how to make 2 = .01 and .01 = 2? - c++

Okay so the title may not make the most sense but I will explain it better here.. what i'm trying to do is take the value of 2 and make it equal to .01 and make .01 = 2, well I tried to hardcode it like this
if (Value = 2)
Value = 0;
else if (Value = 1.99)
Value = .01;
else if (Value = 1.98)
Value = .02;
else if (Value = 1.97)
Value = .03;
else if (Value = 1.96)
Value = .04;
else if (Value = 1.95)
Value = .05;
(I did that all the way down to 0... however it didn't function properly
I also tried to get the inverse of the value like so..
Value = 1 / Value;
Now if the value was 2 it would return it to .5 and if the value was 1 it would set it to 1.. I knew this wouldn't work when I tried I just didn't know what to do... If anyone could lead me in the right direction that would be cool.. (also I think this thread is a little bit better than my past threads seeing how I explained it :^) )

You're using the assignment operator "=". This assigns a value to a variable (such as x = 10). Inside your if-check clause, you want to compare both variables equality with the compare-equality operator, "==".
if (Value == 2.f) // checks if Value is equal to 2
Value = 0.f; // sets Value equal to 0
else if (Value == 1.99f)
Value = .01f;
else if (Value == 1.98f)
Value = .02f;
else if (Value == 1.97f)
Value = .03f;
else if (Value == 1.96f)
Value = .04f;
else if (Value == 1.95f)
Value = .05f;
An alternative yet complete solution to your problem:
if (Value <= 2.f && Value >= 0.f) // checks if Value is between or is 2 or 0
Value = 2.f - Value; // sets !version of Value to Value
Value = 1 / Value; wouldn't work because you're trying to get the !version of Value, not the inversion of Value.
Remember to do f after a float check so you don't run into weird faulty comparison problems.

Related

Why is there a loop in this division as multiplication code?

I got the js code below from an archive of hackers delight (view the source)
The code takes in a value (such as 7) and spits out a magic number to multiply with. Then you bitshift to get the results. I don't remember assembly or any math so I'm sure I'm wrong but I can't find the reason why I'm wrong
From my understanding you could get a magic number by writing ceil(1/divide * 1<<32) (or <<64 for 64bit values, but you'd need bigger ints). If you multiple an integer with imul you'd get the result in one register and the remainder in another. The result register is magically the correct result of a division with this magic number from my formula
I wrote some C++ code to show what I mean. However I only tested with the values below. It seems correct. The JS code has a loop and more and I was wondering, why? Am I missing something? What values can I use to get an incorrect result that the JS code would get correctly? I'm not very good at math so I didn't understand any of the comments
#include <cstdio>
#include <cassert>
int main(int argc, char *argv[])
{
auto test_divisor = 7;
auto test_value = 43;
auto a = test_value*test_divisor;
auto b = a-1; //One less test
auto magic = (1ULL<<32)/test_divisor;
if (((1ULL<<32)%test_divisor) != 0) {
magic++; //Round up
}
auto answer1 = (a*magic) >> 32;
auto answer2 = (b*magic) >> 32;
assert(answer1 == test_value);
assert(answer2 == test_value-1);
printf("%lld %lld\n", answer1, answer2);
}
JS code from hackers delight
var two31 = 0x80000000
var two32 = 0x100000000
function magic_signed(d) { with(Math) {
if (d >= two31) d = d - two32// Treat large positive as short for negative.
var ad = abs(d)
var t = two31 + (d >>> 31)
var anc = t - 1 - t%ad // Absolute value of nc.
var p = 31 // Init p.
var q1 = floor(two31/anc) // Init q1 = 2**p/|nc|.
var r1 = two31 - q1*anc // Init r1 = rem(2**p, |nc|).
var q2 = floor(two31/ad) // Init q2 = 2**p/|d|.
var r2 = two31 - q2*ad // Init r2 = rem(2**p, |d|).
do {
p = p + 1;
q1 = 2*q1; // Update q1 = 2**p/|nc|.
r1 = 2*r1; // Update r1 = rem(2**p, |nc|.
if (r1 >= anc) { // (Must be an unsigned
q1 = q1 + 1; // comparison here).
r1 = r1 - anc;}
q2 = 2*q2; // Update q2 = 2**p/|d|.
r2 = 2*r2; // Update r2 = rem(2**p, |d|.
if (r2 >= ad) { // (Must be an unsigned
q2 = q2 + 1; // comparison here).
r2 = r2 - ad;}
var delta = ad - r2;
} while (q1 < delta || (q1 == delta && r1 == 0))
var mag = q2 + 1
if (d < 0) mag = two32 - mag // Magic number and
shift = p - 32 // shift amount to return.
return mag
}}
In the C CODE:
auto magic = (1ULL<<32)/test_divisor;
We get Integer Value in magic because both (1ULL<<32) & test_divisor are Integers.
The Algorithms requires incrementing magic on certain conditions, which is the next conditional statement.
Now, multiplication also gives Integers:
auto answer1 = (a*magic) >> 32;
auto answer2 = (b*magic) >> 32;
C CODE is DONE !
In the JS CODE:
All Variables are var ; no Data types !
No Integer Division ; No Integer Multiplication !
Bitwise Operations are not easy and not suitable to use in this Algorithm.
Numeric Data is via Number & BigInt which are not like "C Int" or "C Unsigned Long Long".
Hence the Algorithm is using loops to Iteratively add and compare whether "Division & Multiplication" has occurred to within the nearest Integer.
Both versions try to Implement the same Algorithm ; Both "should" give same answer, but JS Version is "buggy" & non-standard.
While there are many Issues with the JS version, I will highlight only 3:
(1) In the loop, while trying to get the best Power of 2, we have these two statements :
p = p + 1;
q1 = 2*q1; // Update q1 = 2**p/|nc|.
It is basically incrementing a counter & multiplying a number by 2, which is a left shift in C++.
The C++ version will not require this rigmarole.
(2) The while Condition has 2 Equality comparisons on RHS of || :
while (q1 < delta || (q1 == delta && r1 == 0))
But both these will be false in floating Point Calculations [[ eg check "Math.sqrt(2)*Math.sqrt(0.5) == 1" : even though this must be true, it will almost always be false ]] hence the while Condition is basically the LHS of || , because RHS will always be false.
(3) The JS version returns only one variable mag but user is supposed to get (& use) even variable shift which is given by global variable access. Inconsistent & BAD !
Comparing , we see that the C Version is more Standard, but Point is to not use auto but use int64_t with known number of bits.
First I think ceil(1/divide * 1<<32) can, depending on the divide, have cases where the result is off by one. So you don't need a loop but sometimes you need a corrective factor.
Secondly the JS code seems to allow for other shifts than 32: shift = p - 32 // shift amount to return. But then it never returns that. So not sure what is going on there.
Why not implement the JS code in C++ as well and then run a loop over all int32_t and see if they give the same result? That shouldn't take too long.
And when you find a d where they differ you can then test a / d for all int32_t a using both magic numbers and compare a / d, a * m_ceil and a * m_js.

Error with two credit card numbers. Identifies the number as the wrong credit card type

These are my current errors, I think I did something wrong with the maths but everything I tried didn't work.
Ps: Sorry if my question's formatting is bad, first time using stackflow.
:) credit.c exists
:) credit.c compiles
:) identifies 378282246310005 as AMEX
:) identifies 371449635398431 as AMEX
:) identifies 5555555555554444 as MASTERCARD
:) identifies 5105105105105100 as MASTERCARD
:) identifies 4111111111111111 as VISA
:) identifies 4012888888881881 as VISA
:) identifies 4222222222222 as VISA
:) identifies 1234567890 as INVALID
:) identifies 369421438430814 as INVALID
:) identifies 4062901840 as INVALID
:) identifies 5673598276138003 as INVALID
:( identifies 4111111111111113 as INVALID
expected "INVALID\n", not "VISA\n"
:( identifies 4222222222223 as INVALID
expected "INVALID\n", not "VISA\n"
#include <cs50.h>
#include <math.h>
// Prompt user for credit card number
int main(void)
{
long credit_card, credit_number;
do
{
credit_card = get_long("Enter credit card number: ");
}
while (credit_card < 0);
credit_number = credit_card;
// Calculate total number of digits
int count = (credit_number == 0) ? 1 : (log10(credit_number) + 1);
int summation = 0;
while (credit_number == 0)
{
int x = credit_number % 10; summation += x;
int y = 2 * ((credit_number / 10) % 10);
int r = (y % 10) + floor((y / 10) % 10); summation += r; credit_number /= 100;
}
string card;
// Identify which card type you get after inputing your credit card number
int test = cc / pow(10, count - 2);
if ((count == 13 || count == 16) && test / 10 == 4)
{
card = "VISA";
}
else if (count == 16 && test >= 51 && test <= 55)
{
card = "MASTERCARD";
}
else if (count == 15 && (test == 34 || test == 37))
{
card = "AMEX";
}
else
{
card = "INVALID";
}
// Final verification
if (sum % 10 == 0)
{
printf("%s\n", card);
}
else
{
printf("INVALID\n");
}
}```
Your algorithm is maybe not fully correct. I would therefore propose a different approach. You can look at each single digit in a loop. And, you can also do the whole checksum calculation in one step.
I will show you how to do and explain the algorithm behind it.
BTW. Chosing the right algorithm is always the key for success.
So, first we need to think on how we can extract digits from a number. This can be done in a loop by repeating the follwoing steps:
Perform a modulo 10 division to get a digit
Do a integer division by 10
Repeat
Let us look at the example 1234.
Step 1 will get the 4 -- (1234 % 10 = 4)
Step 2 will convert original number into 123 -- (1234 / 10 = 123)
Step 1 will get the 3 -- (123 % 10 = 3)
Step 2 will convert the previous number into 12 -- (123 / 10 = 12)
Step 1 will get the 2 -- (12 % 10 = 2)
Step 2 will convert the previous number into 1 -- (12 / 10 = 1)
Step 1 will get the 1 -- (1 % 10 = 1)
Step 2 will convert the previous number into 0 -- (1 / 10 = 0)
Then the loop stops. Additionally we can observe that the loop stops, when the resulting divided becomes 0. And, we see addtionally that the number of loop executions is equal to the number of digits in the number. But this is somehow obvious.
OK, then let us look, what we learned so far
while (creditCardNumber > 0) {
unsigned int digit = creditCardNumber % 10;
creditCardNumber /= 10;
++countOfDigits;
}
This will get all digits and count them.
Good. Lets go to next step.
For later validation and comparison purpose we need to get the most significant digit (the first digit) and the second most significant digit (the second digit) of the number.
For this, we define 2 variables which will hold the number. We simply assign the current evaluated digit (and override it in each loop execution) to the "mostSignificantDigit". At the end of the loop, we will have it in our desired variable.
For the "secondMostSignificantDigit" we will simple copy the "old" or "previous" value of the "mostSignificantDigit", before assigning a new value to "mostSignificantDigit". With that, we will always have both values available.
The loop looks now like this:
while (creditCardNumber > 0) {
const unsigned int digit = creditCardNumber % 10;
secondMostSignificantDigit = mostSignificantDigit;
mostSignificantDigit = digit;
creditCardNumber /= 10;
++countOfDigits;
}
OK, now we come to the maybe more complex part. The cheksum. The calculation method is.
Start with the least significant (the last) digit
Do not multiply the digit, which is equivalent with multiplying it with 1, and add it to the checksum
Goto the next digit. Multiply it by 2. If the result is greater than 10, then get again the single digits and add both digits to the checksum
Repeat
So, the secret is, to analyze the somehow cryptic specification, given here. If we start with the last digit, we do not multiply it, the next digit will be multiplied, the next not and so on and so on.
To "not multiply" is the same as multiplying by 1. This means: In the loop we need to multiply alternating with 1 or with 2.
How to get alternating numbers in a loop? The algorithm for that is fairly simple. If you need alternating numbers, lets say, x,y,x,y,x,y,x..., Then, build the sum of x and y and perform the subtratcion "value = sum - value". Example:
We need alternating values 1 and 2. The sum is 3. To get the next value, we subtract the current value from the sum.
initial value = 1
sum = 3
current value = initial value = 1
next value = 3 - 1 = 2. Current value = 2
next value = 3 - 2 = 1. Current value = 1
next value = 3 - 1 = 2. Current value = 2
next value = 3 - 2 = 1. Current value = 1
next value = 3 - 1 = 2. Current value = 2
next value = 3 - 2 = 1. Current value = 1
. . .
Good, now we understand, how to make alternating values.
Next, If we multiply a digit with 2, then the maximum result maybe a 2 digit value. We get the single digits with a modulo and an integer division by 10.
And, now important, it does not matter, if we multiply or not, because, if we do not multiply, then the upper digit will always be 0. And this will not contribute to the sum.
With all that, we can always do a multiplication and always split the result into 2 digits (many of them having the upper digit 0).
The result will be:
checkSum += (digit * multiplier) % 10 + (digit * multiplier) / 10;
multiplier = 3 - multiplier;
An astonishingly simple formula.
Next, if we know C or C++ we also know that a multiplication with 2 can be done very efficiently with a bit shift left. And, additionally, a "no-multiplication" can be done with a bit shift 0. That is extremely efficient and faster than multiplication.
x * 1 is identical with x << 0
x * 2 is identical with x << 1
For the final result we will use this mechanism, alternate the multiplier between 0 and 1 and do shifts.
This will give us a very effective checksum calculation.
At the end of the program, we will use all gathered values and compare them to the specification.
Thsi will lead to:
int main() {
// Get the credit card number. Unfortunately I do not know CS50. I use the C++ standard iostream lib.
// Please replace the following 4 lines with your CS50 equivalent
unsigned long long creditCardNumber;
std::cout << "Enter credit card number: ";
std::cin >> creditCardNumber;
std::cout << "\n\n";
// We need to count the number of digits for validation
unsigned int countOfDigits = 0;
// Here we will calculate the checksum
unsigned int checkSum = 0;
// We need to multiply digits with 1 or with 2
unsigned int multiplier = 0;
// For validation purposes we need the most significant 2 digits
unsigned int mostSignificantDigit = 0;
unsigned int secondMostSignificantDigit = 0;
// Now we get all digits from the credit card number in a loop
while (creditCardNumber > 0) {
// Get the least significant digits (for 1234 it will be 4)
const unsigned int digit = creditCardNumber % 10;
// Now we have one digit more. In the end we will have the number of all digits
++countOfDigits;
// Simply remember the most significant digits
secondMostSignificantDigit = mostSignificantDigit;
mostSignificantDigit = digit;
// Calculate the checksum
checkSum += (digit << multiplier) % 10 + (digit << multiplier) / 10;
// Multiplier for next loop
multiplier = 1 - multiplier;
creditCardNumber /= 10;
}
// Get the least significant digit of the checksum
checkSum %= 10;
// Validate all calculated values and show the result
if ((0 == checkSum) && // Checksum must be correct AND
(15 == countOfDigits) && // Count of digits must be correct AND
((3 == mostSignificantDigit) && // Most significant digits must be correct
((4 == secondMostSignificantDigit) || (7 == secondMostSignificantDigit)))) {
std::cout << "AMEX\n";
}
else if ((0 == checkSum) && // Checksum must be correct AND
(16 == countOfDigits) && // Count of digits must be correct AND
((5 == mostSignificantDigit) && // Most significant digits must be correct
((secondMostSignificantDigit > 0) && (secondMostSignificantDigit < 6)))) {
std::cout << "MASTERCARD\n";
}
else if ((0 == checkSum) && // Checksum must be correct AND
((16 == countOfDigits) || (13 == countOfDigits)) && // Count of digits must be correct AND
((4 == mostSignificantDigit))) { // Most significant digit must be correct
std::cout << "VISA\n";
}
else {
std::cout << "INVALID\n";
}
return 0;
}
What we learn with this example, is integer division and modulo division and the smart usage of the identity element for binary operations.
In case of questions, please ask
Just to be complete, I will show you a C++ solution, based on a std::string and using modern C++ elements and algorithms.
For example, the whole checksum calculation will be done with one statement. The whole program does not contain any loop.
#include <iostream>
#include <string>
#include <regex>
#include <numeric>
int main() {
// ---------------------------------------------------------------------------------------------------
// Get user input
// Inform user, what to do. Enter a credit card number. We are a little tolerant with the input format
std::cout << "\nPlease enter a credit card number:\t";
// Get the number, in any format from the user
std::string creditCardNumber{};
std::getline(std::cin, creditCardNumber);
// Remove the noise, meaning, all non digits from the credit card number
creditCardNumber = std::regex_replace(creditCardNumber, std::regex(R"(\D)"), "");
// ---------------------------------------------------------------------------------------------------
// Calculate checksum
unsigned int checksum = std::accumulate(creditCardNumber.rbegin(), creditCardNumber.rend(), 0U,
[multiplier = 1U](const unsigned int sum, const char digit) mutable -> unsigned int {
multiplier = 1 - multiplier; unsigned int value = digit - '0';
return sum + ((value << multiplier) % 10) + ((value << multiplier) / 10); });
// We are only interested in the lowest digit
checksum %= 10;
// ---------------------------------------------------------------------------------------------------
// Validation and output
if ((0 == checksum) && // Checksum must be correct AND
(15 == creditCardNumber.length()) && // Count of digits must be correct AND
(('3' == creditCardNumber[0]) && // Most significant digits must be correct
(('4' == creditCardNumber[1]) || ('7' == creditCardNumber[1])))) {
std::cout << "AMEX\n";
}
else if ((0 == checksum) && // Checksum must be correct AND
(16 == creditCardNumber.length()) && // Count of digits must be correct AND
(('5' == creditCardNumber[0]) && // Most significant digits must be correct
((creditCardNumber[1] > '0') && (creditCardNumber[1] < '6')))) {
std::cout << "MASTERCARD\n";
}
else if ((0 == checksum) && // Checksum must be correct AND
((16 == creditCardNumber.length()) || (13 == creditCardNumber.length())) && // Count of digits must be correct AND
(('4' == creditCardNumber[0]))) { // Most significant digit must be correct
std::cout << "VISA\n";
}
else {
std::cout << "INVALID\n";
}
return 0;

Variable changes on it's own in C++

I have a loop going through an array trying to find which index is a string. It should solve for what that value should be.
I can't figure out why, but as soon as the if statements start i becomes 1 which gives my code an error.
I'm not very fluent in C++.
for(int i = 0; i < 4; i++) {
if(auto value = std::get_if<std::string>(&varArr[i])) {
solvedIndex = i;
auto value0 = std::get_if<float>(&varArr[0]);
auto value1 = std::get_if<float>(&varArr[1]);
auto value2 = std::get_if<float>(&varArr[2]);
auto value3 = std::get_if<float>(&varArr[3]);
//i changes to 1 when this if starts??
if(i = 0) {
solvedVar = (*value3 / *value1) * *value2;
} else if (i = 1) {
solvedVar = *value3 / (*value0 / *value2);
} else if (i = 2) {
solvedVar = *value0 / (*value3 / *value1);
} else {
solvedVar = *value1 * (*value0 / *value2);
}
break;
}
}
Note that these variables are declared above. Also, varArr is filled with values:
std::variant<std::string, float> varArr[4];
int solvedIndex;
float solvedVar;
As has been noted, in your if statements, you are using the assignment operator (=) but want the equality comparison operator (==). For your variable i the first if statement sets i equal to 0 and if(0) is the same as if(false). So your program goes to the first else-if which sets i equal to 1 and if(1) evaluates to true. Your code then finishes the block within else if (i = 1) {...} and then ends.
That's because operator= is the assignment operator in C++ (and most languages, actually). That changes the value of the variable to the value on the other side. So, for instance:
x = 0
will change the value of x to 0. Doesn't matter if it's in an if statement. It will always change the value to 0 (or whatever the right hand side value is).
What you are looking for is operator==, which is the comparison (aka relational) operator in C++/ That asks the question "Are these two things equal?" So, for instance:
x == 0
asks is x is equal to 0.

Equality comparison in if-statement

Sorry about this question, this is my first C++ project and I'm a little confused. I'm asking the user to input 3 separate things. For example, I'm starting off with a number, 80. I'm asking the user 3 questions. 1) Do you like blue or yellow? Type 1 for blue, 2 for yellow. If the user enters 1 for blue, multiply the number 80 by 2. If they enter 2 for yellow, multiply 80 by 3.
Can somebody let me know if this looks like it's on the right track? Thanks and sorry again for the beginner question.
cout << "Please enter a color blue or yellow. Type 1 for Blue, 2 for Yellow";
cin >> bp1;
// Multiply by 2 if Blue is chosen, 3 if Yellow is chosen.
if (bp1 = 1)
num = num*2;
if (bp1 = 2)
num = num*3;
There is a problem in your if statement
it must be like this :
if (bp1 == 1)
num = num*2;
if (bp1 == 2)
num = num*3;
Welcome to the world of C++! You're definitely on the right track, but there a couple of problems. First, the operator you use in your if statements is the assignment operator, so your statements will always return true. This should actually be the comparison operator (==). Second, I recommend the use of an if-else if statement here, as you may not need to check both times. The following should be sufficient:
if(bp1 == 1)
{
num = num * 2;
}
else if(bp1 == 2)
{
num = num * 3;
}
you meant to write compare operator ==
if (bp1 == 1)
if (bp1 == 2)
// ^^
if (bp1=1) will always be evaluated to true from operator=
Even simpler:
Instead of:
if(bp1 == 1)
num = num * 2;
else if (bp1 == 2)
num = num * 3;
you can write this
num = num * (bp + 1)
or even
num *= (bp + 1)

Recursion solution for a number raised to an exponent

Hey I have a problem were I have to solve x^n in a number of ways. One of them involves using a recursion formula and its giving me a hard time. So one of the ways I used recursion for x^n for n>=0
int power2(int base, int power){
if (power == 0)
return 1;
else if ( power == 1)
return base;
else
return (base * power2(base, power - 1));
}
this makes sense to me So when i set X = 2 and N = 4, it is decreasing the power, which is acting as a counter, and doing 2x2 power raised to 3, 4*2, power raised to 2, 8 *2 = 16. Than the power is raised to 1, and I have a base case were if the power is raised to 1 it just returns base. However for my next one I have to solve it using three formulas.
x0 = 1
xn if n is even = [xn/2]2
xn if n is odd = x * [xn/2]2
So what I have so far is
int power3(int base, int power){
if(power == 0){
return 1;
}
else if ( power == 1)
return base;
// if power is even
if (power % 2 == 0){
return base*(power3(base,(power/2)));
}
// if power is odd
else{
return 0;
}
}
So im just trying to get even numbers to work first, and when I set x=2 and n=4 it returns 8. Which makes sense to me, since when the power is 4/2 will only loop twice for being >1. So i really am trying to figure out a way to get this to loop one more time while staying true to the formula I was given.and when I added the odd base case now the program will work up untill n^5 but n^6 returns 32
You got a little problem with the interpretation of the formula.
x^n if n is even = [x^n/2]2 doesn't mean:
base*(power3(base,(power/2))) //meaning x * [x^n/2]
rather you'd have
(power3(base,(power/2))) * 2
looking at your formula again it isn't correct even and should be x^n if n is even = [x^n/2]^2
so as code:
(power3(base,(power/2))) * (power3(base,(power/2)))
or:
(power3(base * base,(power/2)))
Your whole function should probably be like this:
int power3(int base, int power){
if(power == 0){
return 1;
}
else if ( power == 1) // you don't really need this case,
return base; // power == 0 is enough as base case
// if power is even
if (power % 2 == 0){
return (power3(base * base,(power/2)));
}
// if power is odd
else{
return base * (power3(base * base,(power/2)));
}
}
Ok, since you seem to still be confused with the odd powers.
Your power variable is int so you get integer division meaning 3/2 = 1 instead of 1.5 (everything behind the decimal point gets truncated).
Now lets look at the odd case in the function:
return base * (power3(base * base,(power/2)));
lets assume base == 4 and power == 5
return 4 * (power3(4 * 4,(5/2))); // 5/2 evaluates to 2
is the same as saying return 4 * (power3(4, 5 - 1))
and then having return (power3(4 * 4, 4 /2)) since we now got an even case.
We basically just do these 2 steps as 1. I think my explanation sounds a bit weird but hope it helps.