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README.md

@algorithm.ts/mcmf


A typescript implementation of the MCMF (Min Cost Max Flow) algorithm.

The MCMF algorithm is an algorithm for solving network flow problems.

Install

  • npm

    npm install --save @algorithm.ts/mcmf

  • yarn

    yarn add @algorithm.ts/mcmf

Usage

  • Codeforces contest 0277 Problem E (https://codeforces.com/contest/277/problem/E):

    import { Mcmf } from '@algorithm.ts/mcmf'

const mcmf = new Mcmf()
export function solveCodeforces0277E(coordinates: Array<[x: number, y: number]>): number {
  const N: number = coordinates.length

  const vertexes: IVertex[] = coordinates
    .map(([x, y]) => ({ x, y }))
    .sort((p, q) => {
      if (p.y === q.y) return p.x - q.x
      return q.y - p.y
    })

  const source = 0
  const target: number = N * 2 + 1
  mcmf.init(source, target, N * 2 + 2)

  for (let i = 0; i < N; ++i) {
    mcmf.addEdge(source, i + 1, 2, 0)
    mcmf.addEdge(N + i + 1, target, 1, 0)
    for (let j = i + 1; j < N; ++j) {
      if (vertexes[i].y === vertexes[j].y) continue
      mcmf.addEdge(i + 1, N + j + 1, 1, dist(vertexes[i], vertexes[j]))
    }
  }

  const { mincost, maxflow } = mcmf.minCostMaxFlow()
  const answer = maxflow === N - 1 ? mincost : -1
  return answer
}

function dist(p: IVertex, q: IVertex): number {
  const d = (p.x - q.x) * (p.x - q.x) + (p.y - q.y) * (p.y - q.y)
  return Math.sqrt(d)
}

interface IVertex {
  x: number
  y: number
}

  • A solution for Codeforces contest 1082 Problem G (https://codeforces.com/contest/1082/problem/G):

    import { Mcmf } from '@algorithm.ts/mcmf'

const mcmf = new Mcmf()
export function solveCodeforces1082G(
  nodes: number[],
  edges: Array<[u: number, v: number, weight: number]>,
): number {
  const n: number = nodes.length
  const m: number = edges.length

  const source = 0
  const target: number = n + m + 1
  mcmf.init(source, target, n + m + 2)

  for (let i = 0; i < n; ++i) {
    const weight: number = nodes[i]
    mcmf.addEdge(i + 1, target, weight, 0)
  }

  let answer = 0
  for (let i = 0; i < m; ++i) {
    const [u, v, weight] = edges[i]
    const x = n + i
    answer += weight
    mcmf.addEdge(source, x, weight, 0)
    mcmf.addEdge(x, u, Number.MAX_SAFE_INTEGER, 0)
    mcmf.addEdge(x, v, Number.MAX_SAFE_INTEGER, 0)
  }

  const { mincost, maxflow } = mcmf.minCostMaxFlow()
  answer -= maxflow
  return answer
}

  • A solution for leetcode "Maximum Students Taking Exam" (https://leetcode.com/problems/maximum-students-taking-exam/):

    import { Mcmf } from '@algorithm.ts/mcmf'

export function maxStudents(seats: string[][]): number {
  const R: number = seats.length
  if (R <= 0) return 0

  const C: number = seats[0].length
  if (C <= 0) return 0

  let total = 0
  const seatCodes: number[][] = new Array(R)
  for (let r = 0; r < R; ++r) seatCodes[r] = new Array(C).fill(-1)

  for (let r = 0; r < R; ++r) {
    for (let c = 0; c < C; ++c) {
      if (seats[r][c] === '.') seatCodes[r][c] = total++
    }
  }

  if (total <= 0) return 0
  if (total === 1) return 1

  const source: number = total * 2
  const target: number = source + 1
  const mcmf = new Mcmf()
  mcmf.init(source, target, target + 1)

  for (let r = 0; r < R; ++r) {
    for (let c = 0; c < C; ++c) {
      const u: number = seatCodes[r][c]
      if (u > -1) {
        mcmf.addEdge(source, u, 1, 0)
        mcmf.addEdge(u + total, target, 1, 0)
        if (r > 0) {
          // Check upper left
          if (c > 0 && seatCodes[r - 1][c - 1] > -1) {
            const v: number = seatCodes[r - 1][c - 1]
            mcmf.addEdge(u, v + total, 1, 0)
            mcmf.addEdge(v, u + total, 1, 0)
          }

          // Check upper right
          if (c + 1 < C && seatCodes[r - 1][c + 1] > -1) {
            const v: number = seatCodes[r - 1][c + 1]
            mcmf.addEdge(u, v + total, 1, 0)
            mcmf.addEdge(v, u + total, 1, 0)
          }
        }

        // Check left
        if (c > 0 && seatCodes[r][c - 1] > -1) {
          const v: number = seatCodes[r][c - 1]
          mcmf.addEdge(u, v + total, 1, 0)
          mcmf.addEdge(v, u + total, 1, 0)
        }
      }
    }
  }

  const { mincost, maxflow } = mcmf.minCostMaxFlow()
  const totalPaired: number = maxflow / 2
  return total - totalPaired
}

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