCase(very beginning): O(1) worstCase(very end): O(n) | O(n) | O(n) |
| Doubly Linked List | O(1) | O(1) | O(n) it is faster than Singly Linked List | O(n) |
| Stack | O(1) | O(1) | O(n) | O(n) |
| Queue | O(1) | O(1) | O(n) | O(n) |
| Binary Search Tree | O( Log n) | - | O(Log n) | - |
| Binary Heap | O( Log n) | O( Log n) | O( n ) | - |
| Hash Tables | O( 1 ) | O( 1 ) | - | O( 1 ) |
class _Node {
constructor(public value: any) {}
public next: _Node | null = null;
}
class SinglyLinkedList {
private _length: number = 0;
private head: _Node | null = null;
private tail: _Node | null = null;
get length() {
return this._length;
}
get print(): null | _Node[] {
if (!this._length) return null;
const arr = [];
let currentNode = this.head;
while (currentNode) {
arr.push(currentNode.value);
currentNode = currentNode.next;
}
return arr;
}
public push(value: any): SinglyLinkedList {
const node = new _Node(value);
if (!this.head || !this.tail) {
this.head = node;
this.tail = this.head;
} else {
this.tail.next = node;
this.tail = node;
}
this._length += 1;
return this;
}
public pop(): _Node | null {
if (!this.head) return null;
let currentNode = this.head;
if (!currentNode.next) {
this.head = null;
this.tail = null;
this._length -= 1;
return currentNode;
}
while (currentNode.next && currentNode.next.next) {
currentNode = currentNode.next;
}
this.tail = currentNode;
this.tail.next = null;
this._length -= 1;
return currentNode.next as _Node;
}
public unShift(value: any): SinglyLinkedList {
const currentHead = this.head;
this.head = new _Node(value);
if (currentHead) {
this.head.next = currentHead;
} else {
this.tail = this.head;
}
this._length += 1;
return this;
}
public shift(): _Node | null {
if (!this.head) return null;
const currentHead = this.head;
this.head = currentHead.next;
this._length -= 1;
if (currentHead === this.tail) this.tail = null;
return currentHead;
}
public get(index: number): _Node | null {
if (index < 0 || index >= this._length) return null;
let currentNode = this.head;
for (let j = 0; j < index; j++) {
if (currentNode && currentNode.next) {
currentNode = currentNode.next;
}
}
return currentNode;
}
public set(index: number, value: any): _Node | null {
const node = this.get(index);
if (node) {
node.value = value;
}
return node;
}
public insert(index: number, value: any): SinglyLinkedList | null {
if (index < 0 || index >= this._length) {
return null;
} else if (index === 0) {
return this.unShift(value);
} else if (index === this._length) {
return this.push(value);
} else {
const prevNode = this.get(index - 1);
if (prevNode) {
const newNode = new _Node(value);
newNode.next = prevNode.next;
prevNode.next = newNode;
this._length += 1;
return this;
}
return prevNode;
}
}
public remove(index: number): _Node | null {
if (index === 0) {
return this.shift();
} else if (index === this._length - 1) {
return this.pop();
} else {
const prevNode = this.get(index - 1);
const currentNode = this.get(index);
if (prevNode && currentNode) {
prevNode.next = currentNode.next;
this._length -= 1;
}
return currentNode;
}
}
public reverse(): SinglyLinkedList | false {
if (this._length <= 1) return false;
let node = this.head;
this.head = this.tail;
this.tail = node;
let next: _Node | null;
let prev: _Node | null = null;
for (let i = 0; i < this._length; i++) {
if (node) {
next = node.next;
node.next = prev;
prev = node;
node = next;
}
}
return this;
}
}class _Node {
public next: _Node | null = null;
public prev: _Node | null = null;
constructor(public value: any) {}
}
class DoublyLinkedList {
private head: _Node | null = null;
private tail: _Node | null = null;
private _length = 0;
get length() {
return this._length;
}
get print(): null | _Node[] {
if (!this._length) return null;
const arr = [];
let currentNode = this.head;
while (currentNode) {
arr.push(currentNode.value);
currentNode = currentNode.next;
}
return arr;
}
public push(value: any): DoublyLinkedList {
const node = new _Node(value);
if (!this.tail) {
this.head = node;
} else {
this.tail.next = node;
node.prev = this.tail;
}
this._length += 1;
this.tail = node;
return this;
}
public pop(): _Node | null {
if (!this.tail) {
return null;
}
const currentTail = this.tail;
if (currentTail.prev) {
this.tail = currentTail.prev;
this.tail.next = null;
currentTail.prev = null;
} else {
this.head = null;
this.tail = null;
}
this._length -= 1;
return currentTail;
}
public shift(): null | _Node {
if (!this.head) {
return null;
}
const currentHead = this.head;
if (currentHead.next) {
this.head = currentHead.next;
this.head.prev = null;
currentHead.next = null;
} else {
return this.pop();
}
this._length -= 1;
return currentHead;
}
public unshift(value: any): DoublyLinkedList {
if (!this.head) {
return this.push(value);
}
const node = new _Node(value);
const currentHead = this.head;
this.head = node;
this.head.next = currentHead;
currentHead.prev = this.head;
this._length += 1;
return this;
}
public get(index: number): null | _Node {
if (index < 0 || index >= this._length) return null;
let currentNode: _Node | null = null;
if (index < Math.floor(this._length / 2)) {
// iterate from head to tail
currentNode = this.head;
for (let i = 0; i < index; i++) {
if (currentNode && currentNode.next) {
currentNode = currentNode.next;
}
}
} else {
// iterate from tail to head
currentNode = this.tail;
for (let i = this._length - 1; i > index; i--) {
if (currentNode && currentNode.prev) {
currentNode = currentNode.prev;
}
return currentNode;
}
}
return currentNode;
}
public set(index: number, value: any): _Node | null {
const node = this.get(index);
if (node) {
node.value = value;
}
return node;
}
public insert(index: number, value: any): DoublyLinkedList | null {
if (index < 0 || index > this._length) {
return null;
} else if (index === 0) {
return this.unshift(value);
} else if (index === this._length) {
return this.push(value);
} else {
const prevNode = this.get(index - 1);
const nextNode = this.get(index);
if (prevNode && nextNode) {
const newNode = new _Node(value);
prevNode.next = newNode;
(newNode.prev = prevNode), (newNode.next = nextNode);
nextNode.prev = newNode;
}
}
this._length += 1;
return this;
}
public remove(index: number): DoublyLinkedList | null {
if (index < 0 || index > this._length) {
return null;
} else if (index === 0) {
this.shift();
} else if (index === this._length - 1) {
this.pop();
} else {
const node = this.get(index);
if (node && node.prev && node.next) {
(node.prev.next = node.next), (node.next.prev = node.prev);
(node.next = null), (node.prev = null);
}
this._length -= 1;
}
return this;
}
}LIFO last in first out
// implement stack using array
const stack = [1, 2, 3];
stack.push(4); // [1,2,3,4]
stack.pop(); // [1,2,3]
// stacks just have push and pop
stack.unshift(0); // [0,1,2,3]
stack.shift(); // [1,2,3]// implementing stack using singly linked list
class _Node {
public next: _Node | null = null;
constructor(public value: any) {}
}
class Stack {
private first: _Node | null = null;
private last: _Node | null = null;
private _length = 0;
get length(): number {
return this._length;
}
push(value: any): Stack {
const node = new _Node(value);
const currentFirst = this.first;
(this.first = node), (this.first.next = currentFirst);
if (!currentFirst) {
this.last = node;
}
this._length += 1;
return this;
}
pop(): _Node | null {
const currentFirst = this.first;
if (currentFirst) {
if (this.first === this.last) this.last = currentFirst.next;
this.first = currentFirst.next;
this._length -= 1;
}
return currentFirst;
}
}FIFO first in first out
// implementing queue using array
const q = [];
q.push(1);
q.push(2);
q.shift(1); // out first items first
// or
q.shift(1);
q.shift(2);
q.pop(); // out first items first// implementing queue using singly linked list
class _Node {
public next: _Node | null = null;
constructor(public value: any) {}
}
class Queue {
private first: _Node | null = null;
private last: _Node | null = null;
private _length = 0;
get length(): number {
return this._length;
}
enqueue(value: any): Queue {
const node = new _Node(value);
if (!this.last) {
(this.first = node), (this.last = node);
} else {
this.last.next = node;
this.last = node;
}
this._length += 1;
return this;
}
dequeue(): _Node | null {
const currentFirst = this.first;
if (currentFirst) {
if (this.first === this.last) this.last = null;
this.first = currentFirst.next;
this._length -= 1;
}
return currentFirst;
}
}- root : top node of tree
- child : a node directly connected to another node when moving away from root
- parent : the converse notion of a child
- sibling : a group of nodes with the same parent
- leaf : a child with no children
- edge : connection from two node
- every parent node has at most two children
- every node to the left of parent node is always less than the parent
- every node to the right of parent node is always greater than the parent
class _Node {
constructor(public value: number) {}
public left: _Node | null = null;
public right: _Node | null = null;
}
class BinarySearchTree {
public root: _Node | null = null;
public insert(value: number): BinarySearchTree | null {
const node = new _Node(value);
if (!this.root) {
this.root = node;
} else {
let currentNode: _Node = this.root;
do {
if (value === currentNode.value) return null;
if (value < currentNode.value) {
if (currentNode.left) {
currentNode = currentNode.left;
} else {
currentNode.left = node;
break;
}
} else {
if (currentNode.right) {
currentNode = currentNode.right;
} else {
currentNode.right = node;
break;
}
}
} while (currentNode);
}
return this;
}
public have(value: number): boolean {
let currentNode = this.root;
while (currentNode) {
if (value === currentNode.value) {
return true;
} else {
if (value < currentNode.value) {
if (currentNode.left) {
currentNode = currentNode.left;
continue;
}
break;
} else {
if (currentNode.right) {
currentNode = currentNode.right;
continue;
}
break;
}
}
}
return false;
}
}there is two main strategies to traversal a tree : Breadth-first-search and Depth-first-search
class _Node {
constructor(public value: number) {}
public left: _Node | null = null;
public right: _Node | null = null;
}
class BinarySearchTree {
public root: _Node | null = null;
public insert(value: number): BinarySearchTree | null {
const node = new _Node(value);
if (!this.root) {
this.root = node;
} else {
let currentNode: _Node = this.root;
do {
if (value === currentNode.value) return null;
if (value < currentNode.value) {
if (currentNode.left) {
currentNode = currentNode.left;
} else {
currentNode.left = node;
break;
}
} else {
if (currentNode.right) {
currentNode = currentNode.right;
} else {
currentNode.right = node;
break;
}
}
} while (currentNode);
}
return this;
}
public have(value: number): boolean {
let currentNode = this.root;
while (currentNode) {
if (value === currentNode.value) {
return true;
} else {
if (value < currentNode.value) {
if (currentNode.left) {
currentNode = currentNode.left;
}
break;
} else {
if (currentNode.right) {
currentNode = currentNode.right;
continue;
}
break;
}
}
}
return false;
}
/*
breadth first search (bfs) : traverse tree horizontally
*/
public bfs(): _Node[] {
const visited: _Node[] = [];
if (this.root) {
const q: _Node[] = [this.root];
while (q.length) {
if (q[0].left) q.push(q[0].left);
if (q[0].right) q.push(q[0].right);
visited.push(q[0]), q.shift();
}
}
return visited;
}
/*
depth first search (dfs) : traverse tree vertically
following contains three dfs searching methods:
1. preOrder : add node => going to left and add left => going to right and add right
2. postOrder : going to left and add left => going to right and add right => going to node and add node
3. inOrder : going to the left and add left => add node => going to the right and add right
*/
public dfsPreOrder(): _Node[] {
const visited: _Node[] = [];
if (this.root) {
(function traverse(node: _Node): void {
visited.push(node);
if (node.left) {
traverse(node.left);
}
if (node.right) {
traverse(node.right);
}
})(this.root);
}
return visited;
}
public dfsPostOrder(): _Node[] {
const visited: _Node[] = [];
if (this.root) {
(function traverse(node: _Node): void {
if (node.left) {
traverse(node.left);
}
if (node.right) {
traverse(node.right);
}
visited.push(node);
})(this.root);
}
return visited;
}
dfsInOrder(): _Node[] {
const visited: _Node[] = [];
if (this.root) {
(function traverse(node: _Node) {
if (node.left) {
traverse(node.left);
}
visited.push(node);
f;
if (node.right) {
traverse(node.right);
}
})(this.root);
}
return visited;
}
}depth-first vs breadth-first : they both timeComplexity is same but spaceComplexity is different if we got a wide tree like this:
breadth-first take up more space. cuz we adding more element to queue.
if we got a depth long tree like this:
depth-first take up more space.
potentially use cases for dfs variants (preOder postOrder inOrder) preOrder is useful when we want a clone of tree. inOrder is useful when we want data in order that it's stored in tree.
- a binary heap is as compact as possible (all the children of each node are as full as they can be and left children and filled out first)
- each parent has at most two children
Max Binary Heap:
- parent nodes are always greater than child nodes but there is no guarantees between sibling
Min Binary Heap:
- child nodes are always greater than parent nodes but there is no guarantees between sibling
class MaxBinaryHeap {
private _values: number[] = [];
get values(): number[] {
return this._values;
}
private sinkingUp(value: number): void {
let valueIndex = this._values.length - 1;
while (valueIndex > 0) {
const parentIndex = Math.floor((valueIndex - 1) / 2);
const parent = this._values[parentIndex];
if (value <= parent) break;
this._values[parentIndex] = value;
this._values[valueIndex] = parent;
valueIndex = parentIndex;
}
}
private sinkingDown(): void {
let targetIndex = 0;
while (true) {
let leftChildIndex = targetIndex * 2 + 1,
rightChildIndex = targetIndex * 2 + 2;
let target = this._values[targetIndex],
leftChild = this._values[leftChildIndex],
rightChild = this._values[rightChildIndex];
if (target < leftChild && target < rightChild) {
if (rightChild > leftChild) {
[
this._values[targetIndex],
this._values[rightChildIndex]
] = [
this._values[rightChildIndex],
this._values[targetIndex]
];
targetIndex = rightChildIndex;
} else {
[
this._values[targetIndex],
this._values[leftChildIndex]
] = [
this._values[leftChildIndex],
this._values[targetIndex]
];
targetIndex = leftChildIndex;
}
continue;
} else if (rightChild >= target) {
[this._values[targetIndex], this._values[rightChildIndex]] = [
this._values[rightChildIndex],
this._values[targetIndex]
];
targetIndex = leftChildIndex;
continue;
} else if (leftChild >= target) {
[this._values[targetIndex], this._values[leftChildIndex]] = [
this._values[leftChildIndex],
this._values[targetIndex]
];
targetIndex = leftChildIndex;
continue;
}
break;
}
}
public insert(value: number): number[] {
this._values.push(value);
this.sinkingUp(value);
return this._values;
}
public extractMax(): number | null {
if (!this._values.length) {
return null;
}
const root = this._values[0];
this._values[0] = this._values[this._values.length - 1];
this._values.pop();
this.sinkingDown();
return root;
}
}A data structure which every element has a priority. Elements with higher priorities are served before elements with lower priorities.
In the following example, we implemented a priority queue using minBinaryHeap but you should know binaryHeaps and priority queue is two different concepts and we just use an abstract of it
interface INode {
value: any;
priority: number;
}
class _Node implements INode {
constructor(public value: any, public priority: number = 0) {}
}
class PriorityQueue {
private _values: INode[] = [];
get values(): INode[] {
return this._values;
}
private sinkingUp(node: INode): void {
let valueIndex = this._values.length - 1;
while (valueIndex > 0) {
const parentIndex = Math.floor((valueIndex - 1) / 2);
const parent = this._values[parentIndex];
if (node.priority >= parent.priority) break;
this._values[parentIndex] = node;
this._values[valueIndex] = parent;
valueIndex = parentIndex;
}
}
private sinkingDown(): void {
let targetIndex = 0;
while (true) {
let leftChildIndex = targetIndex * 2 + 1,
rightChildIndex = targetIndex * 2 + 2;
let target = this._values[targetIndex],
leftChild = this._values[leftChildIndex],
rightChild = this._values[rightChildIndex];
if (
leftChild &&
rightChild &&
target.priority > leftChild.priority &&
target.priority > rightChild.priority
) {
if (rightChild.priority < leftChild.priority) {
[
this._values[targetIndex],
this._values[rightChildIndex]
] = [
this._values[rightChildIndex],
this._values[targetIndex]
];
targetIndex = rightChildIndex;
} else {
[
this._values[targetIndex],
this._values[leftChildIndex]
] = [
this._values[leftChildIndex],
this._values[targetIndex]
];
targetIndex = leftChildIndex;
}
continue;
} else if (rightChild && rightChild.priority <= target.priority) {
[this._values[targetIndex], this._values[rightChildIndex]] = [
this._values[rightChildIndex],
this._values[targetIndex]
];
targetIndex = leftChildIndex;
continue;
} else if (leftChild && leftChild.priority <= target.priority) {
[this._values[targetIndex], this._values[leftChildIndex]] = [
this._values[leftChildIndex],
this._values[targetIndex]
];
targetIndex = leftChildIndex;
continue;
}
break;
}
}
public enqueue({ value, priority }: INode): _Node[] {
const node = new _Node(value, priority);
this._values.push(node);
this.sinkingUp(node);
return this._values;
}
public dequeue(): _Node | null {
if (!this._values.length) {
return null;
}
const root = this._values[0];
this._values[0] = this._values[this._values.length - 1];
this._values.pop();
this.sinkingDown();
return root;
}
}Hash tables are collection of key-value pairs
There is possibility for handle collisions is hash tables :
- Separate chaining ( e.g. using nested arrays of key values implemented in following hash tables )
- linear probing ( if index filled place {key, value} in next position )
type El = [string, any];
class HashTable {
private keyMap: El[][];
constructor(size: number = 53) {
this.keyMap = new Array(size);
}
public _hash(key: string): number {
let total = 0;
const WEIRD_PRIME = 31;
for (let i = 0; i < key.length; i++) {
const characterCode = key.charCodeAt(i) - 96;
total = (total + characterCode * WEIRD_PRIME) % this.keyMap.length;
}
return total;
}
set(key: string, value: any): El[][] {
const index = this._hash(key);
if (!this.keyMap[index]) {
this.keyMap[index] = [];
}
this.keyMap[index].push([key, value]);
return this.keyMap;
}
get(key: string): El | undefined {
const index = this._hash(key);
const elements = this.keyMap[index];
if (elements) {
for (let value of elements) {
if (value[0] === key) return value[1];
}
}
return undefined;
}
get keys(): string[] {
const keys: string[] = [];
for (let value of this.keyMap) {
if (value) {
for (let _value of value) {
keys.push(_value[0]);
}
}
}
return keys;
}
get values(): any[] {
const values = new Set<any>();
for (let value of this.keyMap) {
if (value) {
for (let _value of value) {
values.add(value[1]);
}
}
}
return [...values];
}
}A graph data structure consists of a finite (and possibly mutable) set of vertices or nodes or points, together with a set of unordered pairs of these vertices for an undirected graph or a set of ordered pairs for directed graph.
-
vertex :node
-
edge : connection between nodes
-
directed/ undirected graph: in directed graph there is a direction assigned to vertices an in undirected no direction assigned.
-
weighted/ unweighted graph: in weighted graph there is a weight associated by edges but in unweighted graph no weight assigned to edges
| Operation | Adjacency List | Adjacency Matrix |
|---|---|---|
| Add vertex | O(1) | O(V^2) |
| Add Edge | O(1) | O(1) |
| Remove vertex | O(V+E) | O(V^2) |
| Remove Edge | O(E) | O(1) |
| Query | O(V+E) | O(1) |
| Storage | O(V+E) | O(V^2) |
- |V| : number of Vertices
- |E| : number of Edges
- Adjacency List take less space in sparse graph( when we have a few edges ).
- Adjacency List are faster to iterate over edges.
- Adjacency Matrix are faster to finding a specific edge.
interface AdjacencyList {
[vertex: string]: string[];
}
class Graph {
private _adjacencyList: AdjacencyList = {};
public get adjacencyList(): AdjacencyList {
return this._adjacencyList;
}
public set adjacencyList(value: AdjacencyList) {
this._adjacencyList = value;
}
public addVertex(vertex: string): AdjacencyList {
this._adjacencyList[vertex] = [];
return this._adjacencyList;
}
public addEdge(vertex1: string, vertex2: string): boolean {
if (this._adjacencyList[vertex1] && this._adjacencyList[vertex2]) {
this._adjacencyList[vertex1].push(vertex2),
this._adjacencyList[vertex2].push(vertex1);
return true;
}
return false;
}
public removeEdge(vertex1: string, vertex2: string): boolean {
if (this._adjacencyList[vertex1] && this._adjacencyList[vertex2]) {
(this._adjacencyList[vertex1] = this._adjacencyList[vertex1].filter(
(value: string) => value !== vertex2
)),
(this._adjacencyList[vertex2] = this._adjacencyList[
vertex2
].filter((value: string) => value !== vertex1));
return true;
}
return false;
}
public removeVertex(vertex: string): string | undefined {
if (this._adjacencyList[vertex]) {
for (let key in this._adjacencyList) {
this.removeEdge(key, vertex);
}
delete this._adjacencyList[vertex];
return vertex;
}
return undefined;
}
}interface AdjacencyList {
[vertex: string]: string[];
}
class Graph {
private _adjacencyList: AdjacencyList = {};
public get adjacencyList(): AdjacencyList {
return this._adjacencyList;
}
public set adjacencyList(value: AdjacencyList) {
this._adjacencyList = value;
}
public addVertex(vertex: string): AdjacencyList {
this._adjacencyList[vertex] = [];
return this._adjacencyList;
}
public addEdge(vertex1: string, vertex2: string): boolean {
if (this._adjacencyList[vertex1] && this._adjacencyList[vertex2]) {
this._adjacencyList[vertex1].push(vertex2),
this._adjacencyList[vertex2].push(vertex1);
return true;
}
return false;
}
public removeEdge(vertex1: string, vertex2: string): boolean {
if (this._adjacencyList[vertex1] && this._adjacencyList[vertex2]) {
(this._adjacencyList[vertex1] = this._adjacencyList[vertex1].filter(
(value: string) => value !== vertex2
)),
(this._adjacencyList[vertex2] = this._adjacencyList[
vertex2
].filter((value: string) => value !== vertex1));
return true;
}
return false;
}
public removeVertex(vertex: string): string | undefined {
if (this._adjacencyList[vertex]) {
for (let key in this._adjacencyList) {
this.removeEdge(key, vertex);
}
delete this._adjacencyList[vertex];
return vertex;
}
return undefined;
}
public dfcRecursive(startingVertex: string): string[] {
const results: string[] = [];
const adjacencyList = this._adjacencyList;
let currentVertex = this._adjacencyList[startingVertex];
if (currentVertex) {
const visitedVertex: { [vertex: string]: boolean } = {};
(function traverse(vertex: string | undefined): void {
if (!vertex) return;
if (!visitedVertex[vertex]) {
visitedVertex[vertex] = true;
results.push(vertex);
for (let neighbor of currentVertex) {
if (!visitedVertex[neighbor]) {
currentVertex = adjacencyList[neighbor];
traverse(neighbor);
}
}
}
})(startingVertex);
}
return results;
}
// or
public dfsIterative(startingVertex: string): string[] {
const results: string[] = [];
if (this._adjacencyList[startingVertex]) {
let stack: string[] = [startingVertex];
const visitedVertex: { [vertex: string]: boolean } = {};
while (stack.length) {
debugger;
const currentVertex = stack.pop();
if (currentVertex && !visitedVertex[currentVertex]) {
visitedVertex[currentVertex] = true;
results.push(currentVertex);
stack = [...stack, ...this._adjacencyList[currentVertex]];
}
}
}
return results;
}
public breadthFirstSearch(startingVertex: string): string[] {
const results: string[] = [];
if (this._adjacencyList[startingVertex]) {
let queue = [startingVertex];
const visitedVertex: { [vertex: string]: boolean } = {};
while (queue.length) {
const currentVertex = queue.shift();
if (currentVertex && !visitedVertex[currentVertex]) {
visitedVertex[currentVertex] = true;
results.push(currentVertex);
queue = [...queue, ...this._adjacencyList[currentVertex]];
}
}
}
return results;
}
}Finding shortest path between two vertices in a weighted graph.
interface Value {
value: any;
priority: number;
}
interface Neighbor {
vertex: string;
weight: number;
}
interface AdjacencyList {
[vertex: string]: Neighbor[];
}
// naive priority queue
class PriorityQueue {
private _values: Value[] = [];
public get values(): Value[] {
return this._values;
}
public enqueue(value: any, priority: number): Value[] {
this._values.push({ value, priority });
this.sort();
return this._values;
}
public dequeue(): Value {
const value = this._values.shift();
return value as Value;
}
private sort() {
this._values.sort((a: Value, b: Value) => a.priority - b.priority);
}
}
class WeightedGraph {
private _adjacencyList: AdjacencyList = {};
public get adjacencyList(): AdjacencyList {
return this._adjacencyList;
}
public set adjacencyList(value: AdjacencyList) {
this._adjacencyList = value;
}
public addVertex(vertex: string): AdjacencyList {
this._adjacencyList[vertex] = [];
return this._adjacencyList;
}
public addEdge(vertex1: string, vertex2: string, weight: number): boolean {
if (this._adjacencyList[vertex1]) {
this._adjacencyList[vertex1].push({ vertex: vertex2, weight });
this._adjacencyList[vertex2].push({ vertex: vertex1, weight });
return true;
}
return false;
}
/*
dijkstra shortest path first
*/
dijkstraSPF(startingVertex: string, targetVertex: string): string[] {
let path: string[] = [];
if (
this._adjacencyList[startingVertex] &&
this._adjacencyList[targetVertex]
) {
const pq = new PriorityQueue();
const previousVertex: { [vertex: string]: string | null } = {};
const distances: { [vertex: string]: number } = {};
// build initial states
for (let key in this._adjacencyList) {
if (key === startingVertex) {
(distances[key] = 0), pq.enqueue(key, 0);
} else {
distances[key] = Infinity;
pq.enqueue(key, Infinity);
}
previousVertex[key] = null;
}
while (pq.values.length) {
let smallest = pq.dequeue().value;
if (smallest) {
if (smallest === targetVertex) {
// done build path
while (
previousVertex[smallest] ||
smallest === startingVertex
) {
path.push(smallest);
smallest = previousVertex[smallest];
}
break;
}
for (let neighbor of this._adjacencyList[smallest]) {
const candidate = distances[smallest] + neighbor.weight;
let nextNeighbor = neighbor.vertex;
if (candidate < distances[nextNeighbor]) {
distances[nextNeighbor] = candidate;
previousVertex[nextNeighbor] = smallest;
pq.enqueue(nextNeighbor, candidate);
}
}
}
}
}
return path.reverse();
}
}It's a method for solving a complex problems by breaking it down into a collection of simpler problems, solving their subProblems once and storing their solutions. technically it using knowledge of last problems to solve next by memorization
Let's implement it without dynamic programming:without dynamic programming:
in fibonacci sequence fib(n) = fib(n-2) + fib(n-1) && fin(1) = 1 && fib(2) = 1
O(2^n)
function fib(n: number): number {
if (n <= 2) return 1;
return fib(n - 1) + fib(n - 2);
}
As you see we calculate f(5) two times with current implementation.
Storing the results of expensive function class and returning the cached result when the same inputs occur again.
O(n)
function fib(n: number, memo: number[] = []): number {
if (memo[n]) return memo[n];
if (n <= 2) return 1;
const res = fib(n - 1, memo) + fib(n - 2, memo);
memo[n] = res;
return res;
}
fib(10000); // Maximum callStack exceededfunction fib(n: number): number {
if (n <= 2) return 1;
const fibNumbers = [0, 1, 1];
for (let index = 3; index <= n; index++) {
fibNumbers[index] = fibNumbers[index - 1] + fibNumbers[index - 2];
}
console.log(fibNumbers);
return fibNumbers[n];
}
fib(10000); // Infinity// turn it to boolean
console.log(!!1); // true
console.log(!!0); // false
// group operation
(newNode.prev = prevNode), (newNode.next = nextNode);const str = "hello";
str.search('lo') || .indexOf('lo') // 3
str.includes('lo') // true// regex.test(str: number) Returns a Boolean value that indicates whether or not a pattern exists in a searched string.
function charCount(str: string) {
const result: { [key: string]: number } = {};
for (let char of str) {
char = char.toLowerCase();
if (/[a-z0-9]/.test(char)) {
result[char] = ++result[char] || 1;
}
}
return result;
}
// *** string.chatCodeAt(i: number) Returns the unicode of value on specified location
/*
numeric (0-9) code > 47 && code < 58;
upper alpha (A-Z) code > 64 && code < 91;
lower alpha (a-z) code > 96 && code <123;
*/
function charCount(str: string) {
const result: { [key: string]: number } = {};
for (let char of str) {
if (isAlphaNumeric(char)) {
char = char.toLowerCase();
result[char] = ++result[char] || 1;
}
}
return result;
}
function isAlphaNumeric(char: string) {
const code = char.charCodeAt(0);
if (
!(code > 47 && code < 58) &&
!(code > 64 && code < 91) &&
!(code > 96 && code < 123)
) {
return false;
}
return true;
}const array = ["hello", "world"];
arr.find(el => el === "world"); // world
arr.findIndex(el => el === "world"); // 1
[1, 2].includes(1); // true
Array.from({ length: 2 }, () => ["lol"]); // [["lol"], ["lol"]]
const stack = ["A", "B", "D", "E", "C", "F"];
const s = stack.shift();
const p = stack.pop();
console.log(s); // "A"
console.log(p); // "F"
["a", "b"].reverse(); // ['b', 'a']delete this._adjacencyList[vertex]; // delete key and value from object
delete this._adjacencyList.vertex;const map = new Map();
// store any type of **unique key** of use duplicate key it will override last value
map.set({ 1: "Object" }, "Object");
map.set(["arr"], "arr");
map.set(1, "number");
map.set(false, "boolean");
map.set(() => console.log("Function"), "Function");
console.log(map);
/*
0: {Object => "Object"}
1: {Array(1) => "arr"}
2: {1 => "number"}
3: {false => "boolean"}
4: {function () { return console.log("Function"); } => "Function"}
*/
// iterable by **for (let [key, value] of map)**
for (let [key, value] of map) console.log(key, value);
// map to arr
const arr = [...map]; // :[ [key, value] ]
/*
0: (2) [{…}, "Object"]
1: (2) [Array(1), "arr"]
2: (2) [1, "number"]
3: (2) [false, "boolean"]
4: (2) [ƒ, "Function"]
*/Math.pow(2, 2); // 4
Math.abs(-5); // 5
Math.log10(100); // 10
Math.max(...[1, 2, 3]); // 3
Math.min(...[1, 2, 3]); // 1
React
Typescript
Django
Laravel
Facebook
Microsoft
Google
Alibaba
D3
Tencent