Алгоритм Куна

Простой вариант

bool dfs(vector<vector<int>> &graphA, int vFromA, vector<int> &visited, vector<int> &pairFromA) {
    visited[vFromA] = 1;

    for (int vFromB : graphA[vFromA]) {
        int &toFromA = pairFromA[vFromB];

        if (toFromA == -1 || !visited[toFromA] && dfs(graphA, toFromA, visited, pairFromA)) {
            toFromA = vFromA;
            return 1;
        }
    }

    return 0;
}

vector<int> kuhn(vector<vector<int>> &graphA, int vertexCountB) {
    vector<int> pairFromA(vertexCountB, -1);

    for (int vFromA = 0; vFromA < graphA.size(); vFromA++) {
        vector<int> visited(graphA.size());
        dfs(graphA, vFromA, visited, pairFromA);
    }

    return pairFromA;
}

Более эффективный вариант без обнуления visited

bool dfs(vector<vector<int>> &graphA, int vFromA, vector<int> &visited, int i, vector<int> &pairFromA) {
    visited[vFromA] = i;

    for (int vFromB : graphA[vFromA]) {
        int &toFromA = pairFromA[vFromB];

        if (toFromA == -1 || visited[toFromA] != i && dfs(graphA, toFromA, visited, i, pairFromA)) {
            toFromA = vFromA;
            return 1;
        }
    }

    return 0;
}

vector<int> kuhn(vector<vector<int>> &graphA, int vertexCountB) {
    vector<int> visited(graphA.size(), -1);
    vector<int> pairFromA(vertexCountB, -1);

    for (int vFromA = 0; vFromA < graphA.size(); vFromA++)
        dfs(graphA, vFromA, visited, vFromA, pairFromA);

    return pairFromA;
}

vector<int> kuhnWithGreedyInitialization(vector<vector<int>> &graphA, int vertexCountB) {
    vector<int> greedyVisited(graphA.size());
    vector<int> pairFromA(vertexCountB, -1);

    for (int vFromA = 0; vFromA < graphA.size(); vFromA++) {
        for (int vFromB : graphA[vFromA]) {
            if (pairFromA[vFromB] == -1) {
                greedyVisited[vFromA] = 1;
                pairFromA[vFromB] = vFromA;
                break;
            }
        }
    }

    for (int vFromA = 0; vFromA < graphA.size(); vFromA++) {
        if (!greedyVisited[vFromA]) {
            vector<int> visited(graphA.size());
            dfs(graphA, vFromA, visited, pairFromA);
        }
    }

    return pairFromA;
}

vector<int> kuhnWithGreedyInitialization(vector<vector<int>> &graphA, int vertexCountB) {
    vector<int> greedyVisited(graphA.size());
    vector<int> pairFromA(vertexCountB, -1);

    for (int vFromA = 0; vFromA < graphA.size(); vFromA++) {
        for (int vFromB : graphA[vFromA]) {
            if (pairFromA[vFromB] == -1) {
                greedyVisited[vFromA] = 1;
                pairFromA[vFromB] = vFromA;
                break;
            }
        }
    }

    vector<int> visited(graphA.size(), -1);

    for (int vFromA = 0; vFromA < graphA.size(); vFromA++)
        if (!greedyVisited[vFromA])
            dfs(graphA, vFromA, visited, vFromA, pairFromA);

    return pairFromA;
}

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Алгоритм Куна

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