/**
 * File: hanota.cpp
 * Created Time: 2023-07-17
 * Author: krahets (krahets@163.com)
 */

#include "../utils/common.hpp"

/* Move one disk */
void move(vector<int> &src, vector<int> &tar) {
    // Take a disk from the top of src
    int pan = src.back();
    src.pop_back();
    // Place the disk on top of tar
    tar.push_back(pan);
}

/* Solve the Tower of Hanoi problem f(i) */
void dfs(int i, vector<int> &src, vector<int> &buf, vector<int> &tar) {
    // If only one disk remains to be moved from src, move it directly to tar
    if (i == 1) {
        move(src, tar);
        return;
    }
    // Subproblem f(i-1): move the top i-1 disks from src to buf using tar
    dfs(i - 1, src, tar, buf);
    // Subproblem f(1): move the remaining disk of this subproblem from src to tar
    move(src, tar);
    // Subproblem f(i-1): move the top i-1 disks from buf to tar using src
    dfs(i - 1, buf, src, tar);
}

/* Solve the Tower of Hanoi problem */
void solveHanota(vector<int> &A, vector<int> &B, vector<int> &C) {
    int n = A.size();
    // Move the top n disks from A to C using B
    dfs(n, A, B, C);
}

/* Driver code */
int main() {
    // The end of each list represents the top of the peg
    vector<int> A = {5, 4, 3, 2, 1};
    vector<int> B = {};
    vector<int> C = {};

    cout << "Initial state:\n";
    cout << "A =";
    printVector(A);
    cout << "B =";
    printVector(B);
    cout << "C =";
    printVector(C);

    solveHanota(A, B, C);

    cout << "After moving all disks:\n";
    cout << "A =";
    printVector(A);
    cout << "B =";
    printVector(B);
    cout << "C =";
    printVector(C);

    return 0;
}