I am creating a currency system that is based in 3 types of coins (Gold, Silver and Copper) it works as 100 copper coins converts into 1 silver coin, and, 100 silver coin converts into 1 gold coin.
I made an struct like this
struct Money
{
Money();
Money(int copper, int silver, int gold);
Money(Money& m);
Money operator + (Money const& obj);
Money operator - (Money const& obj);
void operator += (Money const& obj);
void operator -= (Money const& obj);
void Balance();
void Print();
int c, s, g;
};
But the problem comes with the method Balance(). This method does the math to convert all the copper to silver and silver to gold.
I made this but I'm looking for a better solution if somebody can find it.
I think that the performance of my method is poor.
void Money::Balance()
{
if (c > 99) { s += c / 100; c = c % 100; }
if (s > 99) { g += s / 100; s = s % 100; }
if (c < 0 && s >= 0 && g > 0) {
(c += ((c / 101) + 1) * 100);
s -= (c / -101) + 1;
}
if (s < 0 && g > 0) {
(s += ((s / 101) +1) * 100);
g -= (c / -101) + 1;
}
}
EDIT: The last 2 if-blocks are for negative money to convert for example (50g 10s -1c) in (50g 9s 99c) and just have negative in the first currency type. To not have (50g -9s -2c)
EDIT: I checked that there is a bug that if you have g > 0, s = 0 and c < 0 it wont take a silver so it will show negative copper.
Thank you for your answers <3
I tried to convert 100 copper to 1 silver and 100 silver to 100 gold.
I think that my solution works but the performance is poor.
Remove the last part of your code and it works fine:
void Money::Balance()
{
// Convert excess copper coins to silver coins
s += c / 100;
c %= 100;
// Convert excess silver coins to gold coins
g += s / 100;
s %= 100;
}
Related
I want to compute the distance between numbers with help of the system described in the attached image.
For example: distance between 7 and 5 is -2, distance between 7 and 1 is 2 etc...
Any ideas how to do this in c++? The prefered direction is counter clockwise...
I am using a (int) vector.
If you do it in straightforward way (by considering all possibilities) it might look as follows
int distance(int a, int b)
{ // Distance from `a` to `b`
int d = b - a;
return
a <= b ?
(d <= +4 ? d : d - 8) :
(d <= -4 ? d + 8 : d);
}
which, if you prefer, can be rewritten as
int distance(int a, int b)
{ // Distance from `a` to `b`
int d = b - a;
return -4 < d && d <= 4 ? d : (d > 0 ? d - 8 : d + 8);
}
An alternative, more elegant approach would be to always calculate the positive CCW distance and flip it to negative CW distance if it is greater than 4
int distance(int a, int b)
{ // Distance from `a` to `b`
int d = (b + 8 - a) % 8;
// `d` is CCW distance from `a` to `b`
return d <= 4 ? d : d - 8;
}
But if you want the compiler to generate the most efficient code for this, follow the golden rule "use unsigned types everywhere you can, use signed types only if you have to":
int distance(unsigned a, unsigned b)
{ // Distance from `a` to `b`
unsigned d = (b + 8 - a) % 8;
// `d` is CCW distance from `a` to `b`
return d <= 4 ? d : (int) d - 8;
}
These are really complicated answers. Here is a simpler one:
int distance(int x, int y) {
int d = (y - x) & 7;
return d > 4 ? d - 8 : d;
}
This always returns a result in the range -3..+4. Modular arithmetic is a little simpler to write when the ring size is a power of two, as is the case here.
distance(7, 5) = -2
distance(5, 7) = +2
distance(6, 2) = +4
distance(2, 6) = +4
We use & 7 because it is the simplest way to get the modulo. Alternatively, you can use % 8, but you must also add 8 in order to make sure that the input is not negative:
int d = (y - x + 8) % 8; // same result
Alternatively, you can handle negative numbers explicitly:
int d = (y - x) % 8;
if (d < 0) {
d += 8;
}
// same result
This is just a matter of style.
For simplicity you can find the element from std::find and get the distance from start from std::distance
for example
as you mentioned the data saved in int vector
std::vector<int>::iterator it1 = std::find(myvec.begin(), myvec.end(), val_1);
std::vector<int>::iterator it2 = std::find(myvec.begin(), myvec.end(), val_2);
int dist = std::distance(myvec.begin(),it1) - std::distance(myvec.begin.it2);
if(dist < 0) return dist
else(dist > 0) return myvector.size() - dist()
So hope this will give the distance as the image ...
I am pretty sure this works:
list = [0,1,2,3,4,5,6,7]
distance(x,y) {
a = y-x
b = length(list)-abs(y-x)
z = min(abs(a), abs(b))
if(z=abs(a)) { return a }
if(z=abs(b)) { return b }
}
where abs() is the mathematical absolute value function.
I make a few assumptions here.
As #Hédi Ghédiri pointed out, you are not counting counter-clockwise both times. I am assuming you count the shortest path to the number. (I used the mathematical min() function)
You prefer the positive value over the negative value (#Harper's comment). If you prefer the negative value, switch the last two if statements.
There may be a more concise method, but this (hopefully) works. Please comment if it is wrong. Hope this is helpful!
Edit: this is psuedocode. It should be easy to write in c++. Use the abs() function in <stdlib.h> Forget about list and length(list). Use int types for the variables, and everything else should work.
The following code is prepared to meet all of your needs, for example I assume, that if direction is clockwise the distance is to be negative.
#include <iostream>
#define RING_SIZE 8
enum direction
{
clockwise,
counterClockwise
};
int distance(int a, int b, direction dir)
{
int dist;
if(dir == clockwise)
{
if(a>b)
{
dist = -(a-b);
}
else
{
dist =-(RING_SIZE-b+a);
}
}
else
{
if(a<b)
{
dist = b-a;
}
else
{
dist = RING_SIZE-a+b;
}
}
if(a==b) dist = 0;//Add this if distance between same point must to be 0
return dist;
}
int main()
{
std::cout << distance(7, 2, clockwise) << std::endl;
}
I think this should work
int func(a,b)
{
dist=(b-a);
if(dist<0)
dist +=8;
return dist;
}
in case you're really stuck
I'm trying to create long int multiplication function. In math for multiplying 2 numbers for example 123 X 456, I do:
(12 * 10^1 + 3)( 45 * 10^1 + 6) =
(540 * 10^2) + (72 * 10^1) + (135 * 10^1) + 18 = 15129
I created a small program for this algorithm but it didn't work right.
I don't know where my problem is. Can you help me to understand and correct that?
Tnx
int digits(int n) {
int digit = 0;
while (n>0){
n/=10;
digit++;
}
return digit;
}
long int longMult(long int a, long int b) {
long int x,y,w,z;
int digitA = digits(a);
int digitB = digits(b);
if((a==0) || (b==0)) {
return 0;
} else if (digitA < 2 || digitB < 2) {
return a*b;
} else {
int powA = digitA / 2;
int powB = digitB / 2;
//for first number
x = a/(10^powA);
y = a%(10^powA);
//for second number
w = b/(10^powB);
z = b%(10^powB);
return ( longMult(x,w)*(10^(powA*powB)) + longMult(x,z) +
longMult(w,y)*(10^(powA*powB)) + longMult(y,z));
}
}
int main()
{
cout << digits(23) << endl; // for test
cout << longMult(24,24); // must be 576 but output is 96
return 0;
}
The expression
10^powA
does a bitwise exclusive or, and doesn't raise 10 to the power of powA, as you appear to expect.
You may want to define something like
long powli(int b, long e) {return e?b*powli(b,e-1):1;}
Then instead you can use
powli(10,powA)
Edit: There is also a problem with the way the values are combined:
return ( longMult(x,w)*(10^(powA*powB)) + longMult(x,z) +
longMult(w,y)*(10^(powA*powB)) + longMult(y,z));
Look into the maths, because multiplying the exponents makes little sense.
Also the combinations of adjustments to values is wrong, eg (10*a + b)(10*c + d) = 10*10*a*c + 10*a*d + 10*b*d +b*d. So check on your algebra.
I was finding out the algorithm for finding out the square root without using sqrt function and then tried to put into programming. I end up with this working code in C++
#include <iostream>
using namespace std;
double SqrtNumber(double num)
{
double lower_bound=0;
double upper_bound=num;
double temp=0; /* ek edited this line */
int nCount = 50;
while(nCount != 0)
{
temp=(lower_bound+upper_bound)/2;
if(temp*temp==num)
{
return temp;
}
else if(temp*temp > num)
{
upper_bound = temp;
}
else
{
lower_bound = temp;
}
nCount--;
}
return temp;
}
int main()
{
double num;
cout<<"Enter the number\n";
cin>>num;
if(num < 0)
{
cout<<"Error: Negative number!";
return 0;
}
cout<<"Square roots are: +"<<sqrtnum(num) and <<" and -"<<sqrtnum(num);
return 0;
}
Now the problem is initializing the number of iterations nCount in the declaratione ( here it is 50). For example to find out square root of 36 it takes 22 iterations, so no problem whereas finding the square root of 15625 takes more than 50 iterations, So it would return the value of temp after 50 iterations. Please give a solution for this.
There is a better algorithm, which needs at most 6 iterations to converge to maximum precision for double numbers:
#include <math.h>
double sqrt(double x) {
if (x <= 0)
return 0; // if negative number throw an exception?
int exp = 0;
x = frexp(x, &exp); // extract binary exponent from x
if (exp & 1) { // we want exponent to be even
exp--;
x *= 2;
}
double y = (1+x)/2; // first approximation
double z = 0;
while (y != z) { // yes, we CAN compare doubles here!
z = y;
y = (y + x/y) / 2;
}
return ldexp(y, exp/2); // multiply answer by 2^(exp/2)
}
Algorithm starts with 1 as first approximation for square root value.
Then, on each step, it improves next approximation by taking average between current value y and x/y. If y = sqrt(x), it will be the same. If y > sqrt(x), then x/y < sqrt(x) by about the same amount. In other words, it will converge very fast.
UPDATE: To speed up convergence on very large or very small numbers, changed sqrt() function to extract binary exponent and compute square root from number in [1, 4) range. It now needs frexp() from <math.h> to get binary exponent, but it is possible to get this exponent by extracting bits from IEEE-754 number format without using frexp().
Why not try to use the Babylonian method for finding a square root.
Here is my code for it:
double sqrt(double number)
{
double error = 0.00001; //define the precision of your result
double s = number;
while ((s - number / s) > error) //loop until precision satisfied
{
s = (s + number / s) / 2;
}
return s;
}
Good luck!
Remove your nCount altogether (as there are some roots that this algorithm will take many iterations for).
double SqrtNumber(double num)
{
double lower_bound=0;
double upper_bound=num;
double temp=0;
while(fabs(num - (temp * temp)) > SOME_SMALL_VALUE)
{
temp = (lower_bound+upper_bound)/2;
if (temp*temp >= num)
{
upper_bound = temp;
}
else
{
lower_bound = temp;
}
}
return temp;
}
As I found this question is old and have many answers but I have an answer which is simple and working great..
#define EPSILON 0.0000001 // least minimum value for comparison
double SquareRoot(double _val) {
double low = 0;
double high = _val;
double mid = 0;
while (high - low > EPSILON) {
mid = low + (high - low) / 2; // finding mid value
if (mid*mid > _val) {
high = mid;
} else {
low = mid;
}
}
return mid;
}
I hope it will be helpful for future users.
if you need to find square root without using sqrt(),use root=pow(x,0.5).
Where x is value whose square root you need to find.
//long division method.
#include<iostream>
using namespace std;
int main() {
int n, i = 1, divisor, dividend, j = 1, digit;
cin >> n;
while (i * i < n) {
i = i + 1;
}
i = i - 1;
cout << i << '.';
divisor = 2 * i;
dividend = n - (i * i );
while( j <= 5) {
dividend = dividend * 100;
digit = 0;
while ((divisor * 10 + digit) * digit < dividend) {
digit = digit + 1;
}
digit = digit - 1;
cout << digit;
dividend = dividend - ((divisor * 10 + digit) * digit);
divisor = divisor * 10 + 2*digit;
j = j + 1;
}
cout << endl;
return 0;
}
Here is a very simple but unsafe approach to find the square-root of a number.
Unsafe because it only works by natural numbers, where you know that the base respectively the exponent are natural numbers. I had to use it for a task where i was neither allowed to use the #include<cmath> -library, nor i was allowed to use pointers.
potency = base ^ exponent
// FUNCTION: square-root
int sqrt(int x)
{
int quotient = 0;
int i = 0;
bool resultfound = false;
while (resultfound == false) {
if (i*i == x) {
quotient = i;
resultfound = true;
}
i++;
}
return quotient;
}
This a very simple recursive approach.
double mySqrt(double v, double test) {
if (abs(test * test - v) < 0.0001) {
return test;
}
double highOrLow = v / test;
return mySqrt(v, (test + highOrLow) / 2.0);
}
double mySqrt(double v) {
return mySqrt(v, v/2.0);
}
Here is a very awesome code to find sqrt and even faster than original sqrt function.
float InvSqrt (float x)
{
float xhalf = 0.5f*x;
int i = *(int*)&x;
i = 0x5f375a86 - (i>>1);
x = *(float*)&i;
x = x*(1.5f - xhalf*x*x);
x = x*(1.5f - xhalf*x*x);
x = x*(1.5f - xhalf*x*x);
x=1/x;
return x;
}
After looking at the previous responses, I hope this will help resolve any ambiguities. In case the similarities in the previous solutions and my solution are illusive, or this method of solving for roots is unclear, I've also made a graph which can be found here.
This is a working root function capable of solving for any nth-root
(default is square root for the sake of this question)
#include <cmath>
// for "pow" function
double sqrt(double A, double root = 2) {
const double e = 2.71828182846;
return pow(e,(pow(10.0,9.0)/root)*(1.0-(pow(A,-pow(10.0,-9.0)))));
}
Explanation:
click here for graph
This works via Taylor series, logarithmic properties, and a bit of algebra.
Take, for example:
log A = N
x
*Note: for square-root, N = 2; for any other root you only need to change the one variable, N.
1) Change the base, convert the base 'x' log function to natural log,
log A => ln(A)/ln(x) = N
x
2) Rearrange to isolate ln(x), and eventually just 'x',
ln(A)/N = ln(x)
3) Set both sides as exponents of 'e',
e^(ln(A)/N) = e^(ln(x)) >~{ e^ln(x) == x }~> e^(ln(A)/N) = x
4) Taylor series represents "ln" as an infinite series,
ln(x) = (k=1)Sigma: (1/k)(-1^(k+1))(k-1)^n
<~~~ expanded ~~~>
[(x-1)] - [(1/2)(x-1)^2] + [(1/3)(x-1)^3] - [(1/4)(x-1)^4] + . . .
*Note: Continue the series for increased accuracy. For brevity, 10^9 is used in my function which expresses the series convergence for the natural log with about 7 digits, or the 10-millionths place, for precision,
ln(x) = 10^9(1-x^(-10^(-9)))
5) Now, just plug in this equation for natural log into the simplified equation obtained in step 3.
e^[((10^9)/N)(1-A^(-10^-9)] = nth-root of (A)
6) This implementation might seem like overkill; however, its purpose is to demonstrate how you can solve for roots without having to guess and check. Also, it would enable you to replace the pow function from the cmath library with your own pow function:
double power(double base, double exponent) {
if (exponent == 0) return 1;
int wholeInt = (int)exponent;
double decimal = exponent - (double)wholeInt;
if (decimal) {
int powerInv = 1/decimal;
if (!wholeInt) return root(base,powerInv);
else return power(root(base,powerInv),wholeInt,true);
}
return power(base, exponent, true);
}
double power(double base, int exponent, bool flag) {
if (exponent < 0) return 1/power(base,-exponent,true);
if (exponent > 0) return base * power(base,exponent-1,true);
else return 1;
}
int root(int A, int root) {
return power(E,(1000000000000/root)*(1-(power(A,-0.000000000001))));
}
So basically I'm trying to overload the plus operator so that it adds up change in price1 (1, 99) and price2 (2, 99). So 1.99 + 2.99 should equal 4.98 dollars. The code compiles, but I almost have the answer. Instead of 4.98, it gives out 3.1.98, which is not right. How can I fix this? I'm open to any suggestions or ideas
Here's my header file, titled MyClass.h:
#pragma once
class MyClass
{
public:
int bills;
double coins;
MyClass (int, int);
double sum () { return (bills + (coins * 0.01)); }
MyClass operator+ (MyClass);
MyClass(void);
~MyClass(void);
};
and my source file:
#include <iostream>
#include <string>
#include "MyClass.h"
using namespace std;
MyClass::MyClass(void)
{
}
MyClass::~MyClass(void)
{
}
MyClass::MyClass(int d, int c)
{
bills = d;
coins = c;
}
MyClass MyClass::operator+ (MyClass param) {
MyClass temp;
temp.bills = bills + param.bills;
temp.coins = (coins + param.coins) * 0.01; //Here is the problem, I think
return temp;
}
void main()
{
MyClass price1 (1, 99);
MyClass price2 (2, 99);
MyClass total;
total = price1 + price2;
cout << total.bills << "." << total.coins << endl;
}
You have converted coins in sum () already.
update
temp.coins = (coins + param.coins) * 0.01;
to
temp.coins = coins + param.coins;
And output statement is wrong, you print . by yourself
cout << total.sum() << endl;
Curious as to why you're using a double for pennies. You don't usually have fractions of a pennies except when paying for gasoline, so int would make more sense.
A few things of note:
As aforementioned, be sure to do only temp.coins = coins + param.coins;.
You're not transferring the value of the pennies, just the number of pennies.
Also, carry over pennies! 199 cents is 1 dollar 99 cents. This should translate into something like
int totalCoins = coins + param.coins;
temp.bills = bills + param.bills + totalCoins / 100;
temp.coins = totalCoins % 100;
assuming that you've turned coins into an int.
And by the way, you're not dumb. Every master was once a beginner.
you should update
temp.bills = bills + param.bills;
temp.coins = (coins + param.coins) * 0.01;
TO
temp.bills = bills + param.bills + (coins + param.coins) / 100
temp.coins = (coins + param.coins) % 100
by the way, coins should be int type
I am looking to implement the fermat's little theorem for prime testing. Here's the code I have written:
lld expo(lld n, lld p) //2^p mod n
{
if(p==0)
return 1;
lld exp=expo(n,p/2);
if(p%2==0)
return (exp*exp)%n;
else
return (((exp*exp)%n)*2)%n;
}
bool ifPseudoPrime(lld n)
{
if(expo(n,n)==2)
return true;
else
return false;
}
NOTE: I took the value of a(<=n-1) as 2.
Now, the number n can go as large as 10^18. This means that variable exp can reach values near 10^18. Which further implies that the expression (exp*exp) can reach as high as 10^36 hence causing overflow. How do I avoid this.
I tested this and it ran fine till 10^9. I am using C++
If the modulus is close to the limit of the largest integer type you can use, things get somewhat complicated. If you can't use a library that implements biginteger arithmetic, you can roll a modular multiplication yourself by splitting the factors in low-order and high-order parts.
If the modulus m is so large that 2*(m-1) overflows, things get really fussy, but if 2*(m-1) doesn't overflow, it's bearable.
Let us suppose you have and use a 64-bit unsigned integer type.
You can calculate the modular product by splitting the factors into low and high 32 bits, the product then splits into
a = a1 + (a2 << 32) // 0 <= a1, a2 < (1 << 32)
b = b1 + (b2 << 32) // 0 <= b1, b2 < (1 << 32)
a*b = a1*b1 + (a1*b2 << 32) + (a2*b1 << 32) + (a2*b2 << 64)
To calculate a*b (mod m) with m <= (1 << 63), reduce each of the four products modulo m,
p1 = (a1*b1) % m;
p2 = (a1*b2) % m;
p3 = (a2*b1) % m;
p4 = (a2*b2) % m;
and the simplest way to incorporate the shifts is
for(i = 0; i < 32; ++i) {
p2 *= 2;
if (p2 >= m) p2 -= m;
}
the same for p3 and with 64 iterations for p4. Then
s = p1+p2;
if (s >= m) s -= m;
s += p3;
if (s >= m) s -= m;
s += p4;
if (s >= m) s -= m;
return s;
That way is not very fast, but for the few multiplications needed here, it may be fast enough. A small speedup should be obtained by reducing the number of shifts; first calculate (p4 << 32) % m,
for(i = 0; i < 32; ++i) {
p4 *= 2;
if (p4 >= m) p4 -= m;
}
then all of p2, p3 and the current value of p4 need to be multiplied with 232 modulo m,
p4 += p3;
if (p4 >= m) p4 -= m;
p4 += p2;
if (p4 >= m) p4 -= m;
for(i = 0; i < 32; ++i) {
p4 *= 2;
if (p4 >= m) p4 -= m;
}
s = p4+p1;
if (s >= m) s -= m;
return s;
You can perform your multiplications in several stages. For example, say you want to compute X*Y mod n. Take X and Y and write them as X = 10^9*X_1 + X_0, Y = 10^9*Y_1 + Y_0. Then compute all four products X_i*Y_j mod n, and finally compute X = 10^18*(X_1*Y_1 mod n) + 10^9*( X_0*Y_1 + X_1*Y_0 mod n) + X_0*Y_0. Note that in this case, you are operating with numbers half the size of the maximum allowed.
If splitting in two parts do not suffice (I suspect this is the case), split in three parts using the same schema. Splitting in three should work.
A simpler approach is just to multiply the school way. It corresponds to the previous approach, but writing one number in as many parts as digits it has.
Good luck!