@algorithm.ts/dijkstra-bigint NPM

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

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

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

deno

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

Usage

Simple

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.

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]

Example

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

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
  }
}