I need to create program, where in output I'll get the n-th number or sequence. Sequence looks like that:
(-10, 5, -2.5, 1.25, -0.625...)
#include <iostream>
using namespace std;
double count (double n)
{
if (n==1)
return -10;
else
return (-10/((n-1)*(-2)));
}
double n;
main()
{
cout<<"n? : ";
cin>>n;
cout<<count(n);
return 0;
}
For me everythink looks good for me, when I give to the program 1, it gives -10, when I give 2, it gives back 5, but on 3 it gives 2.5, not -2.5, on 4 it gives 1.(6), which doesn't make sense for me. Where's mistake in this code?
An efficient(optimized code) code for your question would be:
#include <iostream>
#include<math.h>
using namespace std;
double count (double n)
{
double x = pow(2, n - 1); //calculate the divisor
return pow(-1, n) * (10 / x); // divide 10 with divisor followed by assigning it a sign
}
int main()
{
int n;
cout<<"n? : ";
cin>>n ;
cout<<count(n) << endl;
return 0;
}
Note: Redundancy occurs due to branching in your code. Better try to write straight-line code(without too many branchings) wherever possible.
When you give n=3, (-10/((n-1)*(-2))) gives you (-10/((3-1)*(-2))) = 2.5. My suggestion would be return (10/((n-1)*2)) * sign(n), where sign(n) return 1 if n is even, and return -1 otherwise.
I think your problem has a really nice & easy recursive solution:
double count(int n){
if (n <= 1) return -10;
return count(n - 1)*-0.5;
}
Example call:
#include <iostream>
#include <iomanip>
int main(){
for (int i = 1; i < 20; ++i){
std::cout << std::setw(15) << count(i) << std::endl;
}
return 0;
}
output:
-10
5
-2.5
1.25
-0.625
0.3125
-0.15625
0.078125
-0.0390625
0.0195313
-0.00976563
0.00488281
-0.00244141
0.0012207
-0.000610352
0.000305176
-0.000152588
7.62939e-005
-3.8147e-005
Related
I am writing some code that prints out a sum series using a loop and a function.
I intend the equation to look like this
m(i) = (1/2) + (2/3) + ... (i / i + 1)
The problem is that my code always gives me incorrect answers and not printing what it's supposed to. For example, when I input 1 into 1 the answer should be 0.5
This is my code:
#include <iostream>
using namespace std;
void sumSeries(int x);
int main() {
sumSeries(1);
return 0;
}
void sumSeries(int x){
double sum = 0;
for(int i = 0; i < x; i++){
sum = (x/x + 1);
sum += sum;
}
cout<<sum;
}
Indeed, you overwrite your sum but also take care of your integer division.
You may change it as sum += i/(double)(i + 1);
#include <iostream>
using namespace std;
void sumSeries(int x);
int main() {
sumSeries(5);
return 0;
}
void sumSeries(int x){
if (x<0)
{
return;
}
double sum = 0;
for(int i = 0; i < x; i++){
sum += i/(double)(i + 1);
}
cout<<sum;
}
I see two problems in your code.
First: (x/x+1) != (x/(x+1)), in this case C++ obeys the normal point before line calculation rules.
Second: You are overwriting your sum in each iteration, instead of that you should direct add to sum: sum+=x/(x+1)
And a third issue, as noted by Simon Kraemer, is that you are using integer division, to get the correct results you must cast at least one of the operands to a floating point number.
What you want is:
void sumSeries(int x){
double sum = 0;
for(int i = 1; i <= x; i++){ // include i in the list
sum += static_cast<double>(i)/(i + 1); // force the operation as double
}
cout<<sum;
}
your mathematical expression has something not normal. Do you mean M(i)= sum(1-i){i/i+1}? , or 1/2 and 1/3 are constants?
in your case as gerum answered it is a small Operator Precedence problem to learn how the C++ compiler prioritize the operators follow here.
your function also should have a guard against zero denominator (undefined values).
Also you should observe that you take int/int division which will ignore the remaining value. then you should consider that by converting the numerator or the denominator to double before the division here .
then your code should be:
#include <iostream>
using namespace std;
void sumSeries(int x);
int main() {
sumSeries(1);
return 0;
}
void sumSeries(int x){
double sum = 0;
for(int i = 0; i < x; i++){
if ((x+1)!=0){
sum += (double)x/(x + 1);
}
// the else will apply only if x==-1
else {
cout<<"the denominator is zero"<<endl;
throw;
}
}
cout<<sum;
}
the point of this exercise is to multiply a digit of a number with its current position and then add it with the others. Example: 1234 = 1x4 + 2x3 + 3x2 + 4x1 .I did this code successfully using 2 parameters and now i'm trying to do it with 1. My idea was to use - return num + mult(a/10) * (a%10) and get the answer, , because from return num + mult(a/10) i get the values 1,2,3,4- (1 is for mult(1), 2 for mult(12), etc.) for num, but i noticed that this is only correct for mult(1) and then the recursion gets wrong values for mult(12), mult(123), mult(1234). My idea is to independently multiply the values from 'num' with a%10 . Sorry if i can't explain myself that well, but i'm still really new to programming.
#include <iostream>
using namespace std;
int mult(int a){
int num = 1;
if (a==0){
return 1;
}
return ((num + mult(a/10)) * (a%10));
}
int main()
{
int a = 1234;
cout << mult(a);
return 0;
}
I find this easier and more logically to do, Hope this helps lad.
int k=1;
int a=1234;
int sum=0;
while(a>0){
sum=sum+k*(a%10);
a=a/10;
k++;
}
If the goal is to do it with recursion and only one argument, you may achieve it with two functions. This is not optimal in terms of number of operations performed, though. Also, it's more of a math exercise than a programming one:
#include <iostream>
using namespace std;
int mult1(int a) {
if(a == 0) return 0;
return a % 10 + mult1(a / 10);
}
int mult(int a) {
if(a == 0) return 0;
return mult1(a) + mult(a / 10);
}
int main() {
int a = 1234;
cout << mult(a) << '\n';
return 0;
}
Program number 1:
In a given range a and b where a<=b, I want to find whether a number is a perfect quare, if yes then print its root. Therefore, I wrote the following code:
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
using namespace std;
float squaredroot(int n) {
float low = 0.0, mid;
float high = (float)n+1;
while ((high-low) > 0.00001) {
mid = (low+high) / 2;
if (mid*mid < n) {
low = mid;
}
else {
high = mid;
}
}
return low;
}
int main() {
int a,b,i=0; cin>>a>>b;
float roo=0.0;
for(i=a;i<=b;i++){
roo=squaredroot(i);
if(floor(roo)==roo){
cout<<roo<<endl;
}
}
return 0;
}
For the given input 1 5 the output should be 2. But, the above program is not printing any value.
Nevertheless, when I tried running another program using the same base concept as Program number 1, that's mentioned above, It was executed perfectly.
The task for the following program is to check whether the input is a perfect square or not. If yes, then print the root of the number, else print "Not a perfect square!". Here is the code for the Program number 2:
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
using namespace std;
float squaredroot(int n) {
float low = 0.0, mid;
float high = (float)n+1;
while ((high-low) > 0.00001) {
mid = (low+high) / 2;
if (mid*mid < n) {
low = mid;
}
else {
high = mid;
}
}
return low;
}
int main() {
int a; cin>>a;
float roo=0.0;
roo=squaredroot(a);
if(floor(roo)==roo){
cout<<roo<<endl;
}
else{
cout<<"Not a perfect square!"<<endl;
}
return 0;
}
I am unable to find the mistake in the first program. Please help.
Instead of messing about with the square root function, consider this:
Consecutive squares are separated by succeeding odd numbers.
It's pretty darned fast to add some integers. Also you are skipping more and more numbers each time.
Square root takes you to floats. This keeps the problem in integers, where it belongs.
So, to solve your problem elegantly, just do this:
#include <iostream>
using std::cout;
void print_perfect_square( int start, int end ) {
int x = 0, nthOdd = 1;
while ( x <= end ) {
if ( x >= start ) {
cout << x << " is a square and its root is "
<< nthOdd - 1 << '\n';
}
x += 2*nthOdd - 1;
++nthOdd;
}
}
int main() {
// it should find 9 and 16
print_perfect_square(6,17);
cout << '\n';
// it sholuld skip negatives
print_perfect_square(-10,5);
cout << '\n';
// it should print 25,36...
print_perfect_square(20,100);
return 0;
}
As Gyro Gearloose said, the problem is that squaredroot(4) returns 1.99999809, so floor(roo)!=roo. One way to fix this is to change the condition (floor(roo)==roo) to (fabs(roo - floor(roo+0.5)) < 0.00001). Notice that I'm using the same 0.00001 from the function squaredroot.
I need help with writing power function. So, I need to write a porogramm, that will output a table from 1 to 10 in a power in a LOOP. NOT USING POW or EXP
Example of output:
0^0 == 1
1^1 == 1
2^2 == 4
3^3 == 27
4^4 == 256
(and so on, up to)
10^10 == 10000000000
NOT USING Cmath (NO POW or EXP)
for example:
e.g. power( 3.0, 5 ) will return 243 because 3*3*3*3*3 is 243
e.g. power( 173, 0 ) will return 1 because any number raised to the power of 0 is 1.
I did this Simple loop, But I have no idea how to insert power formula in it. I was also thinking about while loop
#include <iostream>
#include <string>
using namespace std;
int main(){
int number = 0, tot;
for (int table = 0; table < 10; table++)
{
tot = number * table;
cout << tot << endl;
number++;
}
}
This is a recursive function that can calculate a value raised to an integer power
double power(double base, unsigned int exp)
{
if (exp == 0)
{
return 1.0;
}
else
{
return base * power(base, exp - 1);
}
}
An iterative method to do this would be
double power(double base, unsigned int exp)
{
double product = 1.0;
for (unsigned int i = 0; i < exp; ++i)
{
product *= base;
}
return product;
}
You can test either method with something like
int main()
{
std::cout << power(5, 3);
}
Output
125
I think you already know the answer to your own question by now, but still; some hints:
Exponentiation is a repeated multiplication of the base, the repetition is defined by the exponent.
In C++, or any modern programming language, loops allow repetition of certain blocks of code: when the number of iterations is known beforehand, use the for-loop, otherwise, use the while-loop.
Combining both hints: you'll need to use a loop to repeat a multiplication; the amount of repetition (or iterations) is known beforehand, thus, a for-loop will be best.
int exponentiation(int base, int exponent) {
int result = 1;
for (int i = 0; i < exponent; ++i)
result = result * base;
return result;
}
Note: this will only suffice for integer exponentiation with positive exponents!
You can then call this function in a for-loop to let it compute the values you want:
#include <iostream>
int main(int argc, char** argv) {
for(int i = 0; i <= 10; ++i)
std::cout << exponentiation(i, i) << '\n';
}
i wrote a code that calculates and outputs a difference between the sum of the squares of the first ten natural numbers and the square of the sum.
The problem is with function squareOfSum(). The function should return 3025 but it always returns 3024. Even if i try to put 100 into brackets i get 25502499 (25502500 is correct). No matter what number i put into brackets i always get the same problem.
What am I doing wrong?
Here's a screenshot of my output.
#include <iostream>
#include <cmath>
using namespace std;
int sumOfSquares(int limit);
int squareOfSum(int limit);
int main()
{
cout << sumOfSquares(10) << endl;
cout << squareOfSum(10) << endl;
cout << squareOfSum(10) - sumOfSquares(10) << endl;
}
int sumOfSquares(int limit)
{
int sum = 0;
for(int i = 1; i<=limit; i++)
{
sum +=pow(i,2);
}
return sum;
}
int squareOfSum(int limit)
{
int sum = 0, square = 0;
for(int i = 1; i<=limit; i++)
{
sum +=i;
}
square = pow(sum,2);
return square;
}
Note that pow is a function that works with floating point numbers. Optimizations might lead to rounding errors or truncation during implicit coversion to int. Replace pow(i, 2) with i*i and you'll get pure integer arithmetic and thus exact results.
#include <bits/stdc++.h>
#include <algorithm>
using namespace std;
int main()
{
int higher_limit = 100;
int SquaresOfSum = 0;
int SumOfSquares = 0,count=0;
for(int i=1;i<=higher_limit;i++){
count += i;
SumOfSquares += pow(i,2);
}
SquaresOfSum = pow(count,2);
cout<<SquaresOfSum-SumOfSquares;
}
Using Javascript
const sumSquareDifference = (n) => {
const numbers = [...Array(n + 1).keys()];
const sumOfSquares = numbers.reduce((accumulator, number) => accumulator + (number ** 2));
const squareOfSum = numbers.reduce((accumulator, number) => accumulator + number) ** 2;
return squareOfSum - sumOfSquares;
}
console.log(sumSquareDifference(10));