递归嵌套的自由基C＆＃x2B;＆＃x2B;

发布于 2025-01-21 13:59:06 字数 566 浏览 0 评论 0原文

我正在尝试为sqrt（1+sqrt（2+sqrt（3+...））的第一个n项编写一个函数）在C ++中。约束是该函数必须是递归的，并将n（巢的深度）作为唯一的参数。我不需要返回表达式本身，正是它评估的内容。例如：

n=1 -> sqrt(1)                 # which evaluates to 1  
n=2 -> sqrt(1+sqrt(2))         # which evaluates to 1.55377  
n=3 -> sqrt(1+sqrt(2+sqrt(3))) # which evaluates to 1.7122

我尝试过：

float nestedRadical(float n){
   if (n==1){
       return sqrt(1);
   }else{
       return sqrt(n + nestedRadical(n-1));
   }
}

此代码导致1是最深层的自由基，当它应该是最高的时候。我应该如何解决这个问题？

原文

I'm trying to write a function for the first n terms of sqrt(1+sqrt(2+sqrt(3+...))) in C++. The constraint is that the function must be recursive and take n (the depth of the nest) as the only parameter. I do not need to return the expression itself, just what it evaluates to. For example:

n=1 -> sqrt(1)                 # which evaluates to 1  
n=2 -> sqrt(1+sqrt(2))         # which evaluates to 1.55377  
n=3 -> sqrt(1+sqrt(2+sqrt(3))) # which evaluates to 1.7122

I've tried:

float nestedRadical(float n){
   if (n==1){
       return sqrt(1);
   }else{
       return sqrt(n + nestedRadical(n-1));
   }
}

This code causes 1 to be the most deeply nested radical, when it should be the highest. How should should I approach this problem?

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无声静候 2025-01-28 13:59:06

仔细检查和分析嵌套自由基。在纸上写，即使需要。那你会更好地理解。

尝试以下操作：

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

double recursivelNestedRadicals(int n, int i) {
    double res = 0;

    if(i-1 == n)
        return res;

    else
        res = sqrt(i + recursivelNestedRadicals(n, i+1));
}

int main() {
    int number;
    cout<<"Enter number: ";
    cin>>number;
    cout<<recursivelNestedRadicals(number, 1);
}

Examine and analyze nested radicals carefully. Write on paper, even if needed. then you will understand better.

Try this:

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

double recursivelNestedRadicals(int n, int i) {
    double res = 0;

    if(i-1 == n)
        return res;

    else
        res = sqrt(i + recursivelNestedRadicals(n, i+1));
}

int main() {
    int number;
    cout<<"Enter number: ";
    cin>>number;
    cout<<recursivelNestedRadicals(number, 1);
}

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