C/C++ API 调用实现一个求解无向图的哈密顿回路的程序

好的，下面是一个使用 MiniSAT 求解器的 C++ 实现：

#include <cstdio>
#include <vector>
#include "minisat/core/Solver.h"

using namespace Minisat;

// 判断是否存在从 u 到 v 的边
bool hasEdge(const std::vector<std::vector<bool>>& graph, int u, int v) {
    return graph[u][v] || graph[v][u];
}

// 构造布尔公式
void constructFormula(Solver& solver, const std::vector<std::vector<bool>>& graph) {
    int n = graph.size();
    std::vector<std::vector<Lit>> x(n, std::vector<Lit>(n));

    // 构造变量
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            x[i][j] = mkLit(solver.newVar());
        }
    }

    // 每个顶点恰好在一条回路中出现一次
    for (int i = 0; i < n; i++) {
        vec<Lit> clause;
        for (int j = 0; j < n; j++) {
            clause.push(x[i][j]);
        }
        solver.addClause(clause);

        for (int j = 0; j < n; j++) {
            for (int k = j + 1; k < n; k++) {
                solver.addClause(~x[i][j], ~x[i][k]);
            }
        }
    }

    // 恰好存在一条边与每个顶点相连
    for (int i = 0; i < n; i++) {
        vec<Lit> clause;
        for (int j = 0; j < n; j++) {
            if (i != j && hasEdge(graph, i, j)) {
                clause.push(x[i][j]);
            }
        }
        solver.addClause(clause);

        for (int j = 0; j < n; j++) {
            for (int k = j + 1; k < n; k++) {
                if (hasEdge(graph, i, j) && hasEdge(graph, i, k)) {
                    solver.addClause(~x[i][j], ~x[i][k]);
                }
            }
        }
    }

    // 恰好存在一条回路经过每个顶点
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            for (int k = j + 1; k < n; k++) {
                if (hasEdge(graph, i, j) && hasEdge(graph, i, k)) {
                    solver.addClause(~x[i][j], ~x[k][i]);
                    solver.addClause(~x[j][i], ~x[k][i]);
                }
            }
        }
    }
}

// 解析结果，得到哈密顿回路的路径
std::vector<int> getPath(const Solver& solver, const std::vector<std::vector<bool>>& graph) {
    int n = graph.size();
    std::vector<std::vector<bool>> x(n, std::vector<bool>(n));

    // 获取变量的取值
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (solver.modelValue(i * n + j) == l_True) {
                x[i][j] = true;
            }
        }
    }

    // 构造路径
    std::vector<int> path;
    int cur = 0;
    path.push_back(cur);
    while (path.size() < n) {
        for (int i = 0; i < n; i++) {
            if (i != cur && x[cur][i] && hasEdge(graph, cur, i)) {
                cur = i;
                path.push_back(cur);
                break;
            }
        }
    }
    return path;
}

// 求解哈密顿回路
std::vector<int> solveHamiltonianPath(const std::vector<std::vector<bool>>& graph) {
    Solver solver;
    constructFormula(solver, graph);
    bool res = solver.solve();
    if (res) {
        return getPath(solver, graph);
    } else {
        return std::vector<int>();
    }
}

int main() {
    std::vector<std::vector<bool>> graph = {
        {0, 1, 1, 0},
        {1, 0, 1, 1},
        {1, 1, 0, 1},
        {0, 1, 1, 0}
    };
    std::vector<int> path = solveHamiltonianPath(graph);
    if (path.empty()) {
        printf("No Hamiltonian path found.\n");
    } else {
        printf("Hamiltonian path: ");
        for (int i = 0; i < path.size(); i++) {
            printf("%d ", path[i]);
        }
        printf("\n");
    }
    return 0;
}

这个程序使用 MiniSAT 求解器实现了求解哈密顿回路的功能。具体来说，它首先将无向图转化为布尔公式，然后调用 MiniSAT 求解器进行求解。如果求解器返回的结果合法，程序会解析结果得到哈密顿回路的路径。