79 lines
1.7 KiB
C++
79 lines
1.7 KiB
C++
/**
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* File: recursion.cpp
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* Created Time: 2023-08-24
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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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/* 递归 */
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int recur(int n) {
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// 终止条件
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if (n == 1)
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return 1;
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// 递：递归调用
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int res = recur(n - 1);
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// 归：返回结果
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return n + res;
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}
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/* 使用迭代模拟递归 */
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int forLoopRecur(int n) {
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// 使用一个显式的栈来模拟系统调用栈
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stack<int> stack;
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int res = 0;
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// 递：递归调用
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for (int i = n; i > 0; i--) {
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// 通过“入栈操作”模拟“递”
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stack.push(i);
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}
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// 归：返回结果
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while (!stack.empty()) {
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// 通过“出栈操作”模拟“归”
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res += stack.top();
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stack.pop();
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}
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// res = 1+2+3+...+n
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return res;
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}
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/* 尾递归 */
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int tailRecur(int n, int res) {
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// 终止条件
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if (n == 0)
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return res;
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// 尾递归调用
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return tailRecur(n - 1, res + n);
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}
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/* 斐波那契数列：递归 */
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int fib(int n) {
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// 终止条件 f(1) = 0, f(2) = 1
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if (n == 1 || n == 2)
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return n - 1;
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// 递归调用 f(n) = f(n-1) + f(n-2)
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int res = fib(n - 1) + fib(n - 2);
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// 返回结果 f(n)
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return res;
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}
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/* Driver Code */
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int main() {
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int n = 5;
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int res;
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res = recur(n);
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cout << "\n递归函数的求和结果 res = " << res << endl;
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res = forLoopRecur(n);
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cout << "\n使用迭代模拟递归求和结果 res = " << res << endl;
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res = tailRecur(n, 0);
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cout << "\n尾递归函数的求和结果 res = " << res << endl;
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res = fib(n);
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cout << "\n斐波那契数列的第 " << n << " 项为 " << res << endl;
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return 0;
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}
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