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递归

视频讲解

🎥 视频讲解

递归

递归是指在函数的定义中调用函数自身的方法。

例题1

洛谷：求 1+2+3+...+N 的值

代码实现

参考实现 
#include <bits/stdc++.h>
using namespace std;

int f(int u) {
    if (u == 1) return 1;
    return u + f(u - 1);
}

int main() {
    int n;
    cin >> n;
    cout << f(n);
    return 0;
}

import java.util.Scanner;

public class Main {

    static int f(int u) {
        if (u == 1) return 1;
        return u + f(u - 1);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        System.out.println(f(n));
    }
}

def f(u: int) -> int:
    if u == 1:
        return 1
    return u + f(u - 1)

n = int(input())
print(f(n))

例题2

洛谷：求 f(x,n)

代码实现

参考实现 
#include <bits/stdc++.h>
using namespace std;

double f(double x, double n) {
    if (n == 1) return sqrt(n + x);
    return sqrt(n + f(x, n - 1));
}

int main() {
    double x, n;
    cin >> x >> n;
    cout << fixed << setprecision(2) << f(x, n);
    return 0;
}

import java.util.Scanner;

public class Main {

    static double f(double x, double n) {
        if (n == 1) return Math.sqrt(n + x);
        return Math.sqrt(n + f(x, n - 1));
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        double x = sc.nextDouble();
        double n = sc.nextDouble();
        System.out.printf("%.2f", f(x, n));
    }
}

import math

def f(x: float, n: int) -> float:
    if n == 1:
        return math.sqrt(n + x)
    return math.sqrt(n + f(x, n - 1))


x, n = map(float, input().split())
n = int(n)
print(f"{f(x, n):.2f}")

例题3

洛谷：Roads Around The Farm S

代码实现

参考实现 
#include <bits/stdc++.h>
using namespace std;

int n, k;
int ans = 0;

void f(int u, int k) {
    int x = (u + k) / 2;
    int y = u - x;
    if (u % 2 == k % 2 && x > 0 && y > 0) {
        f(x, k);
        f(y, k);
    } else {
        ans++;
    }
}

int main() {
    cin >> n >> k;
    f(n, k);
    cout << ans;
    return 0;
}

import java.util.Scanner;

public class Main {

    static int ans = 0;

    static void f(int u, int k) {
        int x = (u + k) / 2;
        int y = u - x;
        if (u % 2 == k % 2 && x > 0 && y > 0) {
            f(x, k);
            f(y, k);
        } else {
            ans++;
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        f(n, k);
        System.out.println(ans);
    }
}

ans = 0

def f(u: int, k: int):
    global ans
    x = (u + k) // 2
    y = u - x
    if u % 2 == k % 2 and x > 0 and y > 0:
        f(x, k)
        f(y, k)
    else:
        ans += 1


n, k = map(int, input().split())
f(n, k)
print(ans)

练习题单

递归