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graph matching"],"repository":{"type":"git","url":"git+https://github.com/guanghechen/algorithm.ts.git#@algorithm.ts","directory":"packages/bipartite-matching"},"description":"The algorithm to find the maximum matching of the bipartite graph.","maintainers":[{"name":"lemonclown","email":"me.guanghechen@gmail.com"}],"readme":"<header>\n  <h1 align=\"center\">\n    <a href=\"https://github.com/guanghechen/algorithm.ts/tree/@algorithm.ts/bipartite-matching@4.0.4/packages/bipartite-matching#readme\">@algorithm.ts/bipartite-matching</a>\n  </h1>\n  <div align=\"center\">\n    <a href=\"https://www.npmjs.com/package/@algorithm.ts/bipartite-matching\">\n      <img\n        alt=\"Npm Version\"\n        src=\"https://img.shields.io/npm/v/@algorithm.ts/bipartite-matching.svg\"\n      />\n    </a>\n    <a href=\"https://www.npmjs.com/package/@algorithm.ts/bipartite-matching\">\n      <img\n        alt=\"Npm Download\"\n        src=\"https://img.shields.io/npm/dm/@algorithm.ts/bipartite-matching.svg\"\n      />\n    </a>\n    <a href=\"https://www.npmjs.com/package/@algorithm.ts/bipartite-matching\">\n      <img\n        alt=\"Npm License\"\n        src=\"https://img.shields.io/npm/l/@algorithm.ts/bipartite-matching.svg\"\n      />\n    </a>\n    <a href=\"#install\">\n      <img\n        alt=\"Module Formats: cjs, esm\"\n        src=\"https://img.shields.io/badge/module_formats-cjs%2C%20esm-green.svg\"\n      />\n    </a>\n    <a href=\"https://github.com/nodejs/node\">\n      <img\n        alt=\"Node.js Version\"\n        src=\"https://img.shields.io/node/v/@algorithm.ts/bipartite-matching\"\n      />\n    </a>\n    <a href=\"https://github.com/vitest-dev/vitest\">\n      <img\n        alt=\"Tested with Jest\"\n        src=\"https://img.shields.io/badge/tested_with-vitest-6E9F18.svg\"\n      />\n    </a>\n    <a href=\"https://github.com/prettier/prettier\">\n      <img\n        alt=\"Code Style: prettier\"\n        src=\"https://img.shields.io/badge/code_style-prettier-ff69b4.svg?style=flat-square\"\n      />\n    </a>\n  </div>\n</header>\n<br/>\n\nA typescript implementation of the algorithm to find the maximum [matching][wikipedia-matching] of\nthe [bipartite graph][wikipedia-bipartite-graph].\n\nThe following definition is quoted from Wikipedia\n(https://en.wikipedia.org/wiki/Matching_(graph_theory)):\n\n> A maximal matching is a matching $M$ of a graph $G$ that is not a subset of any other matching. A\n> matching $M$ of a graph $G$ is maximal if every edge in $G$ has a non-empty intersection with at\n> least one edge in $M$.\n>\n> A maximum matching (also known as maximum-cardinality matching) is a matching that contains the\n> largest possible number of edges. There may be many maximum matchings. The matching number\n> $\\displaystyle \\nu (G)$ of a graph $G$ is the size of a maximum matching. Every maximum matching\n> is maximal, but not every maximal matching is a maximum matching. The following figure shows\n> examples of maximum matchings in the same three graphs.\n\n## Install\n\n- npm\n\n  ```bash\n  npm install --save @algorithm.ts/bipartite-matching\n  ```\n\n- pnpm\n\n  ```bash\n  pnpm add @algorithm.ts/bipartite-matching\n  ```\n\n## Usage\n\n- Simple\n\n  ```typescript\n  import type { IBipartiteMatcher } from '@algorithm.ts/bipartite-matching'\n  import { HungarianDfs } from '@algorithm.ts/bipartite-matching'\n\n  const matcher: IBipartiteMatcher = new HungarianDfs()\n  matching.init(4)\n  matching.maxMatch() // => 0\n\n  matching.addEdge(0, 1)\n  matching.addEdge(0, 2)\n  matching.addEdge(0, 3)\n  matching.maxMatch() // => 1\n\n  matching.addEdge(2, 3)\n  matching.maxMatch() // => 2\n  ```\n\n## Example\n\n- A solution for leetcode \"Maximum Students Taking Exam\"\n  (https://leetcode.com/problems/maximum-students-taking-exam/):\n\n  ```typescript\n  import type { IBipartiteMatcher } from '@algorithm.ts/bipartite-matching'\n  import { HungarianDfs } from '@algorithm.ts/bipartite-matching'\n\n  const matcher: IBipartiteMatcher = new HungarianDfs()\n  export function maxStudents(seats: string[][]): number {\n    const R: number = seats.length\n    if (R <= 0) return 0\n\n    const C: number = seats[0].length\n    if (C <= 0) return 0\n\n    let total = 0\n    const seatCodes: number[][] = new Array(R)\n    for (let r = 0; r < R; ++r) seatCodes[r] = new Array(C).fill(-1)\n\n    for (let r = 0; r < R; ++r) {\n      for (let c = 0; c < C; ++c) {\n        if (seats[r][c] === '.') {\n          seatCodes[r][c] = total\n          total += 1\n        }\n      }\n    }\n\n    if (total <= 0) return 0\n    if (total === 1) return 1\n\n    matcher.init(total)\n    for (let r = 0; r < R; ++r) {\n      for (let c = 0; c < C; ++c) {\n        const u: number = seatCodes[r][c]\n        if (u > -1) {\n          if (r > 0) {\n            // Check upper left\n            if (c > 0 && seatCodes[r - 1][c - 1] > -1) {\n              matcher.addEdge(u, seatCodes[r - 1][c - 1])\n            }\n\n            // Check upper right\n            if (c + 1 < C && seatCodes[r - 1][c + 1] > -1) {\n              matcher.addEdge(u, seatCodes[r - 1][c + 1])\n            }\n          }\n\n          // Check left\n          if (c > 0 && seatCodes[r][c - 1] > -1) {\n            matcher.addEdge(u, seatCodes[r][c - 1])\n          }\n        }\n      }\n    }\n\n    const totalPaired: number = matcher.maxMatch().count\n    return total - totalPaired\n  }\n  ```\n\n## Related\n\n- 《算法竞赛入门经典（第 2 版）》（刘汝佳）： P347-P348 二分图最大匹配\n- [二分图 | 光和尘][bipartite-graph]\n- [Bipartite graph | Wikipedia][wikipedia-bipartite-graph]\n- [Matching (graph theory) | Wikipedia][wikipedia-matching]\n\n[homepage]:\n  https://github.com/guanghechen/algorithm.ts/tree/@algorithm.ts/bipartite-matching@4.0.4/packages/bipartite-matching#readme\n[wikipedia-bipartite-graph]: https://en.wikipedia.org/wiki/Bipartite_graph\n[wikipedia-matching]: https://en.wikipedia.org/wiki/Matching_(graph_theory)\n[bipartite-graph]: https://me.guanghechen.com/post/algorithm/graph/bipartite-graph/\n","readmeFilename":"README.md","bugs":{"url":"https://github.com/guanghechen/algorithm.ts/issues"}}