A typescript implementation of the dijkstra algorithm (bigint version).

The following definition is quoted from Wikipedia (https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm):

> Dijkstra's algorithm (/ˈdaɪkstrəz/ DYKE-strəz) is an algorithm for finding
> the shortest paths between nodes in a graph, which may represent, for example,
> road networks. It was conceived by computer scientist Edsger W. Dijkstra in
> 1956 and published three years later.

Install

* npm

``bash
npm install --save @algorithm.ts/dijkstra-bigint
`

* yarn

`bash
yarn add @algorithm.ts/dijkstra-bigint
`

* deno

`typescript
import dijkstra from 'https://raw.githubusercontent.com/guanghechen/algorithm.ts/main/packages/dijkstra-bigint/src/index.ts'
`

Usage

* Simple

`typescript
import dijkstra from '@algorithm.ts/dijkstra-bigint'

const dist: bigint[] = dijkstra({
N: 4,
source: 0,
edges: [
{ to: 1, cost: 2n },
{ to: 2, cost: 2n },
{ to: 3, cost: 2n },
{ to: 3, cost: 1n },
],
G: [[0], [1, 2], [3], []],
})
// => [0n, 2n, 4n, 4n]
//
// Which means:
// 0 --> 0: cost is 0n
// 0 --> 1: cost is 2n
// 0 --> 2: cost is 4n
// 0 --> 3: cost is 4n
`

* Pass custom dist array.

`typescript
import dijkstra from '@algorithm.ts/dijkstra-bigint'

const dist: bigint[] = []
dijkstra({
N: 4,
source: 0,
edges: [
{ to: 1, cost: 2n },
{ to: 2, cost: 2n },
{ to: 3, cost: 2n },
{ to: 3, cost: 1n },
],
G: [[0], [1, 2], [3], []],
dist,
})

dist // => [0n, 2n, 4n, 4n]
`

$3

* A solution for leetcode "Number of Ways to Arrive at Destination"
(https://leetcode.com/problems/number-of-ways-to-arrive-at-destination/):

`typescript
import type { IEdge } from '@algorithm.ts/dijkstra-bigint'
import dijkstra from '@algorithm.ts/dijkstra-bigint'

const MOD = BigInt(1e9 + 7)
export function countPaths(N: number, roads: number[][]): number {
const edges: IEdge[] = []
const G: number[][] = new Array(N)
for (let i = 0; i < N; ++i) G[i] = []
for (const [from, to, _cost] of roads) {
const cost = BigInt(_cost)

G[from].push(edges.length)
edges.push({ to, cost })

G[to].push(edges.length)
edges.push({ to: from, cost })
}

const source = 0
const target = N - 1
const dist: bigint[] = dijkstra({ N, source: target, edges, G, dist: customDist }, { INF: BigInt(1e12) })

const dp: bigint[] = new Array(N).fill(-1n)
return Number(dfs(source))

function dfs(o: number): bigint {
if (o === target) return 1n

let answer = dp[o]
if (answer !== -1n) return answer

answer = 0n
const d = dist[o]
for (const idx of G[o]) {
const e: IEdge = edges[idx]
if (dist[e.to] + e.cost === d) {
const t = dfs(e.to)
answer = modAdd(answer, t)
}
}
dp[o] = answer
return answer
}
}
``

Related

* 《算法竞赛入门经典（第2版）》（刘汝佳）： P359-P362 Dijkstra 算法
* [dijkstra 算法 | 光和尘][dijkstra]
* [dijkstra | Wikipedia][wikipedia-dijkstra]
* [@algorithm.ts/dijkstra][]
* [@algorithm.ts/priority-queue][]

[homepage]: https://github.com/guanghechen/algorithm.ts/tree/release-2.x.x/packages/dijkstra-bigint#readme
[wikipedia-dijkstra]: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
[dijkstra]: https://me.guanghechen.com/post/algorithm/graph/shortest-path/dijkstra
[@algorithm.ts/dijkstra]: https://github.com/guanghechen/algorithm.ts/tree/release-2.x.x/packages/dijkstra
[@algorithm.ts/priority-queue]: https://github.com/guanghechen/algorithm.ts/tree/release-2.x.x/packages/priority-queue