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✨ feat: implement '@algorithm.ts/dijkstra'
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Diff for: ‎.vscode/settings.json

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"findset",
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"gitmoji",
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"guanghechen",
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"leetcode",
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"lowbit",
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"maxflow",
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"mcmf",

Diff for: ‎README.md

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@@ -56,6 +56,7 @@ Package | Description
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:----------------------------------:|:--------------------------
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[@algorithm.ts/binary-index-tree][] | Binary Index Tree.
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[@algorithm.ts/circular-queue][] | Circular queue.
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[@algorithm.ts/dijkstra][] | Dijkstra algorithm optimized with [@algorithm.ts/priority-queue][]. #ShortestPath.
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[@algorithm.ts/dinic][] | Dinic algorithm. #MaxFlow, #NetworkFlow.
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[@algorithm.ts/dlx][] | DLX algorithm.
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[@algorithm.ts/findset][] | Find set.
@@ -75,6 +76,7 @@ algorithm.ts is [MIT licensed](https://github.com/guanghechen/algorithm.ts/blob/
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[homepage]: https://github.com/guanghechen/algorithm.ts
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[@algorithm.ts/binary-index-tree]: ./packages/binary-index-tree
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[@algorithm.ts/circular-queue]: ./packages/circular-queue
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[@algorithm.ts/dijkstra]: ./packages/dijkstra
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[@algorithm.ts/dinic]: ./packages/dinic
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[@algorithm.ts/dlx]: ./packages/dlx
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[@algorithm.ts/findset]: ./packages/findset

Diff for: ‎packages/dijkstra/README.md

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<header>
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<h1 align="center">
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<a href="https://github.com/guanghechen/algorithm.ts/tree/main/packages/dijkstra#readme">@algorithm.ts/dijkstra</a>
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</h1>
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<div align="center">
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<a href="https://www.npmjs.com/package/@algorithm.ts/dijkstra">
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<img
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alt="Npm Version"
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src="https://img.shields.io/npm/v/@algorithm.ts/dijkstra.svg"
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/>
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</a>
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<a href="https://www.npmjs.com/package/@algorithm.ts/dijkstra">
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<img
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alt="Npm Download"
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src="https://img.shields.io/npm/dm/@algorithm.ts/dijkstra.svg"
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/>
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</a>
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<a href="https://www.npmjs.com/package/@algorithm.ts/dijkstra">
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<img
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alt="Npm License"
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src="https://img.shields.io/npm/l/@algorithm.ts/dijkstra.svg"
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/>
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</a>
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<a href="#install">
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<img
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alt="Module Formats: cjs, esm"
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src="https://img.shields.io/badge/module_formats-cjs%2C%20esm-green.svg"
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/>
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</a>
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<a href="https://github.com/nodejs/node">
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<img
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alt="Node.js Version"
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src="https://img.shields.io/node/v/@algorithm.ts/dijkstra"
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/>
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</a>
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<a href="https://github.com/facebook/jest">
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<img
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alt="Tested with Jest"
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src="https://img.shields.io/badge/tested_with-jest-9c465e.svg"
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/>
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</a>
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<a href="https://github.com/prettier/prettier">
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<img
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alt="Code Style: prettier"
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src="https://img.shields.io/badge/code_style-prettier-ff69b4.svg?style=flat-square"
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/>
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</a>
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</div>
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</header>
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<br/>
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A typescript implementation of the **dijkstra** algorithm.
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The following definition is quoted from Wikipedia (https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm):
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> Dijkstra's algorithm (/ˈdaɪkstrəz/ *DYKE-strəz*) is an algorithm for finding
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> the shortest paths between nodes in a graph, which may represent, for example,
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> road networks. It was conceived by computer scientist Edsger W. Dijkstra in
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> 1956 and published three years later.
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## Install
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* npm
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```bash
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npm install --save @algorithm.ts/dijkstra
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```
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* yarn
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```bash
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yarn add @algorithm.ts/dijkstra
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```
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## Usage
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A solution for leetcode "Number of Ways to Arrive at Destination"
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(https://leetcode.com/problems/number-of-ways-to-arrive-at-destination/):
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```typescript
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import type { DijkstraEdge } from '@algorithm.ts/dijkstra'
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import dijkstra from '@algorithm.ts/dijkstra'
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export function countPaths(N: number, roads: number[][]): number {
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const MOD = 1e9 + 7
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const G: Array<Array<DijkstraEdge<number>>> = new Array(N)
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for (let i = 0; i < N; ++i) G[i] = []
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for (const road of roads) {
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G[road[0]].push({ to: road[1], cost: road[2] })
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G[road[1]].push({ to: road[0], cost: road[2] })
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}
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const source = 0
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const target = N - 1
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const dist: number[] = dijkstra<number>(N, target, G, 0, 0x3f3f3f)
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const dp: number[] = new Array(N).fill(-1)
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return dfs(source)
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function dfs(o: number): number {
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if (o === target) return 1
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let answer = dp[o]
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if (answer !== -1) return answer
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answer = 0
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const d = dist[o]
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for (const e of G[o]) {
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if (dist[e.to] + e.cost === d) {
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const t = dfs(e.to)
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answer = modAdd(answer, t)
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}
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}
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dp[o] = answer
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return answer
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}
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function modAdd(x: number, y: number): number {
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const z: number = x + y
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return z < MOD ? z : z - MOD
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}
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}
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```
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## Related
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* [dijkstra 算法][dijkstra]
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* [@algorithm.ts/priority-queue][]
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[homepage]: https://github.com/guanghechen/algorithm.ts/tree/main/packages/dijkstra#readme
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[dijkstra]: https://me.guanghechen.com/post/algorithm/graph/shortest-path/dijkstra
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[@algorithm.ts/priority-queue]: https://github.com/guanghechen/algorithm.ts/tree/main/packages/priority-queue

Diff for: ‎packages/dijkstra/__test__/dijkstra.spec.ts

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import type { DijkstraEdge } from '../src'
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import dijkstra from '../src'
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describe('dijkstra', function () {
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// https://leetcode.com/problems/number-of-ways-to-arrive-at-destination/
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test('leetcode/number-of-ways-to-arrive-at-destination', function () {
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const data: any[] = [
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{
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input: [
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7,
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[
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[0, 6, 7],
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[0, 1, 2],
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[1, 2, 3],
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[1, 3, 3],
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[6, 3, 3],
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[3, 5, 1],
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[6, 5, 1],
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[2, 5, 1],
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[0, 4, 5],
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[4, 6, 2],
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],
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],
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answer: 4,
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},
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{
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input: [2, [[1, 0, 10]]],
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answer: 1,
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},
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]
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for (const kase of data) {
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expect(countPaths(kase.input[0], kase.input[1])).toEqual(kase.answer)
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}
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})
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})
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const MOD = 1e9 + 7
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function countPaths(N: number, roads: number[][]): number {
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const G: Array<Array<DijkstraEdge<number>>> = new Array(N)
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for (let i = 0; i < N; ++i) G[i] = []
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for (const road of roads) {
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G[road[0]].push({ to: road[1], cost: road[2] })
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G[road[1]].push({ to: road[0], cost: road[2] })
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}
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const source = 0
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const target = N - 1
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const dist: number[] = dijkstra<number>(N, target, G, 0, 0x3f3f3f)
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const dp: number[] = new Array(N).fill(-1)
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return dfs(source)
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function dfs(o: number): number {
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if (o === target) return 1
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let answer = dp[o]
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if (answer !== -1) return answer
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answer = 0
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const d = dist[o]
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for (const e of G[o]) {
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if (dist[e.to] + e.cost === d) {
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const t = dfs(e.to)
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answer = modAdd(answer, t)
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}
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}
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dp[o] = answer
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return answer
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}
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}
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function modAdd(x: number, y: number): number {
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const z: number = x + y
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return z < MOD ? z : z - MOD
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}

Diff for: ‎packages/dijkstra/package.json

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{
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"name": "@algorithm.ts/dijkstra",
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"version": "1.0.11",
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"description": "Dancing link + Algorithm X",
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"author": {
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"name": "guanghechen",
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"url": "https://github.com/guanghechen/"
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},
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"repository": {
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"type": "git",
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"url": "https://github.com/guanghechen/algorithm.ts.git",
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"directory": "packages/dijkstra"
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},
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"homepage": "https://github.com/guanghechen/algorithm.ts/tree/main/packages/dijkstra#readme",
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"keywords": [
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"algorithm",
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"dijkstra",
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"dijkstra + priority-queue",
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"shortest path",
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"single source shortest path"
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],
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"main": "lib/cjs/index.js",
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"module": "lib/esm/index.js",
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"types": "lib/types/index.d.ts",
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"source": "src/index.ts",
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"license": "MIT",
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"engines": {
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"node": ">= 14.15.0"
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},
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"files": [
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"lib/",
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"!lib/**/*.js.map",
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"!lib/**/*.d.ts.map",
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"package.json",
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"CHANGELOG.md",
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"LICENSE",
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"README.md"
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],
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"scripts": {
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"build": "cross-env NODE_ENV=production rollup -c ../../rollup.config.js",
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"prebuild": "rimraf lib/ && tsc -p tsconfig.src.json --emitDeclarationOnly",
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"prepublishOnly": "cross-env ROLLUP_SHOULD_SOURCEMAP=false yarn build",
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"test": "cross-env TS_NODE_FILES=true jest --config ../../jest.config.js --rootDir ."
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},
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"dependencies": {
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"@algorithm.ts/priority-queue": "^1.0.11"
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}
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}

Diff for: ‎packages/dijkstra/src/index.ts

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import { createPriorityQueue } from '@algorithm.ts/priority-queue'
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export interface DijkstraEdge<T extends number | bigint> {
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/**
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* The other end of the edge.
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*/
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to: number
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/**
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* The cost of walking along this side.
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*/
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cost: T
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}
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/**
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* The dijkstra algorithm, optimized with priority queue.
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*
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* @param N the number of nodes in the graph
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* @param source the source node
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* @param G edges of the graph. G[i] represent the edge list start from node i.
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* @param ZERO 0 for number, 0n for bigint.
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* @param INF a big number, such as Number.MAX_SAFE_INTEGER
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* @returns
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*
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* @see https://me.guanghechen.com/post/algorithm/graph/shortest-path/dijkstra
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*/
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export function dijkstra<T extends number | bigint>(
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N: number,
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source: number,
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G: ReadonlyArray<ReadonlyArray<DijkstraEdge<T>>>,
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ZERO: T,
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INF: T,
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): T[] {
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const dist: T[] = new Array(N).fill(INF)
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const Q = createPriorityQueue<{ pos: number; cost: T }>(
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(x, y) => y.cost - x.cost,
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)
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// eslint-disable-next-line no-param-reassign
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dist[source] = ZERO
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Q.enqueue({ pos: source, cost: ZERO })
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while (Q.size() > 0) {
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const { pos, cost } = Q.dequeue()!
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if (dist[pos] < cost) continue
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for (const e of G[pos]) {
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const candidate: T = (dist[pos] as any) + e.cost
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if (dist[e.to] > candidate) {
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// eslint-disable-next-line no-param-reassign
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dist[e.to] = candidate
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Q.enqueue({ pos: e.to, cost: dist[e.to] })
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}
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}
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}
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return dist
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}
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export default dijkstra

Diff for: ‎packages/dijkstra/tsconfig.json

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{
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"extends": "../../tsconfig",
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"include": ["src", "script", "__test__"]
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}

Diff for: ‎packages/dijkstra/tsconfig.src.json

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{
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"extends": "../../tsconfig.settings",
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"compilerOptions": {
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"declarationDir": "lib/types",
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"rootDir": "src"
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},
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"include": ["src"]
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}

Diff for: ‎tsconfig.json

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"paths": {
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"@algorithm.ts/binary-index-tree": ["packages/binary-index-tree/src"],
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"@algorithm.ts/circular-queue": ["packages/circular-queue/src"],
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"@algorithm.ts/dijkstra": ["packages/dijkstra/src"],
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"@algorithm.ts/dinic": ["packages/dinic/src"],
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"@algorithm.ts/dlx": ["packages/dlx/src"],
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"@algorithm.ts/findset": ["packages/findset/src"],

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