Error in saving degrees of polynomial for Polynomial Calculator - c++

Question

I am creating a polynomial calculator for 2 polynomials in C++. For different operations, I have created different functions. Below is my approach for the function for multiplication. For multiplying, first I must save all the possible degrees. This should mean a max of highest degree of polynomial1+polynomial2, and least of smallest degree of either. I am first just saving all the possible degree options taking into consideration polynomial1 and polynomial 2. I will then sort the degrees in descending order, perform calculations on coefficients, and save the coefficient according to the degree calculated.
However I am unable to properly save all the possible degree options, and can't spot the error. The values that are actually being saved, I can't seem to understand, why they are being saved, and where is the error. I am writing this program without utilising external libraries like for performing calculations. Kindly spot the error, and how I can successfully save all the possible degree options correctly. The comments are my understanding of what is happening/ should be happening. Thanks.
The ideal output should be:
"99, 97, 95, 93, 91, 89, 98, 96, 94, 92, 90, 88...."
The current output is:
"99 96 93 90 87 84 81 78 75 72 688904896 32629 119 114 109 104 97 94 89 84 79 74 1377809792 65258 218 210 202 194 184 178"
#include <iostream>
using namespace std;
void multiply(int degree_poly1[], int terms_poly1, int degree_poly2[], int terms_poly2, int degree_result[])
{
int temp=0;
for(int a=0; a<terms_poly1*terms_poly2; a++)
{//this is first term
//degrees
for(int b=0; b<=a; b++)
{//this is 2nd term
if(degree_result[b]==0){
//checks if location is empty or not
//dr[0]=0, so go on
temp=degree_poly1[a]+degree_poly2[b];
for(int c=0; c<=b; c++)
{
if(temp==degree_result[c]){
//checks if there is already a value temp in previous array throughout. yes means stop
break;
}
if(temp!=degree_result[c]){
//checks
degree_result[b]=temp;
}
}
temp=0;
}
}
}
for(int a=0; a<terms_poly1*terms_poly2; a++)
{
cout<<degree_result[a]<<" ";
}
}
int main()
{
int degree_poly11[10]={79,78,77,76,75}, terms_poly11=5, degree_poly22[10]={20,18,16,14,12}, terms_poly22=6, degree_resultt[100]={};
/*
The whole program saves a polynomial 5x^9 + 7x^3 + 2x^2 as coefficients 5,7,2 in coefficient1[0], coefficient1[1], coefficient1[2] AND the degrees 9,3,2 in degree_poly11[0], degree_poly11[1], degree_poly11[2]. terms_poly11 gives the no. of total terms in the equation i.e. 3.
This array is currently not present here but is present in complete program.
Similarly for another polynomial2 in coefficient22[] and degree_poly22[].
*/
multiply(degree_poly11, terms_poly11, degree_poly22, terms_poly22, degree_resultt);
return 0;
}

Answer 1

One problem in your code is
temp=degree_poly1[a]+degree_poly2[b];
both a and b loop till 30, but both arrays have only 10 elements. You are accessing the arrays out of bounds and your code has undefined behavior. Even if all the rest would be ok, the output of the code could be anything because of this out-of-bounds access.
It is hard to understand the intended logic of your multiply function. Naming variables is a big issue in your code. a, b and c are completely meaningless to the reader of the code. Though already in main names are confusing.
You have
int degree_poly11[10]={79,78,77,76,75}, terms_poly11=5, ...;
I suppose degree_poly11 are the coefficients of the first polynome. Further, I guess that terms_poly11=5 is the degree of the polynome. If thats the case then name them like that.
When you need arrays of variable size you should think: std::vector.
I suggest to take pen and paper and calculate some examples (not one, but some). When you multiply two polynomials, their degrees add up and the coefficients are:
( poly1 * poly2)_{i} = sum_{j,k,j+k==i} ( poly1_{j} * poly2_{k} )
ie, the i-th coefficient is a sum of all products of coefficients from the input polynomials, such that their indices add up to i. Frankly, I don't see anything like that in your code.
Just this directly translated to code can look like this:
#include <vector>
#include <iostream>
std::vector<double> mult(const std::vector<double>& a,const std::vector<double>& b) {
std::vector<double> result(a.size() + b.size() - 1);
for (int i=0; i< result.size(); ++i) {
for (int j = 0; j <= i && j < a.size(); ++j) {
int k = i-j;
if (k >= b.size()) continue;
result[i] += a[j] * b[k];
}
}
return result;
}
int main(){
auto res = mult( {-1,1},{1,1});
for (int i=0;i<res.size();++i){
std::cout << res[i] << "*x^" << i << " + ";
}
}
Output is:
-1*x^0 + 0*x^1 + 1*x^2 +
Seems to be correct, because (x+1)*(x-1) == (x^2 -1). I didn't test more yet.
(x+1) and (x-1) are of degree 1, thats one less than they have coefficients, and the result has one coefficient more than its degree (a polynomial of degree 0 is a constant, it has 1 coefficient). Hence the size of the output vector a.size() + b.size() - 1.
The outer loop is to calculate i-th coefficient. Loop counters are choosen such that all combinations of j and k that add up to i are passed and included in the sum. Because I know my first attempt is off by one somewhere I have additional checks to be sure that j < a.size() and k < b.size().