@algorithm.ts/isap

A typescript implementation of the ISAP (Improved SAP) algorithm.

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

Install

• npm

  npm install --save @algorithm.ts/isap

• yarn

  yarn add @algorithm.ts/isap

Usage

• Simple

  import { Isap } from '@algorithm.ts/isap'
  
  const isap = createIsap()
  isap.init(0, 1, 4)
  isap.addEdge(0, 2, 1)
  isap.addEdge(0, 3, 2)
  isap.addEdge(3, 1, 1)
  
  isap.maxFlow() // => 1
  
  // Access current residual network.
  class CustomIsap extends Isap {
    public getSnapshot() {
      return {
        N: this._N,
        source: this._source,
        sink: this._sink,
        G: this.G,
        edges: this._edges,
        edgesTot: this._edgesTot,
        dist: this._dist
      }
    }
  }

Example

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

  import { Isap } from '@algorithm.ts/isap'
  
  const isap = new Isap()
  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
    isap.init(source, target, n + m + 2)
  
    for (let i = 0; i < n; ++i) {
      const weight: number = nodes[i]
      isap.addEdge(i + 1, target, weight)
    }
  
    let answer = 0
    for (let i = 0; i < m; ++i) {
      const [u, v, weight] = edges[i]
      const x = n + i
      answer += weight
      isap.addEdge(source, x, weight)
      isap.addEdge(x, u, Number.MAX_SAFE_INTEGER)
      isap.addEdge(x, v, Number.MAX_SAFE_INTEGER)
    }
    answer -= isap.maxflow()
    return answer
  }

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

  import { Isap } from '@algorithm.ts/isap'
  
  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
    isap.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) {
          isap.addEdge(source, u, 1)
          isap.addEdge(u + total, target, 1)
          if (r > 0) {
            // Check upper left
            if (c > 0 && seatCodes[r - 1][c - 1] > -1) {
              const v: number = seatCodes[r - 1][c - 1]
              isap.addEdge(u, v + total, 1)
              isap.addEdge(v, u + total, 1)
            }
  
            // Check upper right
            if (c + 1 < C && seatCodes[r - 1][c + 1] > -1) {
              const v: number = seatCodes[r - 1][c + 1]
              isap.addEdge(u, v + total, 1)
              isap.addEdge(v, u + total, 1)
            }
          }
  
          // Check left
          if (c > 0 && seatCodes[r][c - 1] > -1) {
            const v: number = seatCodes[r][c - 1]
            isap.addEdge(u, v + total, 1)
            isap.addEdge(v, u + total, 1)
          }
        }
      }
    }
  
    const totalPaired: number = isap.maxflow() / 2
    return total - totalPaired
  }

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