CSE225(1)Lab1 [Bisection & False-Position]

// Bisection and False Position Method
// Author   : Shakib Haris
// Date     : 17 May 2017

#include <iomanip>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#define eps 0.01
#define MAX 5 // maximum degree 4
#define MAX_LOOP 100
using namespace std;

int degreeOfEquation;
int numberOfRoots;
int aN[MAX]; // array to hold the coefficients
double ranges[MAX][2]; // array to hold the ranges for the roots
double roots[MAX]; // array to hold the roots;

bool confirm () {
    char ch;
    while (true) {
        cin.sync();
        ch = getchar();
        if (ch == 'y' || ch == 'Y' || ch == '\0')
            return true;
        else if (ch == 'n' || ch == 'N')
            return false;
        else
            cout << "Invalid input" << endl << "Try again!" << endl << "(Y/n): ";
    }
}

double f (double x) { //
    double total = 0.0;
    for (int i = 0; i <= degreeOfEquation; i++)
        total += aN[i] * pow (x, degreeOfEquation - i);
    return total;
}

void getRanges () {
    cout << "Find Ranges automatically? (Y/n): ";
    if (confirm()) {
        int xMax = abs ((int) ceil (sqrt (pow ((((double) aN[1]) / aN[0]), 2) - 2 * (((double) aN[2]) / aN[0]))));
        cout << "Xmax is " << xMax << endl;
        for (int i = (-1) * (xMax); i < xMax; i++) {
            if (f (i) == 0) {
                ranges[numberOfRoots][0] = i;
                ranges[numberOfRoots][1] = i;
                numberOfRoots++;
            }
            else if ((f (i) * f (i + 1)) < 0) {
                ranges[numberOfRoots][0] = i;
                ranges[numberOfRoots][1] = i + 1;
                numberOfRoots++;
            }
        }
        cout << "Found " << numberOfRoots << " Range(s)" << endl;
    }
    else {
        cout << "Number of ranges: ";
        cin >> numberOfRoots;
        for (int i = 0; i < numberOfRoots; i++) {
            cout << "Range " << i + 1 << " Lower Bound: ";
            cin >> ranges[i][0];
            cout << "Range " << i + 1 << " Upper Bound: ";
            cin >> ranges[i][1];
        }
    }

    // print ranges
    for (int i = 0; i < numberOfRoots; i++)
        cout << "Range " << i + 1 << ": " << ranges[i][0] << ", " << ranges[i][1] << endl;
    cout << endl << endl;
}

void getCoefficients () {
    cout << "Enter the Coefficients for all the degrees of X" << endl;
    for (int i = 0; i <= degreeOfEquation; i++) {
        cout << "An-" << i << ": ";
        cin >> aN[i];
    }
}

void bisect () {
    double x0, x1, x2;
    double f0, f1, f2;
    int loopCount;

    for (int i = 0; i < numberOfRoots; i++) {
        x1 = ranges[i][0];
        x2 = ranges[i][1];
        x0 = (x1 + x2) / 2;

        f1 = f(x1);
        f2 = f(x2);
        f0 = f(x0);

        loopCount = 0;
        while (fabs (f0) >= eps && loopCount < MAX_LOOP) {
            if (f0 * f1 < 0) {
                x2 = x0;
                f2 = f0;
            }
            else {
                x1 = x0;
                f1 = f0;
            }
            x0 = (x1 + x2) / 2;
            f0 = f(x0);
            loopCount++;
        }
        if (loopCount != MAX_LOOP) {
            roots[i] = x0;
            cout << "Found Root " << x0 << endl;
        }
        else {
            cout << "Root not Found for Range: " << ranges[i][0] << ", " << ranges[i][1] << endl;
            roots[i] = INT_MAX;
        }
    }
}

void falsePosition () {
    double x0, x1, x2;
    double f0, f1, f2;
    int loopCount;

    for (int i = 0; i < numberOfRoots; i++) {
        x1 = ranges[i][0];
        x2 = ranges[i][1];

        f1 = f(x1);
        f2 = f(x2);

        if (x1 != x2)
            x0 = x1 - (f1 * ((x2 - x1) / (f2 - f1)));
        else
            x0 = x1;

        f0 = f(x0);

        loopCount = 0;
        while (fabs (f0) >= eps && loopCount < MAX_LOOP) {
            if (f0 * f1 < 0) {
                x2 = x0;
                f2 = f0;
            }
            else {
                x1 = x0;
                f1 = f0;
            }
            x0 = x1 - (f1 * ((x2 - x1) / (f2 - f1)));
            f0 = f(x0);
            loopCount++;
        }
        if (loopCount != MAX_LOOP) {
            roots[i] = x0;
            cout << "Found Root " << x0 << endl;
        }
        else {
            cout << "Root not Found for Range: " << ranges[i][0] << ", " << ranges[i][1] << endl;
            roots[i] = INT_MAX;
        }
    }
}


int main () {
    cout << "Degree of the Equation: ";
    cin >> degreeOfEquation;

    // user inputs the coefficients
    getCoefficients ();
    system("cls");

    // getting ranges
    getRanges();

    if (numberOfRoots <= 0) {
        cout << "No Root Found" << endl;
        return 0;
    }

    // system("cls");
    cout << "running BISECTION Method" << endl;
    bisect ();
    cout << endl << endl;
    cout << "running FALSE-POSITION Method" << endl;
    falsePosition ();
    //system("cls");

    // printing the roots
    // cout << "Root(s): ";
    // for (int i = 0; i < numberOfRoots; i++)
    //  cout << fixed << setprecision(4) << roots[i] << " ";
    // cout << endl;

    return 0;
}