From 269f6fd1a0ffacf266f4ac6fb35424e0042a7457 Mon Sep 17 00:00:00 2001 From: mistlog Date: Sun, 22 Dec 2019 14:48:08 +0800 Subject: [PATCH] init --- .github/workflows/build.yml | 31 + .gitignore | 2 + jest.config.js | 5 + package-lock.json | 5206 +++++++++++++++++ package.json | 25 + .../linear-list/polynomial-addition.md | 199 + source-view/linear-list/topological-sort.md | 248 + source-view/tree/huffman-tree.md | 41 + source-view/tree/inorder-traverse.md | 75 + src/common/binary-tree.ts | 33 + src/linear-list/polynomial-addition.ts | 51 + src/linear-list/polynomial-addition.tsx | 244 + src/linear-list/topological-sort.ts | 69 + src/linear-list/topological-sort.tsx | 289 + src/tree/huffman-tree.ts | 23 + src/tree/huffman-tree.tsx | 49 + src/tree/inorder-traverse.ts | 38 + src/tree/inorder-traverse.tsx | 79 + test/__snapshots__/tree.test.ts.snap | 105 + test/linear-list.test.ts | 104 + test/tree.test.ts | 41 + tsconfig.json | 8 + 22 files changed, 6965 insertions(+) create mode 100644 .github/workflows/build.yml create mode 100644 .gitignore create mode 100644 jest.config.js create mode 100644 package-lock.json create mode 100644 package.json create mode 100644 source-view/linear-list/polynomial-addition.md create mode 100644 source-view/linear-list/topological-sort.md create mode 100644 source-view/tree/huffman-tree.md create mode 100644 source-view/tree/inorder-traverse.md create mode 100644 src/common/binary-tree.ts create mode 100644 src/linear-list/polynomial-addition.ts create mode 100644 src/linear-list/polynomial-addition.tsx create mode 100644 src/linear-list/topological-sort.ts create mode 100644 src/linear-list/topological-sort.tsx create mode 100644 src/tree/huffman-tree.ts create mode 100644 src/tree/huffman-tree.tsx create mode 100644 src/tree/inorder-traverse.ts create mode 100644 src/tree/inorder-traverse.tsx create mode 100644 test/__snapshots__/tree.test.ts.snap create mode 100644 test/linear-list.test.ts create mode 100644 test/tree.test.ts create mode 100644 tsconfig.json diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml new file mode 100644 index 0000000..6e12679 --- /dev/null +++ b/.github/workflows/build.yml @@ -0,0 +1,31 @@ +name: build + +on: [push] + +jobs: + build: + + runs-on: ubuntu-latest + + strategy: + matrix: + node-version: [8.x, 10.x, 12.x] + + steps: + - uses: actions/checkout@v1 + - name: Use Node.js ${{ matrix.node-version }} + uses: actions/setup-node@v1 + with: + node-version: ${{ matrix.node-version }} + - name: npm install, build, and test + run: | + npm ci + npm run build --if-present + npm test + env: + CI: true + - name: Coveralls GitHub Action + uses: coverallsapp/github-action@v1.0.1 + with: + token: ${{ secrets.CODECOV_TOKEN }} + github-token: ${{ secrets.github_token }} \ No newline at end of file diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..3091757 --- /dev/null +++ b/.gitignore @@ -0,0 +1,2 @@ +node_modules +coverage \ No newline at end of file diff --git a/jest.config.js b/jest.config.js new file mode 100644 index 0000000..cbade16 --- /dev/null +++ b/jest.config.js @@ -0,0 +1,5 @@ +module.exports = { + preset: 'ts-jest', + testEnvironment: 'node', + notify: true +}; \ No newline at end of file diff --git a/package-lock.json b/package-lock.json new file mode 100644 index 0000000..a1c2b08 --- /dev/null +++ b/package-lock.json @@ -0,0 +1,5206 @@ +{ + "name": "lit-algorithm", + "version": "0.0.1", + "lockfileVersion": 1, + "requires": true, + "dependencies": { + "@babel/code-frame": { + "version": "7.5.5", + "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.5.5.tgz", + "integrity": "sha512-27d4lZoomVyo51VegxI20xZPuSHusqbQag/ztrBC7wegWoQ1nLREPVSKSW8byhTlzTKyNE4ifaTA6lCp7JjpFw==", + "dev": true, + "requires": { + "@babel/highlight": "7.5.0" + } + }, + "@babel/core": { + "version": "7.7.7", + "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.7.7.tgz", + "integrity": 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a/source-view/linear-list/polynomial-addition.md b/source-view/linear-list/polynomial-addition.md new file mode 100644 index 0000000..c0dd303 --- /dev/null +++ b/source-view/linear-list/polynomial-addition.md @@ -0,0 +1,199 @@ +# Polynomial Addition + +## Item + +```typescript +export class Item { + m_Coefficient: number; + m_Exponential: number; +} +``` + +The item is in the form of $ ax^{e_1}y^{e_2}z^{e_3} $, and $ -6xy^{5} = -6x^{1}y^{5}z^{0} $ will be represented as: +```json +{ + m_Coefficient:-6, + m_Exponential:150 +} +``` + +## Polynomial + +Polynomial is a collection of items: + +```typescript +export class Polynomial { + m_Items: Array; +} +``` + +As for polynomial, $x^6-6xy^5+5y^6$ would be represented as: +```json +[ + { + m_Coefficient:1, + m_Exponential:600 + }, + { + m_Coefficient:-6, + m_Exponential:150 + }, + { + m_Coefficient:5, + m_Exponential:60 + } +] +``` + +The convention is that items of polynomial are stored so that exponential is in decreasing order. + +## Addtion Algorithm + +In this algo, we add **this** polynomial to **another**, and **another** polynomial will be modified. + +For example, let $p=x+y+z$ and $q=x^2-2y-z$, after adding $p$ to $q$, $q$ would be $x^2+x-y$. + +```typescript + + + function Add(this: Polynomial, another: Polynomial) { + const P = this.m_Items; + const Q = [...another.m_Items]; + let p = 0; + let q = 0; + for (;;) { + if (P[p].m_Exponential < Q[q].m_Exponential) { + ; + } else if (P[p].m_Exponential === Q[q].m_Exponential) { + ; + ; + } else if (P[p].m_Exponential > Q[q].m_Exponential) { + ; + } + } + }; +``` + +### Overview + +The essence of this algo is that we will maintain two pointers $p$ and $q$, and during each iteration we will find opportunity to add item of $P$ to $Q$. + +### Exponential: item at p < item at q + +For example, when adding $x+y+z$ to $x^2-2y-z$, we set $p$ and $q$ to 0, which means we want to add $x$ to $x^2$. + +However, we find that it's impossible because exponential of $x$ is less than $x^2$, which means this item can't be added to this position in $q$. + +> Don't forget about the convention that exponential is in decreasing order. + +In this situation, we keep $p$ and advance $q$ to next position to inspect next item of $Q$, that's because items are stored in decreasing order and exp at $p$ is less than that at $q$, and there may be oppotunity to add it to next item with smaller exp of $Q$. + +### Items with same exponential + +It's intuitive to handle this case: + +```typescript +function AddCoefficients(P: Array, Q: Array, p: number, q: number) { + Q[q].m_Coefficient += P[p].m_Coefficient; + ; +} +``` + +If we add $y$ to $-2y$, we can just sum up the coefficient, however, the sum can be zero. For example if we add $z$ to $-z$, we get $0z$, it's not necessary to store it in polynomial. + +```typescript +function CheckIfDeleteZeroItem(Q: Array, p: number, q: number) { + if (Q[q].m_Coefficient === 0) { + ; + } else { + ; + } + ; +} +``` + +Removing item at $q$ results in $q$ pointing to next item of $Q$ so that we should do nothing about $q$. + +In addtion to adding coefficients, there is another case that we reach both end of polynomial: + +```typescript +function CheckIfFinishedAndReturn(P: Array, Q: Array, p: number) { + /** + * the last item of any polynomial is always + * { + m_Coefficient:0, + m_Exponential:-1 + * } + */ + if (P[p].m_Exponential < 0) { + Q.pop(); + return Reflect.construct(Polynomial, [Q]); + } +} +``` + +### Insert item + +Let's return to adding $x$ to $x^2$, we move to $-2y$ and find that exp of $x$ is greater than that of $y$, which means you can't find a place to add $x$, because if you move to next item of $Q$, you still get item with exp less than $x$. + +Instead, we will insert $x$ as an item to $Q$: + +```typescript +function InsertNewItem(P: Array, Q: Array, p: number, q: number) { + const new_item = Reflect.construct(Item, [P[p].m_Coefficient, P[p].m_Exponential]); + ; + ; + ; +} +``` + +## Appendix + +### Trival Initialization + +```typescript + + + function constructor(this: Item, coefficient: number, exponential: number) { + this.m_Coefficient = coefficient; + this.m_Exponential = exponential; + }; +``` + +```typescript + + + function constructor(this: Polynomial, items: Array) { + /** + * trick: add a sentinel node at the end of every polynomial for consistence + */ + this.m_Items = [...items, Reflect.construct(Item, [0, -1])]; + }; +``` + +### Trival Implementation + +```typescript +function MoveToNextItemOfQ(q: number) { + q += 1; +} +``` + +```typescript +function MoveToNextItemOfP(p: number) { + p += 1; +} +``` + +```typescript +function RemoveItemAtQ(Q: Array, q: number) { + Q.splice(q, 1); +} +``` + +```typescript +function InsertItemAtQ(Q: Array, q: number, new_item: Item) { + Q.splice(q, 0, new_item); +} +``` + +# Reference + +This algo is adapted from TAOCP I 2.2.4. \ No newline at end of file diff --git a/source-view/linear-list/topological-sort.md b/source-view/linear-list/topological-sort.md new file mode 100644 index 0000000..7f33e74 --- /dev/null +++ b/source-view/linear-list/topological-sort.md @@ -0,0 +1,248 @@ +# Topological Sort + +## Relation + +```typescript +export class Relation { + m_X: number; + m_Y: number | null; +} +``` + +The relation is in the form of $x y +} +``` + +When $y$ is null, it means that $x$ has no successor and predecessor, and we will represent $x; +} +``` + +We want to process relation and get most out of it. For each number, we will associate a relation info with it. + +```dot +digraph G { + 1 -> 2 + 1 -> 3 + 0 -> 1 + -1 -> 1 +} +``` + +For example, if we have $1<2$,$1<3$,$0<1$ and $-1<1$, then the info associated with $1$ would be: + +```json +{ + m_DirectPredecessorsCount:2, + m_DirectSuccessors:[2,3] + +} +``` + +## Sort Algorithm + +```typescript +export class TopologicalSort { + m_RelationsInfo: Map; + m_OutputQueue: Array; + m_Output: Array; +} +``` + +```typescript + + + function Sort(this: TopologicalSort) { + while (this.m_OutputQueue.length !== 0) { + ; + ; + } + return this.m_Output; + }; +``` + +In this algo, we will maintain an output queue. For example, if we have relations $0 3 + 2 -> 4 + 3 -> 4 +} +``` + +We want to at first pick up all numbers that has no predecessor. As it's obvious that we can arrange them first so that there won't be any conflict. + +For example, initially, $0$ and $2$ will be added to output queue. + +### Dequeue + +```typescript +function AddToOutput(this: TopologicalSort) { + const front = this.m_OutputQueue.shift(); + this.m_Output.push(front); +} +``` + +We can safely dequeue an number and add it to the final output array, and then erase all relations related to it, since it's already in the finnal output, we can remove it from the diagram. + +### Erase Relations + +```typescript +function EraseRelations(this: TopologicalSort, front: number) { + const front_info = this.m_RelationsInfo.get(front); + front_info.m_DirectSuccessors.forEach(successor => { + ; + ; + }); +} +``` + +For example, we remove $0$ from the diagram and get: + +```dot +digraph G { + 2 -> 3 + 2 -> 4 + 3 -> 4 +} +``` + +then we will remove 2 and get: + +```dot +digraph G { + 3 -> 4 +} +``` + +at this point, the output array is +```json +[0,2] +``` + +Then, it's obvious that we can continue to find number that has no predecessor and repeat untill there is no more number in the diagram, that's what ```CheckIfAddToOuputQueue ``` does: + +```typescript +function CheckIfAddToOuputQueue(successor_info: RelationInfo, successor: number) { + if (successor_info.m_DirectPredecessorsCount === 0) { + this.m_OutputQueue.push(successor); + } +} +``` + +### Initialize m_RelationsInfo + +As is shown above, ```m_RelationsInfo``` is the essence of this algo, but how to initialize it? + +```typescript + + + function constructor(this: TopologicalSort, relations: Array) { + ; + ; + }; +``` + +```typescript +function InitializeFromRawRelations(this: TopologicalSort, relations: Array) { + relations.forEach(relation => { + ; + ; + }); + ; +} +``` + +For each relation, we will update info related to both $x$ and $y$: + +```typescript +function EnsureRelationInfoExists(this: TopologicalSort, relation: Relation) { + [relation.m_X, relation.m_Y].forEach(value => { + if (value !== null && !this.m_RelationsInfo.has(value)) { + this.m_RelationsInfo.set(value, new RelationInfo()); + } + }); +} +``` + +```typescript +function RecordRelations(this: TopologicalSort, relation: Relation) { + if (relation.m_Y) { + const x_info = this.m_RelationsInfo.get(relation.m_X); + x_info.m_DirectSuccessors.push(relation.m_Y); + const y_info = this.m_RelationsInfo.get(relation.m_Y); + y_info.m_DirectPredecessorsCount += 1; + } +} +``` + +### Initialize m_OutputQueue + +Here zero means "zero predecessor". + +```typescript +function ScanForZeros(this: TopologicalSort) { + this.m_RelationsInfo.forEach((info, key) => { + if (info.m_DirectPredecessorsCount === 0) { + this.m_OutputQueue.push(key); + } + }); +} +``` + +## Appendix + +### Trival Initialization + +```typescript + + + function constructor(this: Relation, x: number, y: number | null) { + this.m_X = x; + this.m_Y = y; + }; +``` + +```typescript + + + function constructor(this: RelationInfo) { + this.m_DirectPredecessorsCount = 0; + this.m_DirectSuccessors = new Array(); + }; +``` + +```typescript +function InitializeMember(this: TopologicalSort) { + this.m_RelationsInfo = new Map(); + this.m_OutputQueue = new Array(); + this.m_Output = new Array(); +} +``` + +### Trival Implementation + +```typescript +function DecreaseDirectPredecessorsCount(this: TopologicalSort, successor: number) { + const successor_info = this.m_RelationsInfo.get(successor); + successor_info.m_DirectPredecessorsCount -= 1; +} +``` + +# Reference + +This algo is adapted from TAOCP I 2.2.3. \ No newline at end of file diff --git a/source-view/tree/huffman-tree.md b/source-view/tree/huffman-tree.md new file mode 100644 index 0000000..cc46892 --- /dev/null +++ b/source-view/tree/huffman-tree.md @@ -0,0 +1,41 @@ +```typescript +export class HuffmanTree { + m_Root: HuffmanNode; +} +``` + +```typescript +export class HuffmanNode extends NumberNode {} +``` + +```typescript + + + function constructor(this: HuffmanTree, values: Array) { + ; + ; + ; + }; +``` + +```typescript +function PrepareQueue(values: Array) { + const queue = new PriorityQueue({ comparator: (a: HuffmanNode, b: HuffmanNode) => a.m_Info - b.m_Info, initialValues: values.map(each => new NumberNode(each)) }); +} +``` + +```typescript +function SetRoot(this: HuffmanTree, queue: PriorityQueue) { + this.m_Root = queue.dequeue(); +} +``` + +```typescript +function CombineNodes(queue: PriorityQueue) { + while (queue.length !== 1) { + const left = queue.dequeue(); + const right = queue.dequeue(); + const node = new HuffmanNode(left.m_Info + right.m_Info, left, right); + queue.queue(node); + } +} +``` \ No newline at end of file diff --git a/source-view/tree/inorder-traverse.md b/source-view/tree/inorder-traverse.md new file mode 100644 index 0000000..ef7b09a --- /dev/null +++ b/source-view/tree/inorder-traverse.md @@ -0,0 +1,75 @@ +```typescript +export class InorderTraverse { + m_Stack: Array; + m_Visited: Array; +} +``` + +```typescript + + + function Traverse(this: InorderTraverse & IInorderTraverse, root: StringNode) { + let current = root; + for (;;) { + if (current) { + ; + } else { + ; + ; + ; + } + } + }; +``` + +```typescript +function AddCurrentToTobeVisited(this: InorderTraverse, current: StringNode) { + this.m_Stack.push(current); + current = current.m_Left as StringNode; +} +``` + +```typescript +function CheckIfFinished(this: InorderTraverse) { + if (this.m_Stack.length === 0) { + return; + } +} +``` + +```typescript +function VisitStringNode(this: IInorderTraverse, current: StringNode) { + this.Visit(current); + current = current.m_Right as StringNode; +} +``` + +```typescript +function SetCurrentAsTobeVisited(this: InorderTraverse, current: StringNode) { + current = this.m_Stack.pop(); +} +``` + +```typescript + + + function constructor(this: InorderTraverse) { + this.m_Stack = new Array(); + this.m_Visited = new Array(); + }; +``` + +```typescript +export interface IInorderTraverse { + Visit(node: StringNode): void; +} +``` + +```typescript + + + function Visit(this: InorderTraverse, node: StringNode) { + this.m_Visited.push(node.m_Info); + }; +``` + +# Reference + +This algo is adapted from TAOCP I 2.3.1 \ No newline at end of file diff --git a/src/common/binary-tree.ts b/src/common/binary-tree.ts new file mode 100644 index 0000000..ea21aa0 --- /dev/null +++ b/src/common/binary-tree.ts @@ -0,0 +1,33 @@ +export class Node +{ + m_Left: Node; + m_Right: Node; + + constructor(left?: Node, right?: Node) + { + this.m_Left = left || null; + this.m_Right = right || null; + } +} + +export class StringNode extends Node +{ + m_Info: string; + + constructor(info: string, left?: Node, right?: Node) + { + super(left, right); + this.m_Info = info; + } +} + +export class NumberNode extends Node +{ + m_Info: number; + + constructor(info: number, left?: Node, right?: Node) + { + super(left, right); + this.m_Info = info; + } +} \ No newline at end of file diff --git a/src/linear-list/polynomial-addition.ts b/src/linear-list/polynomial-addition.ts new file mode 100644 index 0000000..1b235ff --- /dev/null +++ b/src/linear-list/polynomial-addition.ts @@ -0,0 +1,51 @@ +export class Item { + m_Coefficient: number; + m_Exponential: number; + + constructor(coefficient: number, exponential: number) { + this.m_Coefficient = coefficient; + this.m_Exponential = exponential; + } + +} +export class Polynomial { + m_Items: Array; + + Add(another: Polynomial) { + const P = this.m_Items; + const Q = [...another.m_Items]; + let p = 0; + let q = 0; + + for (;;) { + if (P[p].m_Exponential < Q[q].m_Exponential) { + q += 1; + } else if (P[p].m_Exponential === Q[q].m_Exponential) { + if (P[p].m_Exponential < 0) { + Q.pop(); + return Reflect.construct(Polynomial, [Q]); + } + + Q[q].m_Coefficient += P[p].m_Coefficient; + + if (Q[q].m_Coefficient === 0) { + Q.splice(q, 1); + } else { + q += 1; + } + + p += 1; + } else if (P[p].m_Exponential > Q[q].m_Exponential) { + const new_item = Reflect.construct(Item, [P[p].m_Coefficient, P[p].m_Exponential]); + Q.splice(q, 0, new_item); + p += 1; + q += 1; + } + } + } + + constructor(items: Array) { + this.m_Items = [...items, Reflect.construct(Item, [0, -1])]; + } + +} \ No newline at end of file diff --git a/src/linear-list/polynomial-addition.tsx b/src/linear-list/polynomial-addition.tsx new file mode 100644 index 0000000..757b042 --- /dev/null +++ b/src/linear-list/polynomial-addition.tsx @@ -0,0 +1,244 @@ +/* +# Polynomial Addition +*/ + +/* +## Item +*/ +export class Item +{ + m_Coefficient: number; + m_Exponential: number; +} + +/* +The item is in the form of $ ax^{e_1}y^{e_2}z^{e_3} $, and $ -6xy^{5} = -6x^{1}y^{5}z^{0} $ will be represented as: +```json +{ + m_Coefficient:-6, + m_Exponential:150 +} +``` +*/ + +/* +## Polynomial +*/ + +/* +Polynomial is a collection of items: +*/ + +export class Polynomial +{ + m_Items: Array; +} + +/* +As for polynomial, $x^6-6xy^5+5y^6$ would be represented as: +```json +[ + { + m_Coefficient:1, + m_Exponential:600 + }, + { + m_Coefficient:-6, + m_Exponential:150 + }, + { + m_Coefficient:5, + m_Exponential:60 + } +] +``` + +The convention is that items of polynomial are stored so that exponential is in decreasing order. +*/ + +/* +## Addtion Algorithm +*/ + +/* +In this algo, we add **this** polynomial to **another**, and **another** polynomial will be modified. + +For example, let $p=x+y+z$ and $q=x^2-2y-z$, after adding $p$ to $q$, $q$ would be $x^2+x-y$. +*/ + + function Add(this: Polynomial, another: Polynomial) +{ + const P = this.m_Items; + const Q = [...another.m_Items]; + + let p = 0; + let q = 0; + + for (; ;) + { + if (P[p].m_Exponential < Q[q].m_Exponential) + { + //@ts-ignore + ; + } + else if (P[p].m_Exponential === Q[q].m_Exponential) + { + //@ts-ignore + ; + //@ts-ignore + ; + } + else if (P[p].m_Exponential > Q[q].m_Exponential) + { + //@ts-ignore + ; + } + } +}; + +/* +### Overview + +The essence of this algo is that we will maintain two pointers $p$ and $q$, and during each iteration we will find opportunity to add item of $P$ to $Q$. +*/ + +/* +### Exponential: item at p < item at q + +For example, when adding $x+y+z$ to $x^2-2y-z$, we set $p$ and $q$ to 0, which means we want to add $x$ to $x^2$. + +However, we find that it's impossible because exponential of $x$ is less than $x^2$, which means this item can't be added to this position in $q$. + +> Don't forget about the convention that exponential is in decreasing order. + +In this situation, we keep $p$ and advance $q$ to next position to inspect next item of $Q$, that's because items are stored in decreasing order and exp at $p$ is less than that at $q$, and there may be oppotunity to add it to next item with smaller exp of $Q$. +*/ + +/* +### Items with same exponential + +It's intuitive to handle this case: + +*/ + + +function AddCoefficients(P: Array, Q: Array, p: number, q: number) +{ + Q[q].m_Coefficient += P[p].m_Coefficient; + //@ts-ignore + ; +} + +/* +If we add $y$ to $-2y$, we can just sum up the coefficient, however, the sum can be zero. For example if we add $z$ to $-z$, we get $0z$, it's not necessary to store it in polynomial. +*/ + +function CheckIfDeleteZeroItem(Q: Array, p: number, q: number) +{ + if (Q[q].m_Coefficient === 0) + { + //@ts-ignore + ; + } + else + { + //@ts-ignore + ; + } + //@ts-ignore + ; +} + +/* +Removing item at $q$ results in $q$ pointing to next item of $Q$ so that we should do nothing about $q$. +*/ + +/* +In addtion to adding coefficients, there is another case that we reach both end of polynomial: +*/ + +function CheckIfFinishedAndReturn(P: Array, Q: Array, p: number) +{ + /** + * the last item of any polynomial is always + * { + m_Coefficient:0, + m_Exponential:-1 + * } + */ + if (P[p].m_Exponential < 0) + { + Q.pop(); + return Reflect.construct(Polynomial, [Q]); + } +} + +/* +### Insert item + +Let's return to adding $x$ to $x^2$, we move to $-2y$ and find that exp of $x$ is greater than that of $y$, which means you can't find a place to add $x$, because if you move to next item of $Q$, you still get item with exp less than $x$. + +Instead, we will insert $x$ as an item to $Q$: +*/ + +function InsertNewItem(P: Array, Q: Array, p: number, q: number) +{ + const new_item = Reflect.construct(Item, [P[p].m_Coefficient, P[p].m_Exponential]); + //@ts-ignore + ; + //@ts-ignore + ; + //@ts-ignore + ; +} + +/* +## Appendix +*/ + +/* +### Trival Initialization +*/ + + function constructor(this: Item, coefficient: number, exponential: number) +{ + this.m_Coefficient = coefficient; + this.m_Exponential = exponential; +}; + + + function constructor(this: Polynomial, items: Array) +{ + /** + * trick: add a sentinel node at the end of every polynomial for consistence + */ + this.m_Items = [...items, Reflect.construct(Item, [0, -1])]; +}; + +/* +### Trival Implementation +*/ + +function MoveToNextItemOfQ(q: number) +{ + q += 1; +} + +function MoveToNextItemOfP(p: number) +{ + p += 1; +} + +function RemoveItemAtQ(Q: Array, q: number) +{ + Q.splice(q, 1); +} + +function InsertItemAtQ(Q: Array, q: number, new_item: Item) +{ + Q.splice(q, 0, new_item); +} + +/* +# Reference + +This algo is adapted from TAOCP I 2.2.4. + +*/ \ No newline at end of file diff --git a/src/linear-list/topological-sort.ts b/src/linear-list/topological-sort.ts new file mode 100644 index 0000000..41f432d --- /dev/null +++ b/src/linear-list/topological-sort.ts @@ -0,0 +1,69 @@ +export class Relation { + m_X: number; + m_Y: number | null; + + constructor(x: number, y: number | null) { + this.m_X = x; + this.m_Y = y; + } + +} +export class RelationInfo { + m_DirectPredecessorsCount: number; + m_DirectSuccessors: Array; + + constructor() { + this.m_DirectPredecessorsCount = 0; + this.m_DirectSuccessors = new Array(); + } + +} +export class TopologicalSort { + m_RelationsInfo: Map; + m_OutputQueue: Array; + m_Output: Array; + + Sort() { + while (this.m_OutputQueue.length !== 0) { + const front = this.m_OutputQueue.shift(); + this.m_Output.push(front); + const front_info = this.m_RelationsInfo.get(front); + front_info.m_DirectSuccessors.forEach(successor => { + const successor_info = this.m_RelationsInfo.get(successor); + successor_info.m_DirectPredecessorsCount -= 1; + + if (successor_info.m_DirectPredecessorsCount === 0) { + this.m_OutputQueue.push(successor); + } + }); + } + + return this.m_Output; + } + + constructor(relations: Array) { + this.m_RelationsInfo = new Map(); + this.m_OutputQueue = new Array(); + this.m_Output = new Array(); + relations.forEach(relation => { + [relation.m_X, relation.m_Y].forEach(value => { + if (value !== null && !this.m_RelationsInfo.has(value)) { + this.m_RelationsInfo.set(value, new RelationInfo()); + } + }); + + if (relation.m_Y) { + const x_info = this.m_RelationsInfo.get(relation.m_X); + x_info.m_DirectSuccessors.push(relation.m_Y); + const y_info = this.m_RelationsInfo.get(relation.m_Y); + y_info.m_DirectPredecessorsCount += 1; + } + }); + this.m_RelationsInfo.forEach((info, key) => { + if (info.m_DirectPredecessorsCount === 0) { + this.m_OutputQueue.push(key); + } + }); + } + +} \ No newline at end of file diff --git a/src/linear-list/topological-sort.tsx b/src/linear-list/topological-sort.tsx new file mode 100644 index 0000000..1bfec5c --- /dev/null +++ b/src/linear-list/topological-sort.tsx @@ -0,0 +1,289 @@ +/* +# Topological Sort +*/ + + +/* +## Relation +*/ + +export class Relation +{ + m_X: number; + m_Y: number | null; +} + + +/* + +The relation is in the form of $x y +} +``` + +When $y$ is null, it means that $x$ has no successor and predecessor, and we will represent $x; +} + +/* +We want to process relation and get most out of it. For each number, we will associate a relation info with it. + +```dot +digraph G { + 1 -> 2 + 1 -> 3 + 0 -> 1 + -1 -> 1 +} +``` + +For example, if we have $1<2$,$1<3$,$0<1$ and $-1<1$, then the info associated with $1$ would be: + +```json +{ + m_DirectPredecessorsCount:2, + m_DirectSuccessors:[2,3] + +} +``` +*/ + +/* +## Sort Algorithm +*/ +export class TopologicalSort +{ + m_RelationsInfo: Map; + m_OutputQueue: Array; + m_Output: Array; +} + + + function Sort(this: TopologicalSort) +{ + while (this.m_OutputQueue.length !== 0) + { + ; + + //@ts-ignore + ; + } + + return this.m_Output; +}; + +/* +In this algo, we will maintain an output queue. For example, if we have relations $0 3 + 2 -> 4 + 3 -> 4 +} +``` + +We want to at first pick up all numbers that has no predecessor. As it's obvious that we can arrange them first so that there won't be any conflict. + +For example, initially, $0$ and $2$ will be added to output queue. +*/ + +/* +### Dequeue +*/ + +function AddToOutput(this: TopologicalSort) +{ + const front = this.m_OutputQueue.shift(); + this.m_Output.push(front); +} + +/* +We can safely dequeue an number and add it to the final output array, and then erase all relations related to it, since it's already in the finnal output, we can remove it from the diagram. +*/ + +/* +### Erase Relations +*/ +function EraseRelations(this: TopologicalSort, front: number) +{ + const front_info = this.m_RelationsInfo.get(front); + front_info.m_DirectSuccessors.forEach(successor => + { + //@ts-ignore + ; + + //@ts-ignore + ; + + }) +} + +/* +For example, we remove $0$ from the diagram and get: + +```dot +digraph G { + 2 -> 3 + 2 -> 4 + 3 -> 4 +} +``` + +then we will remove 2 and get: + +```dot +digraph G { + 3 -> 4 +} +``` + +at this point, the output array is +```json +[0,2] +``` + +Then, it's obvious that we can continue to find number that has no predecessor and repeat untill there is no more number in the diagram, that's what ```CheckIfAddToOuputQueue ``` does: +*/ + +function CheckIfAddToOuputQueue(successor_info: RelationInfo, successor: number) +{ + if (successor_info.m_DirectPredecessorsCount === 0) + { + this.m_OutputQueue.push(successor); + } +} + +/* +### Initialize m_RelationsInfo + +As is shown above, ```m_RelationsInfo``` is the essence of this algo, but how to initialize it? +*/ + + + function constructor(this: TopologicalSort, relations: Array) +{ + ; + //@ts-ignore + ; +}; + +function InitializeFromRawRelations(this: TopologicalSort, relations: Array) +{ + relations.forEach(relation => + { + //@ts-ignore + ; + + //@ts-ignore + ; + }); + + //@ts-ignore + ; +} + +/* +For each relation, we will update info related to both $x$ and $y$: +*/ + +function EnsureRelationInfoExists(this: TopologicalSort, relation: Relation) +{ + [relation.m_X, relation.m_Y].forEach(value => + { + if (value !== null && !this.m_RelationsInfo.has(value)) + { + this.m_RelationsInfo.set(value, new RelationInfo()); + } + }) +} + +function RecordRelations(this: TopologicalSort, relation: Relation) +{ + if (relation.m_Y) + { + const x_info = this.m_RelationsInfo.get(relation.m_X); + x_info.m_DirectSuccessors.push(relation.m_Y); + + const y_info = this.m_RelationsInfo.get(relation.m_Y); + y_info.m_DirectPredecessorsCount += 1; + } +} + +/* +### Initialize m_OutputQueue + +Here zero means "zero predecessor". + +*/ + +function ScanForZeros(this: TopologicalSort) +{ + this.m_RelationsInfo.forEach((info, key) => + { + if (info.m_DirectPredecessorsCount === 0) + { + this.m_OutputQueue.push(key); + } + }); +} + +/* +## Appendix +*/ + +/* +### Trival Initialization +*/ + + + function constructor(this: Relation, x: number, y: number | null) +{ + this.m_X = x; + this.m_Y = y; +}; + + + function constructor(this: RelationInfo) +{ + this.m_DirectPredecessorsCount = 0; + this.m_DirectSuccessors = new Array(); +}; + +function InitializeMember(this: TopologicalSort) +{ + this.m_RelationsInfo = new Map(); + this.m_OutputQueue = new Array(); + this.m_Output = new Array(); +} + +/* +### Trival Implementation +*/ + +function DecreaseDirectPredecessorsCount(this: TopologicalSort, successor: number) +{ + const successor_info = this.m_RelationsInfo.get(successor); + successor_info.m_DirectPredecessorsCount -= 1; +} + +/* +# Reference + +This algo is adapted from TAOCP I 2.2.3. + +*/ diff --git a/src/tree/huffman-tree.ts b/src/tree/huffman-tree.ts new file mode 100644 index 0000000..14bafc1 --- /dev/null +++ b/src/tree/huffman-tree.ts @@ -0,0 +1,23 @@ +import { NumberNode } from "../common/binary-tree"; +import { default as PriorityQueue } from "ts-priority-queue"; +export class HuffmanTree { + m_Root: HuffmanNode; + + constructor(values: Array) { + const queue = new PriorityQueue({ + comparator: (a: HuffmanNode, b: HuffmanNode) => a.m_Info - b.m_Info, + initialValues: values.map(each => new NumberNode(each)) + }); + + while (queue.length !== 1) { + const left = queue.dequeue(); + const right = queue.dequeue(); + const node = new HuffmanNode(left.m_Info + right.m_Info, left, right); + queue.queue(node); + } + + this.m_Root = queue.dequeue(); + } + +} +export class HuffmanNode extends NumberNode {} \ No newline at end of file diff --git a/src/tree/huffman-tree.tsx b/src/tree/huffman-tree.tsx new file mode 100644 index 0000000..112de04 --- /dev/null +++ b/src/tree/huffman-tree.tsx @@ -0,0 +1,49 @@ +import { NumberNode } from "../common/binary-tree"; +import { default as PriorityQueue } from "ts-priority-queue"; + + +export class HuffmanTree +{ + m_Root: HuffmanNode; +} + +export class HuffmanNode extends NumberNode +{ + +} + + + function constructor(this: HuffmanTree, values: Array) +{ + //@ts-ignore + ; + + //@ts-ignore + ; + + //@ts-ignore + ; +} + +function PrepareQueue(values: Array) +{ + const queue = new PriorityQueue({ + comparator: (a: HuffmanNode, b: HuffmanNode) => a.m_Info - b.m_Info, + initialValues: values.map(each => new NumberNode(each)) + }); +} + +function SetRoot(this: HuffmanTree, queue: PriorityQueue) +{ + this.m_Root = queue.dequeue(); +} + +function CombineNodes(queue: PriorityQueue) +{ + while (queue.length !== 1) + { + const left = queue.dequeue(); + const right = queue.dequeue(); + const node = new HuffmanNode(left.m_Info + right.m_Info, left, right); + queue.queue(node); + } +} \ No newline at end of file diff --git a/src/tree/inorder-traverse.ts b/src/tree/inorder-traverse.ts new file mode 100644 index 0000000..86b3941 --- /dev/null +++ b/src/tree/inorder-traverse.ts @@ -0,0 +1,38 @@ +import { StringNode } from "../common/binary-tree"; +export class InorderTraverse { + m_Stack: Array; + m_Visited: Array; + + Traverse(root: StringNode) { + let current = root; + + for (;;) { + if (current) { + this.m_Stack.push(current); + current = (current.m_Left as StringNode); + } else { + if (this.m_Stack.length === 0) { + return; + } + + current = this.m_Stack.pop(); + this.Visit(current); + current = (current.m_Right as StringNode); + } + } + } + + constructor() { + this.m_Stack = new Array(); + this.m_Visited = new Array(); + } + + Visit(node: StringNode) { + this.m_Visited.push(node.m_Info); + } + +} +export interface IInorderTraverse { + Visit(node: StringNode): void; +} +; \ No newline at end of file diff --git a/src/tree/inorder-traverse.tsx b/src/tree/inorder-traverse.tsx new file mode 100644 index 0000000..16b50e2 --- /dev/null +++ b/src/tree/inorder-traverse.tsx @@ -0,0 +1,79 @@ +import { StringNode } from "../common/binary-tree"; + +export class InorderTraverse +{ + m_Stack: Array; + m_Visited: Array; +} + + + function Traverse(this: InorderTraverse & IInorderTraverse, root: StringNode) +{ + let current = root; + + for (; ;) + { + if (current) + { + //@ts-ignore + ; + } + else + { + ; + + //@ts-ignore + ; + + //@ts-ignore + ; + } + } +}; + +function AddCurrentToTobeVisited(this: InorderTraverse, current: StringNode) +{ + this.m_Stack.push(current) + current = current.m_Left as StringNode; +} + +function CheckIfFinished(this: InorderTraverse) +{ + if (this.m_Stack.length === 0) + { + return; + } +} + +function VisitStringNode(this: IInorderTraverse, current: StringNode) +{ + this.Visit(current); + current = current.m_Right as StringNode; +} + +function SetCurrentAsTobeVisited(this: InorderTraverse, current: StringNode) +{ + current = this.m_Stack.pop(); +} + + + function constructor(this: InorderTraverse) +{ + this.m_Stack = new Array(); + this.m_Visited = new Array(); +}; + +export interface IInorderTraverse +{ + Visit(node: StringNode): void; +}; + + + function Visit(this: InorderTraverse, node: StringNode) +{ + this.m_Visited.push(node.m_Info); +} + +/* +# Reference + +This algo is adapted from TAOCP I 2.3.1 + +*/ \ No newline at end of file diff --git a/test/__snapshots__/tree.test.ts.snap b/test/__snapshots__/tree.test.ts.snap new file mode 100644 index 0000000..36b1dcb --- /dev/null +++ b/test/__snapshots__/tree.test.ts.snap @@ -0,0 +1,105 @@ +// Jest Snapshot v1, https://goo.gl/fbAQLP + +exports[`binary tree huffman 1`] = ` +HuffmanNode { + "m_Info": 238, + "m_Left": HuffmanNode { + "m_Info": 95, + "m_Left": HuffmanNode { + "m_Info": 42, + "m_Left": NumberNode { + "m_Info": 19, + "m_Left": null, + "m_Right": null, + }, + "m_Right": NumberNode { + "m_Info": 23, + "m_Left": null, + "m_Right": null, + }, + }, + "m_Right": HuffmanNode { + "m_Info": 53, + "m_Left": HuffmanNode { + "m_Info": 24, + "m_Left": NumberNode { + "m_Info": 11, + "m_Left": null, + "m_Right": null, + }, + "m_Right": NumberNode { + "m_Info": 13, + "m_Left": null, + "m_Right": null, + }, + }, + "m_Right": NumberNode { + "m_Info": 29, + "m_Left": null, + "m_Right": null, + }, + }, + }, + "m_Right": HuffmanNode { + "m_Info": 143, + "m_Left": HuffmanNode { + "m_Info": 65, + "m_Left": NumberNode { + "m_Info": 31, + "m_Left": null, + "m_Right": null, + }, + "m_Right": HuffmanNode { + "m_Info": 34, + "m_Left": HuffmanNode { + "m_Info": 17, + "m_Left": NumberNode { + "m_Info": 7, + "m_Left": null, + "m_Right": null, + }, + "m_Right": HuffmanNode { + "m_Info": 10, + "m_Left": NumberNode { + "m_Info": 5, + "m_Left": null, + "m_Right": null, + }, + "m_Right": HuffmanNode { + "m_Info": 5, + "m_Left": NumberNode { + "m_Info": 2, + "m_Left": null, + "m_Right": null, + }, + "m_Right": NumberNode { + "m_Info": 3, + "m_Left": null, + "m_Right": null, + }, + }, + }, + }, + "m_Right": NumberNode { + "m_Info": 17, + "m_Left": null, + "m_Right": null, + }, + }, + }, + "m_Right": HuffmanNode { + "m_Info": 78, + "m_Left": NumberNode { + "m_Info": 37, + "m_Left": null, + "m_Right": null, + }, + "m_Right": NumberNode { + "m_Info": 41, + "m_Left": null, + "m_Right": null, + }, + }, + }, +} +`; diff --git a/test/linear-list.test.ts b/test/linear-list.test.ts new file mode 100644 index 0000000..9efe1de --- /dev/null +++ b/test/linear-list.test.ts @@ -0,0 +1,104 @@ +import { Relation } from "../src/linear-list/topological-sort"; +import { TopologicalSort } from "../src/linear-list/topological-sort"; +import { Polynomial, Item } from "../src/linear-list/polynomial-addition"; + +describe("topological sort", () => +{ + /** + * example taken from https://www.cs.usfca.edu/~galles/visualization/TopoSortDFS.html + */ + test("topological-sort.1", () => + { + const relations = [ + new Relation(0, 1), + new Relation(0, 2), + new Relation(1, 2), + new Relation(2, 4), + new Relation(2, 6), + new Relation(3, null), + new Relation(4, 6), + new Relation(5, 6), + new Relation(6, null), + new Relation(7, null), + ]; + + const algo = new TopologicalSort(relations); + const result = algo.Sort(); + expect(result).toEqual([ + 0, 3, 5, 7, 1, 2, 4, 6 + ]); + }) + + /** + * example taken from TAOCP I 2.2.3 fig.7 + */ + test("topological-sort.2", () => + { + const relations = [ + new Relation(9, 2), + new Relation(3, 7), + new Relation(7, 5), + new Relation(5, 8), + new Relation(8, 6), + new Relation(4, 6), + new Relation(1, 3), + new Relation(7, 4), + new Relation(9, 5), + new Relation(2, 8), + ]; + + const algo = new TopologicalSort(relations); + const result = algo.Sort(); + expect(result).toEqual([ + 9, 1, 2, 3, 7, 5, 4, 8, 6 + ]); + }) + + /** + * Reference: + * + * algo that generates all topological sorts: https://www.geeksforgeeks.org/all-topological-sorts-of-a-directed-acyclic-graph/ + * visualize algo: https://visualgo.net/en/dfsbfs + * online IDE: https://www.onlinegdb.com/online_c++_compiler + * + */ +}) + +describe("addition of polynomial", () => +{ + /** + * example taken from TAOCP I 2.2.4 + */ + + test("polynomial.addtion", () => + { + /** + * p = x + y + z + */ + const p = new Polynomial([ + new Item(1, 100), + new Item(1, 10), + new Item(1, 1) + ]); + + /** + * q = x^2 - 2y - z + */ + const q = new Polynomial([ + new Item(1, 200), + new Item(-2, 10), + new Item(-1, 1), + ]); + + const sum = q.Add(p); + + /** + * sum = x^2 + x - y + */ + expect(sum).toEqual(new Polynomial([ + new Item(1, 200), + new Item(1, 100), + new Item(-1, 10) + ])); + }) +}) \ No newline at end of file diff --git a/test/tree.test.ts b/test/tree.test.ts new file mode 100644 index 0000000..2a3e5b6 --- /dev/null +++ b/test/tree.test.ts @@ -0,0 +1,41 @@ +import { StringNode } from "../src/common/binary-tree"; +import { InorderTraverse } from "../src/tree/inorder-traverse"; +import { HuffmanTree } from "../src/tree/huffman-tree"; + +describe("binary tree", () => +{ + /** + * example taken from TAOCP I 2.3.1 + */ + test("traverse.inorder", () => + { + /** + * + */ + const A = new StringNode("A"); + const B = A.m_Left = new StringNode("B"); + const D = B.m_Left = new StringNode("D"); + const C = A.m_Right = new StringNode("C"); + const E = C.m_Left = new StringNode("E"); + const G = E.m_Right = new StringNode("G"); + const F = C.m_Right = new StringNode("F"); + const H = F.m_Left = new StringNode("H"); + const J = F.m_Right = new StringNode("J"); + + /** + * + */ + const algo = new InorderTraverse(); + algo.Traverse(A); + expect(algo.m_Visited).toEqual(["D", "B", "A", "E", "G", "C", "H", "F", "J"]); + }) + + /** + * example taken from TAOCP I 2.3.4.5 + */ + test("huffman", () => + { + const tree = new HuffmanTree([2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]); + expect(tree.m_Root).toMatchSnapshot(); + }) +}) \ No newline at end of file diff --git a/tsconfig.json b/tsconfig.json new file mode 100644 index 0000000..300719c --- /dev/null +++ b/tsconfig.json @@ -0,0 +1,8 @@ +{ + "compilerOptions": { + "target": "es6", + "module": "commonjs", + "moduleResolution": "node", + "jsx": "preserve" + } +} \ No newline at end of file