目录

7-1 递归 递推

7-2 函数的递归调用

7-3 A010 递归练习1

7-4 A011 递归练习2

7-5 A012 递归练习3

7-6 PG009 循环与递归

7-7 计算Fibonacci数列—递归

7-8 整数转换为字符串

7-9 简单的归并

---

AC： 9 / 9

用时：1 h 4 min

递归专题。

7-1 递归 递推

#include <iostream>
#include <algorithm>
#include <cstring>

using namespace std;

const int N = 110;

int n, f1, a, b;

int func(int x)
{
    if(x == 1) return f1;

    return a * func(x - 1) + b;
}

int main()
{
    while(scanf("%d%d%d%d", &n, &f1, &a, &b) != EOF)
    {
        cout << func(n) << endl;
    }

    return 0;
}

 注意，输入内容中没有给出数据组数或者结束输入的标志。

7-2 函数的递归调用

#include <iostream>
#include <algorithm>
#include <cstring>

using namespace std;

const int N = 110;

int n;

int func(int x)
{
    if(x == 0 || x == 1) return 1;

    return x * func(x - 1);
}

int main()
{
    cin >> n;

    if(n < 0)
        printf("%d<0，no value!no value!", n);
    else
        printf("%d!=%d", n, func(n));

    return 0;
}

n < 0时那个逗号是全角符号，建议直接复制粘贴。

7-3 A010 递归练习1

#include <iostream>
#include <algorithm>
#include <cstring>

using namespace std;

const int N = 110;

int n, m, k;

int f(int x)
{
    if(x == 1) return k;

    return f(x - 1) + m;
}

int main()
{
    while(scanf("%d%d%d", &n, &m, &k) != EOF)
    {
        cout << f(n) << endl;
    }

    return 0;
}

7-4 A011 递归练习2

#include <iostream>
#include <algorithm>
#include <cstring>

using namespace std;

const int N = 110;

int n, m, t;

int f(int x, int y)
{
    if(y == 1) return x;
    if(x < 0 || y < 0 || x < y) return 0;
    return f(x - 1, y) + f(x - 1, y - 1);
}

int main()
{
    cin >> t;

    while(t--)
    {
        cin >> n >> m;

        cout << f(n, m) << endl;
    }

    return 0;
}

7-5 A012 递归练习3

#include <iostream>
#include <algorithm>
#include <cstring>

using namespace std;

const int N = 110;

int t;

struct Node
{
    int a;
    int b;
}node;

struct Node f(int x)
{
    if(x == 0) return {1, 0};

    struct Node tem = f(x - 1);
    return {tem.b, tem.a * 3 + tem.b * 2};
}

int main()
{

    while(scanf("%d", &t) != EOF)
    {

        node = f(t);

        cout << node.a << ' ' << node.b << endl;
    }

    return 0;
}

7-6 PG009 循环与递归

#include <iostream>
#include <algorithm>
#include <cstring>

using namespace std;

const int N = 110;

int jie(int x)
{
    if(x == 1 || x == 0) return 1;

    return x * jie(x - 1);
}

double f(int x)
{
    if(x == 1) return 1;

    double sign = (x % 2 == 0 ? -1 : 1);

    double res = sign / jie(2 * x - 1);

    return res + f(x - 1);
}

int main()
{
    int n;

    while(scanf("%d", &n) != EOF)
    {
        printf("%.5f\n", f(n));
    }

    return 0;
}

7-7 计算Fibonacci数列—递归

#include <stdio.h>

long Fib(int n);

int count=0;

int main()
{
    int n;
    long f;
    
    scanf("%d", &n);
    
    f = Fib(n);
    
    printf("Fib(%d)=%ld, count=%d\n", n, f, count);
    
    return 0;
}

long Fib(int n)
{
    count++;
    
    if(n == 1 || n == 2) return 1;

    return Fib(n - 1) + Fib(n - 2);
}

7-8 整数转换为字符串

#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>

using namespace std;

string f(int x)
{
    string s;

    if(x >= 0 && x <= 9) return s += '0' + x;

    int tem = x % 10;

    return f(x / 10) += '0' + tem;
}

int main()
{
    int t;
    cin >> t;

    while(t--)
    {
        int x;
        cin >> x;

        string s;
        if(x >= 0) s = f(x);
        else s = '-' + f(-x);

        cout << s << endl;
    }

    return 0;
}

递归函数只对非负整数进行处理，负整数在主函数中另外处理。

7-9 简单的归并

#include <iostream>
#include <algorithm>
#include <cstring>
#include <set>

using namespace std;

multiset<int> box;

int main()
{
    int t;
    cin >> t;

    while(t--)
    {
        box.clear();

        int n, m;

        cin >> n;

        while(n--)
        {
            int x;
            cin >> x;

            box.insert(x);
        }

        cin >> m;

        while(m--)
        {
            int x;
            cin >> x;

            box.insert(x);
        }

        for(set<int>::iterator it = box.begin(); it != box.end(); it++)
        {
            cout << *it;
            if(++it != box.end())
            {
                cout << ' ';
            }
            it--;
        }
        puts("");
    }

    return 0;
}

 这个能递归吗......