数据结构算法(1)--递归转化

数据结构算法(1)--递归转化

总结并记录学习数据结构过程中遇到的问题及算法.

---

一些常见算法：

Note:

• 基础应用.
• 递归的非递归转化.

阶乘

递归实现:

#include <iostream>
using namespace std;
int F(int n)
{
	if (n == 0 || n == 1)
		return 1;
	else
		return n * F(n - 1);
}

int main()
{
	int s;
	cin >> s;
	int result = F(s);
	cout << result << endl;
	system("pause");
}

非递归实现:

#include <iostream>
#include<stack>
using namespace std;

int main()
{
	int s, result = 1;
	cin >> s;
	stack<int> F;
	F.push(s);
	while (F.size() != 0)
	{
		int temp = F.top();
		F.pop();
		if(temp>1)
		{
			result *= temp;
			F.push(temp - 1);
		}
	}
	cout << result << endl;
	system("pause");
}

二阶斐波那函数

题目略.

递归实现:

#include <iostream>
using namespace std;
int F(int n)
{
	if (n == 0)
		return 0;
	else if (n == 1)
		return 1;
	else
		return F(n - 1) + F(n - 2);
}

int main()
{
	int s;
	cin >> s;
	int result = F(s);
	cout << result << endl;
	system("pause");
}

非递归实现:

#include <iostream>
#include<stack>
using namespace std;

int main()
{
	int s;
	cin >> s;
	stack<int> F;
	int sum = 0;
	F.push(s);
	while (F.size() != 0)
	{
		int temp = F.top();
		F.pop();
		if (temp > 1)
		{
			F.push(temp - 1);
			F.push(temp - 2);
		}
		else if (temp == 1)
			++sum;
	}
	cout << sum << endl;
	system("pause");
}

二阶斐波那函数

递归实现:

#include <iostream>
#include<stdio.h>
using namespace std;

void move(char a, char b)
{
	cout << a << "-->" << b << endl;
}
void hanoit(int n, char a, char b, char c)
{
	if (n == 1)
		move(a, c);
	else
	{
		hanoit(n - 1, a, c, b);
		move(a, c);
		hanoit(n - 1, b, a, c);
	}
}

int main()
{
	int n;
	cin >> n;
	hanoit(n, 'A', 'B', 'C');
	system("pause");
}

非递归实现:

博客 https://blog.csdn.net/yhf_naive/article/details/53384148

#include<iostream>
#include<algorithm>
#include <stack>
#include <cstdio>
#include<cmath>
using namespace std;
int temp1 = -1, temp2 = -1;
char s[4] = { 'q','a','b','c' };//为了解题简便，我是从1开始算的
stack<int> a[4];
int c1 = 0;
int rank1[4];
bool compare(int a1, int b1) { //给栈顶元素排序用
	if (a[a1].top() >= a[b1].top())
		return true;
	if (a[a1].top() < a[b1].top())
		return false;
	return false;
}
bool move1(int before, int after) {   //移动物块
	if ((a[after].top() - a[before].top()) % 2 == 0)
		return false;
	a[after].push(a[before].top());
	a[before].pop();
	temp1 = before; temp2 = after;  //记录上一次移动的物块位置
	printf("%c -> %c\n", s[temp1], s[temp2]);//printf比cout要快
	c1++;
	return true;
}
int main() {
	int i, N;
	cin >> N;
	a[1].push(N + 1);          //保证栈不会为空
	for (i = 0; i < N; i++)
		a[1].push(N - i);   //初始化
	a[2].push(N + 2);
	a[3].push(N + 3);
	if (N % 2 == 1) {        //N为奇数还是偶数，第一次移物块到哪里是不同的
		move1(1, 3);
		temp1 = 1;
		temp2 = 3;
	}
	else {
		move1(1, 2);
		temp1 = 1; temp2 = 2;
	}
	for (i = 1; i <= 3; i++)//初始化栈排序表
		rank1[i] = i;
	int tt;
	while (c1 < pow(2, N) - 1) {
		sort(rank1 + 1, rank1 + 4, compare);//按compare函数排序
		if (temp2 == rank1[2]) { //刚移动过的物块不会再被移动
			if (tt == temp1)   //别问我为什么，找规律找出来的
				move1(rank1[3], rank1[2]);
			else
				move1(rank1[3], rank1[1]);
		}
		else
			move1(rank1[2], rank1[1]);
		tt = rank1[2];
	}
}