hamiltons_cycle.cpp

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#include <cassert>
#include <iostream>
#include <vector>

bool hamilton_cycle(const std::vector<std::vector<bool>> &routes) {
    const size_t n = routes.size();
    // height of dp array which is 2^n
    const size_t height = 1 << n;
    std::vector<std::vector<bool>> dp(height, std::vector<bool>(n, false));
 
    // to fill in the [2^i, i] cells with true
    for (size_t i = 0; i < n; ++i) {
        dp[1 << i][i] = true;
    }
    for (size_t i = 1; i < height; i++) {
        std::vector<size_t> zeros, ones;
        // finding positions with 1s and 0s and separate them
        for (size_t pos = 0; pos < n; ++pos) {
            if ((1 << pos) & i) {
                ones.push_back(pos);
            } else {
                zeros.push_back(pos);
            }
        }
 
        for (auto &o : ones) {
            if (!dp[i][o]) {
                continue;
            }
 
            for (auto &z : zeros) {
                if (!routes[o][z]) {
                    continue;
                }
                dp[i + (1 << z)][z] = true;
            }
        }
    }
 
    bool is_cycle = false;
    for (size_t i = 0; i < n; i++) {
        is_cycle |= dp[height - 1][i];
        if (is_cycle) {  // if true, all subsequent loop will be true. hence
                         // break
            break;
        }
    }
    return is_cycle;
}

static void test1() {
    std::vector<std::vector<bool>> arr{
        std::vector<bool>({true, true, false, false}),
        std::vector<bool>({false, true, true, false}),
        std::vector<bool>({false, false, true, true}),
        std::vector<bool>({false, false, false, true})};
 
    bool ans = hamilton_cycle(arr);
    std::cout << "Test 1... ";
    assert(ans);
    std::cout << "passed\n";
}

static void test2() {
    std::vector<std::vector<bool>> arr{
        std::vector<bool>({true, true, false, false}),
        std::vector<bool>({false, true, true, true}),
        std::vector<bool>({false, false, true, false}),
        std::vector<bool>({false, false, false, true})};
 
    bool ans = hamilton_cycle(arr);
 
    std::cout << "Test 2... ";
    assert(!ans);  // not a cycle
    std::cout << "passed\n";
}

static void test3() {
    std::vector<std::vector<bool>> arr{
        std::vector<bool>({true, true, true, true}),
        std::vector<bool>({true, true, true, true}),
        std::vector<bool>({true, true, true, true}),
        std::vector<bool>({true, true, true, true})};
 
    bool ans = hamilton_cycle(arr);
 
    std::cout << "Test 3... ";
    assert(ans);
    std::cout << "passed\n";
}

int main() {
    test1();
    test2();
    test3();
    return 0;
}