Coursera Algorithm Ⅱ week3 baseball

原创于 2022-09-25 18:25:49 发布 · 311 阅读

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本文介绍了一个使用最大流算法确定哪些棒球队伍无法赢得冠军的应用案例。通过构建特殊的流网络，并利用Ford-Fulkerson算法计算最大流，可以有效判断哪些队伍已无夺冠可能。文章详细展示了如何构建流网络及实现最大流计算。

全部代码https://github.com/Joshmomel/Princeton_Algorithms/tree/baseball

Context

通过maxflow来计算哪只队伍不能夺冠
在这里插入图片描述

在这里插入图片描述

g[i][j]代表i, j队伍还有多少场比赛
这些比赛都连到team vertices, 图中有4队伍
t就是w[x] + r[x] - w[i], 代表i对最多能赢多少才不超过x队

对于图中w4+r4-w2代表49+27-69=7, Boston最多能赢6场比赛

代码

这次assignment的重点就是构建FlowNetwork

第一部分是构建g[i][j] 以及team vertices

    FlowNetwork flowNetwork = new FlowNetwork(this.vertices);
    List<String> computeTeams = teams.stream().filter(s -> !s.equals(team)).collect(Collectors.toList());

    int computeTeamLength = computeTeams.size();
    int counter = 0;
    for (int i = 0; i < computeTeamLength; i++) {
      for (int j = i + 1; j < computeTeamLength; j++) {
        counter += 1;
        flowNetwork.addEdge(new FlowEdge(0, counter, this.against(computeTeams.get(i), computeTeams.get(j))));
        flowNetwork.addEdge(new FlowEdge(counter, i + 1 + this.teamCombinations, Double.POSITIVE_INFINITY));
        flowNetwork.addEdge(new FlowEdge(counter, j + 1 + this.teamCombinations, Double.POSITIVE_INFINITY));
      }
    }

第二部分是把team vertices连接到t

    ArrayList<String> teamList = new ArrayList<>();
    int compareTeam = this.wins(teams.get(teams.indexOf(team))) + this.remaining(teams.get(teams.indexOf(team)));
    int i = 0;
    for (String computeTeam : computeTeams) {
      i += 1;
      if (compareTeam - this.wins(computeTeam) < 0) {
        teamList.add(computeTeam);
        return teamList;
      }
      flowNetwork.addEdge(new FlowEdge(i + this.teamCombinations, this.vertices - 1, compareTeam - this.wins(computeTeam)));
    }

第三部分是计算maxflow

    FordFulkerson maxflow = new FordFulkerson(flowNetwork, 0, this.vertices - 1);
    for (int v = 0; v < flowNetwork.V(); v++) {
      if (maxflow.inCut(v)) {
        int teamIndex = v - this.teamCombinations - 1;
        if (teamIndex >= 0) {
          String name = computeTeams.get(teamIndex);
          teamList.add(name);
        }
      }
    }

    return teamList.size() > 0 ? teamList : null;