hw0: EX2 done
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2 changed files with 66 additions and 19 deletions
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@ -20,47 +20,91 @@ void print_fraction_array(fraction frac_array[], int n)
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fraction square_fraction(fraction frac)
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fraction square_fraction(fraction frac)
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{
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{
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//TODO: implement function 2
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struct fraction square = {
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.num = frac.num * frac.num;
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.denom = frac.denom * frac.denom;
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};
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return square;
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}
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}
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//TODO: implement function 3
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void square_fraction_inplace(fraction& frac)
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{
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frac.num *= frac.num;
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frac.denom *= frac.denom;
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}
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double fraction2double(fraction frac)
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double fraction2double(fraction frac)
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{
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{
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//TODO: implement function 4
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return (double) frac.num / (double) frac.denom;
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}
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}
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int gcd(int a, int b)
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int gcd(int a, int b)
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{
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{
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//TODO: implement function 5
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return b == 0 ? a : gcd(b, a % b);
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}
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}
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//TODO: implement function 6
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int gcd(fraction frac) {
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int a = frac.num, b = frac.denom;
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while (b != 0) {
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int t = b;
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b = a % b;
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a = t;
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}
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return a;
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}
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void reduce_fraction_inplace(fraction & frac)
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void reduce_fraction_inplace(fraction & frac)
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{
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{
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//TODO: implement function 7
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// the called function is the one implementing the iterative algorithm
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// because gcd is called with one argument of type fraction (the reference
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// is implicitly copied and passed by value), matching the signature of the
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// iterative implementation
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int g = gcd(frac);
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//TODO: add short comment to explain which of the gcd() functions your code is calling
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frac.num /= g;
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frac.denom /= g;
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}
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}
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fraction add_fractions(fraction frac1, fraction frac2)
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fraction add_fractions(fraction frac1, fraction frac2)
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{
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{
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//TODO: implement function 8
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int g = gcd(frac1.denom, frac2.denom);
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{
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int fac1 = frac1.denom / g;
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frac1.num *= fac1;
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frac1.denom *= fac1;
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}
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{
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int fac2 = frac2.denom / g;
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frac2.num *= fac2;
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frac2.denom *= fac2;
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}
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struct fraction total = {
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.num = frac1.num + frac2.num;
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.denom = g;
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};
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return total;
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}
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}
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double sum_fraction_array_approx(fraction frac_array[], int n)
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double sum_fraction_array_approx(fraction frac_array[], int n)
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{
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{
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//TODO: implement function 9
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struct fraction sum = { .num = 0, .denom = 0 };
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for (int i = 0; i < n; i++) {
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struct fraction frac = frac_array[i];
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sum = add_fractions(sum, frac);
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}
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//TODO: add short comment to explain why this function is approximate
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return fraction2double(sum);
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// the approximation in this function is given by the fact that floating
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// point numbers cannot represent precisely rational numbers due to the
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// fixed size of significant digits they can hold in the mantissa. This
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// implementation minimizes the approximation by computing the sum into a
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// fraction FIRST before performing the double conversion.
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}
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}
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//TODO: implement function 10
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void fill_fraction_array(fraction frac_array[], int n)
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void fill_fraction_array(fraction frac_array[], int n)
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{
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{
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fraction temp_frac;
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fraction temp_frac;
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@ -1,6 +1,9 @@
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#include <iostream>
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#include <iostream>
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//TODO: implement fraction datatype
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struct fraction {
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int num;
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int denom;
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}
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void print_fraction(fraction frac);
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void print_fraction(fraction frac);
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@ -8,7 +11,7 @@ void print_fraction_array(fraction frac_array[], int n);
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fraction square_fraction(fraction frac);
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fraction square_fraction(fraction frac);
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//TODO: add function declaration for function 3
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void square_fraction_inplace(fraction& frac);
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double fraction2double(fraction frac);
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double fraction2double(fraction frac);
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