Program to identify the closest value from a range of values

[youknowme]

I need to write a program that has as input a floating point number e.g. 2.3162
The program then generates a range of floating point numbers and it must them identify which number within the range generated comes the closest to the given value:

This does not work. It gives the last number as the closeset - which is wrong. Is there a simple way to achieve this?
------------
#include <iostream>
#include <cmath>
#include <vector>

int main()
{
// place floating point values in a vector
std::vector<double> numbers;
for(int i = 0; i <= 10; ++i)
{
numbers.push_back(sqrt(i));
std::cout << numbers[i] << '\n';
}

const double myval(2.3162);

// variables to store the differnce?
double difference(0);
double smallestdifference(0); // arbitrary

//go through the vector and determine the closest number to myval 2.3162
for(int i = 0; i <= 10; ++i)
{
//THIS GIVE ME WRONG RESULTS
difference = myval-numbers[i];
std::cout << "difference is " << difference << '\n';
if(difference < smallestdifference)
smallestdifference = numbers[i];
}

std::cout << "The number with the smallest difference is " << smallestdifference << '\n';
}
------------------
Output gives:
0
1
1.41421
1.73205
2
2.23607
2.44949
2.64575
2.82843
3
3.16228
difference is 2.3162
difference is 1.3162
difference is 0.901986
difference is 0.584149
difference is 0.3162
difference is 0.080132
difference is -0.13329
difference is -0.329551
difference is -0.512227
difference is -0.6838
difference is -0.846078
The number with the smallest difference is 3.16228
---------------------------------

how can i do this?

[Scipio]

if(difference < smallestdifference)
smallestdifference = numbers[i];

This statement stores the value into "smallesdifference", not the difference.

[Bazzy]

you should initialize smallestdifference to a high value or it would always be smaller than difference, difference should be set to abs( myval-numbers[i] )
and if difference is smaller than smallestdifference you should set smallestdifference to difference, not to numbers[i]

[youknowme]

Unfortunately this is not working. Also i must find a solution without using abs() The output is giving me the number which has the greatest difference as the number with the smallest difference:
#include <iostream>
#include <cmath>
#include <vector>

int main()
{
std::vector<double> numbers;
for(int i = 0; i <= 10; ++i)
{
numbers.push_back(sqrt(i));
std::cout << "number " << i << " has a sqrt of " << sqrt(i) << '\n';
}

const double myval(2.3162);

double difference(0);
double smallestdifference(10); // arbitrary
std::cout << "My value is 2.3162 \n";
for(int i = 0; i <= 10; ++i)
{

std::cout << "number " << i << " with sqrt " << sqrt(i) << '\n';
difference = myval-numbers[i];
std::cout << " has a difference from my value of " << difference << '\n';
if(difference < smallestdifference)
smallestdifference = difference;
}

std::cout << "The number with the smallest difference from my value is " << smallestdifference << '\n';
}
--------------------
output
number 0 has a sqrt of 0
number 1 has a sqrt of 1
number 2 has a sqrt of 1.41421
number 3 has a sqrt of 1.73205
number 4 has a sqrt of 2
number 5 has a sqrt of 2.23607
number 6 has a sqrt of 2.44949
number 7 has a sqrt of 2.64575
number 8 has a sqrt of 2.82843
number 9 has a sqrt of 3
number 10 has a sqrt of 3.16228
My value is 2.3162
number 0 with sqrt 0
has a difference from my value of 2.3162
number 1 with sqrt 1
has a difference from my value of 1.3162
number 2 with sqrt 1.41421
has a difference from my value of 0.901986
number 3 with sqrt 1.73205
has a difference from my value of 0.584149
number 4 with sqrt 2
has a difference from my value of 0.3162
number 5 with sqrt 2.23607
has a difference from my value of 0.080132
number 6 with sqrt 2.44949
has a difference from my value of -0.13329
number 7 with sqrt 2.64575
has a difference from my value of -0.329551
number 8 with sqrt 2.82843
has a difference from my value of -0.512227
number 9 with sqrt 3
has a difference from my value of -0.6838
number 10 with sqrt 3.16228
has a difference from my value of -0.846078
The number with the smallest difference from my value is -0.846078

------------------------
10 with a square root of 3.16228 is the FAREST away from my value of 2.3162. The program must identify the closest number to this value.

[Scipio]

It's because it's negative. You could use difference=sqrt(difference*difference). (I know about the pow() function, but I forgot it's exact syntax :) ).

[youknowme]

I dont understand what you mean. can you explain this please

[Scipio]

Let's say we have a smallest difference of 0.5. Now we find a difference of -2. This will be set as new smallest difference, since -2<0.5 will return true. To avoid this, you can multiply it by itself, and then take the sqrt of it:


5 -> 5*5 = 25 -> sqrt(25) = 5
-5->-5*-5=25 -> sqrt(25) = 5

[youknowme]

i tried to substitute the statement that you suggested but this does not produce the result that i need. Am i wrong in saying that you are suggesting i should remove the variable myval? The whole point of diference is to say how much a number differs from myval - without it the program is meaningless.

Suppose i want to find the closest positive floating point number to myval - the value of difference should not change if differnce goes below zero. So what i need is the closest positive number to zero.

How can i express this in code using a if statement? (to prevent difference from going below zero)

[Scipio]

No, I'm not saying you should remove myval. You are searching the difference with some point and myval. This difference is the distance between those points; it's an abosolute value (it can only be positive).

De difference between 1 and 5 is 4, you will agree with me on that. But in your program it's found as -4, since 1-5 returns -4. Now, the normal syntax to find the absolute returnvalue, is by taking the squareroot of it's square. This will always return a positive value, like i showed with the examples of 5 and -5 in my previous post.
So before you check or the current difference is smaller as the smallest difference, you need to make sure "difference" is positive by using the code I showed previous.

[youknowme]

Please can you change this program so it works to output the value which is CLOSEST to myval? I have re-written it from earlier:
Can you please incorporate the change that you have said would fix it? Thank you

#include <iostream>
#include <cmath>
#include <vector>

int main()
{
std::vector<double> numbers;
for (int i = 1; i <= 100; ++i)
{
numbers.push_back(sqrt(i));
}
const double myval(2.3162);

double difference(0);
double smallestdifference(10); // arbitrary
std::cout << "My value is 2.3162 \n";
for (int i = 1; i <= 100; ++i)
{
std::cout << "number " << i << " with sqrt " << sqrt(i) << '\n';
// only change difference while value remains positive
if ((myval-sqrt(numbers[i])) > 0)
{
// identify the last positive number closest to myval
difference = myval - sqrt(numbers[i]);

std::cout << " has a difference from my value of " << difference << '\n';
if (difference < smallestdifference)
smallestdifference = difference;
}
else
difference = difference;
}

std::cout << "The number with the smallest difference from my value is " << smallestdifference << '\n';
}

[Scipio]

I don't completly follow your new version and I dont have the time to figure that out now. Here is your old version with a line added so it will find the smallest difference:

#include <iostream>
#include <cmath>
#include <vector>

int main()
{
std::vector<double> numbers;
for(int i = 0; i <= 10; ++i)
{
numbers.push_back(sqrt(i));
std::cout << "number " << i << " has a sqrt of " << sqrt(i) << '\n';
}

const double myval(2.3162);

double difference(0);
double smallestdifference(10); // arbitrary
std::cout << "My value is 2.3162 \n";
for(int i = 0; i <= 10; ++i)
{

std::cout << "number " << i << " with sqrt " << sqrt(i) << '\n';
difference = myval-numbers[i];
std::cout << " has a difference from my value of " << difference << '\n';

difference = sqrt(pow(difference,2)); //make sure difference is positive

if(difference < smallestdifference)
smallestdifference = difference;
}

std::cout << "The number with the smallest difference from my value is " << smallestdifference << '\n';
std::cin.ignore();
}

Now it the program will find the smallest difference, now you need to add a variable in wich you can store wich number is the closest to myVal (in this case sqrt(5) ).

[youknowme]

ok - thanks. I have run this and it seems to give correct output. I needed this as part of a bigger program solution.
Thank you for you help.