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@evandrix evandrix/p438.cpp
Created Jan 11, 2014

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Project Euler Problem 438
#include <iostream>
#include <cmath>
#include <stdlib.h>
#include <cstring>
using namespace std;
/**
* Problem 438
*
* Example:
* x^4-(1/2)x^3-(30)x^2+x+2 = 0
* a= -(1/2)
* b= -30
* c= 1
* d= 2
* x1= 0.2751
* x2= -0.24275
* x3= -5.24368
* x4= 5.71133
*
*
* */
//@Author Xavier
//@Date 4 Oct 2013
// Newton horner's method:
// http://ganeshtiwaridotcomdotnp.blogspot.pt/2009/12/c-c-code-newton-horners-method-for.html
// x1, ..., xn SORTED, ⌊xi⌋ = i for 1 ≤ i ≤ n
int computePolynomial(double *solution ,int n, double *coeficients)
{
// limit of 50 iterations to find the roots
int i, limit = 50, rootCount = 0;
double x = 1.0, a[n], b[n],c[n];
while(n>0 && limit > 0)
{
c[0]=b[0]=a[0];
for(i=1;i<=n;i++)
b[i]=a[i]+b[i-1]*x;
for(i=1;i<n;i++)
c[i]=b[i]+c[i-1]*x;
if(fabs(c[n-1])==0.0) // "Divide by Zero : ERROR !! "
break;
x-=b[n]/c[n-1];
if(fabs(b[n]/c[n-1])<0.00001)
{
solution[rootCount++] = x;
for(i=1;i<n;i++)
a[i]=b[i];
n--;
}
limit --;
}
if (!limit) return 0; // no solution
return 1; // true
}
void *threadExec()
{
int i, j, n = 4;
double* solution, *coeficients , aux, sum = 0.0, reset = -10000.0;
bool conditionMet = false;
solution = (double*) malloc (n * sizeof(double));
memset(solution, 0, n * sizeof(double));
coeficients[0] = 1.0;
coeficients[1] = reset;
coeficients[2] = reset;
coeficients[3] = reset;
coeficients[4] = reset;
do
{
if (computePolynomial(solution, n, coeficients))
{
for (i = 1; i <= n; i++)
{
cout << "[" << coeficients[i-1] << "] X" << i << " is: " << fixed << solution[i - 1] << endl;
}
cout << "[" << coeficients[n] << "]" << endl;
// you found roots. sort solutions
for (i = 0; i < n; i++)
{
for (j = i + 1; j < n; j++)
{
if (solution[j] < solution[i])
{
aux = solution[i];
solution[i] = solution[j];
solution[j] = aux;
}
}
}
conditionMet = true;
for (i = 1; i <= n; i++)
{
if (floor(solution[i - 1]) != i) conditionMet = false;
}
if (conditionMet) // we found a solution
{
for (i = 1; i <= n; i++) sum += fabs(coeficients[i]);
cout << "conditions Met! SUM: " << sum << endl;
return (void*)1;
}
}
// increment coeficients
if (coeficients[4] < 10000)
{
//cout << "[\t" <<coeficients[1] << "\t|\t" <<coeficients[2] << "\t|\t" <<coeficients[3] << "\t|\t" <<coeficients[4] << "\t]" << endl;
coeficients[4] ++;
}
else if (coeficients[3] < 10000)
{
//cout << "[\t" <<coeficients[1] << "\t|\t" <<coeficients[2] << "\t|\t" <<coeficients[3] << "\t|\t" <<coeficients[4] << "\t]" << endl;
coeficients[3] ++;
coeficients[4] = reset;
}
else if (coeficients[2] < 10000)
{
//cout << "[\t" <<coeficients[1] << "\t|\t" <<coeficients[2] << "\t|\t" <<coeficients[3] << "\t|\t" <<coeficients[4] << "\t]" << endl;
coeficients[2] ++;
coeficients[3] = reset;
coeficients[4] = reset;
}
else if (coeficients[2] < 10000)
{
cout << "[\t" <<coeficients[1] << "\t|\t" <<coeficients[2] << "\t|\t" <<coeficients[3] << "\t|\t" <<coeficients[4] << "\t]" << endl;
coeficients[2] ++;
coeficients[3] = reset;
coeficients[4] = reset;
}
else if (coeficients[1] < 10000)
{
cout << "[\t" <<coeficients[1] << "\t|\t" <<coeficients[2] << "\t|\t" <<coeficients[3] << "\t|\t" <<coeficients[4] << "\t]" << endl;
coeficients[1] ++;
coeficients[2] = reset;
coeficients[3] = reset;
coeficients[4] = reset;
}
else
{
cout << "No solution found" << endl;
return (void*) 0;
}
}
while(!conditionMet);
return (void*) 0;
}
int main()
{
int i,n = 4;
double *coeficients;
cout << "The degree of equations is : " << n << endl;
coeficients = (double*) malloc ((n + 1) * sizeof(double));
threadExec();
return 1;
}
#include <iostream>
#include <math.h>
#include <stdlib.h>
#include <cstring>
using namespace std;
/**
* Problem 438
*
* Example:
* x^4-(1/2)x^3-(30)x^2+x+2 = 0
* a= -(1/2)
* b= -30
* c= 1
* d= 2
* x1= 0.2751
* x2= -0.24275
* x3= -5.24368
* x4= 5.71133
*
*
* */
//@Author Xavier
//@Date 4 Oct 2013
// Newton horner's method:
// http://ganeshtiwaridotcomdotnp.blogspot.pt/2009/12/c-c-code-newton-horners-method-for.html
int computePolynomial(double *solution ,int n, double *coeficients)
{
// limit of 50 iterations to find the roots
int i, limit = 50, rootCount = 0;
double x = 1.0, b[n],c[n];
while(n>0 && limit > 0)
{
c[0]=b[0]=coeficients[0];
for(i=1;i<=n;i++)
b[i]=coeficients[i]+b[i-1]*x;
for(i=1;i<n;i++)
c[i]=b[i]+c[i-1]*x;
if(fabs(c[n-1])==0.0) // "Divide by Zero : ERROR !! "
break;
x-=b[n]/c[n-1];
if(fabs(b[n]/c[n-1])<0.00001)
{
solution[rootCount++] = x;
for(i=1;i<n;i++)
coeficients[i]=b[i];
n--;
}
limit --;
}
if (!limit) return 0; // no solution
return 1; // true
}
int main()
{
int n,i;
double* solution, *coeficients;
cout << "Enter the degree of equations : ";
cin >> n;
solution = (double*) malloc (n * sizeof(double));
coeficients = (double*) malloc ((n + 1) * sizeof(double));
memset(solution, 0, n * sizeof(double));
cout<<"Enter all coefficients \n";
for(i = 0; i <= n; i++)
cin >> coeficients[i];
if (computePolynomial(solution, n, coeficients))
{
for (i = 1; i <= n; i++)
{
cout << "\nRoot X" << i << " is: " << fixed << solution[i - 1] << endl;
}
}
else
cout << "No Solution Found!" << endl;
return 0;
}
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