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67 lines
1.5 KiB
67 lines
1.5 KiB
/**
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* File: hanota.cpp
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* Created Time: 2023-07-17
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 移動一個圓盤 */
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void move(vector<int> &src, vector<int> &tar) {
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// 從 src 頂部拿出一個圓盤
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int pan = src.back();
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src.pop_back();
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// 將圓盤放入 tar 頂部
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tar.push_back(pan);
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}
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/* 求解河內塔問題 f(i) */
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void dfs(int i, vector<int> &src, vector<int> &buf, vector<int> &tar) {
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// 若 src 只剩下一個圓盤，則直接將其移到 tar
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if (i == 1) {
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move(src, tar);
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return;
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}
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// 子問題 f(i-1) ：將 src 頂部 i-1 個圓盤藉助 tar 移到 buf
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dfs(i - 1, src, tar, buf);
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// 子問題 f(1) ：將 src 剩餘一個圓盤移到 tar
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move(src, tar);
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// 子問題 f(i-1) ：將 buf 頂部 i-1 個圓盤藉助 src 移到 tar
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dfs(i - 1, buf, src, tar);
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}
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/* 求解河內塔問題 */
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void solveHanota(vector<int> &A, vector<int> &B, vector<int> &C) {
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int n = A.size();
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// 將 A 頂部 n 個圓盤藉助 B 移到 C
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dfs(n, A, B, C);
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}
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/* Driver Code */
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int main() {
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// 串列尾部是柱子頂部
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vector<int> A = {5, 4, 3, 2, 1};
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vector<int> B = {};
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vector<int> C = {};
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cout << "初始狀態下：\n";
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cout << "A =";
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printVector(A);
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cout << "B =";
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printVector(B);
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cout << "C =";
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printVector(C);
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solveHanota(A, B, C);
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cout << "圓盤移動完成後：\n";
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cout << "A =";
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printVector(A);
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cout << "B =";
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printVector(B);
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cout << "C =";
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printVector(C);
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return 0;
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}
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