Question

Create an array called h one element at a time. Start with the first entry as 1. The next entry is the previous entry cut in half:

h(i + 1) = h(i) / 2

We want small values, but we'll stop when the last entry is less than 10^-13. A while loop is useful here because we don't know how many entries this requires, but we can keep cutting in half while each entry satisfies a certain criteria. To be clear, the very last entry will be less than 10^-13, but all other entries will be greater than 10^-13

Answer 1

• Since you didn't mention any specific programming language so I'm giving the code in C++.
• As we don't know what will be the array size, so there can be two solutions: first to statically decide the array size to some large value or we can use dynamic array i.e, vector in c++. I'm providing solution for both the cases

NOTE: I have added two main() functions, one by taking float array and one by taking vector, one more thing read the comments in code for your understanding and remove them as per your requirements

#include <iostream>

#include <vector>

#include <cmath>

using namespace std;

// cmath and vector is library which we need to import to use pow() function and vector in c++

//vector code is below

int main() {

vector<float> h;

float val = 1;

while(true){

val = val/2;

if(val < pow(10,-13)){

//here this pow can be replace by `0.0000000000001` also to avoid using cmath library

h.push_back(val);

break;

}

h.push_back(val);

}

// printing final array upto size = index which is the actual size of the array after every insertion

for (int i=0;i<h.size(); i++)

cout<<h[i]<<"\n";

// this is the check whether last element in lesser than 10^-13 or not, you can remove this part

if(h[h.size()-1]>pow(10,-13)){

cout<<true;

}

}

// using static array size code is below, you can use either of them

int main() {

float h[50];

float val = 1;

int index=0;

// index is iterator to maintain final array size and index

while(true){

val = val/2;

if(val < pow(10,-13)){

//here this pow can be replace by `0.0000000000001` also to avoid using cmath library

h[index] = val;

index++;

break;

}

h[index] = val;

index++;

}

//printing final array upto size = index which is the actual size of the array after every insertion

for (int i=0;i<index; i++)

cout<<h[i]<<"\n";

// this is the check whether last element in lesser than 10^-13 or not, you can remove this part

if(h[index-1]<pow(10,-13)){

cout<<true;

}

}

:- Code is working fine in my compiler, check for some copy error if it doesn't work for you. Feel free to ask in comments and like too.