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# juanfal/t11e07.polynomials.cpp

Last active Jan 17, 2022
polynomials with open arrays
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 // t11e07.polynomials.cpp // juanfc 2018-12-17 // https://gist.github.com/baf068a06eafb1ecba8a584fe375b780 #include #include using namespace std; const int N = 100; struct TMono { int deg; float coef; }; typedef array TVec; struct TPoly { int noel; TVec ar; }; void print(TPoly p); float eval(TPoly p, float x); float horner(TPoly p, float x); TPoly add(TPoly p, TMono m); TPoly derivative(TPoly p); TPoly derivative2(TPoly p); void derivative3(TPoly& p); int main() { TPoly p = { 3, { { { 4, 1 }, { 2, -2 }, { 1, 1 } } } }; print(p); print(derivative2(p)); derivative3(p); print(p); cout << eval(p, 0) << endl; cout << horner(p, 0) << endl; cout << eval(p, 2) << endl; cout << horner(p, 2) << endl; p = (TPoly) { 0 }; print(p = add(p, (TMono) { 2, 3 })); print(p = add(p, (TMono) { 1, -5 })); print(p = add(p, (TMono) { 0, 1 })); print(p = add(p, (TMono) { 33, 0 })); cout << eval(p, 1) << endl; return 0; } TPoly add(TPoly p, TMono m) { TPoly r; if (m.coef == 0) // !! r = p; else { int j = 0; bool found = false; for (int i = 0; i < p.noel; ++i) { if (m.deg == p.ar[i].deg) { found = true; float c = m.coef + p.ar[i].coef; if (c != 0) { r.ar[j++] = (TMono) { m.deg, c }; } } else { if (p.ar[i].deg < m.deg) { found = true; r.ar[j++] = m; } else r.ar[j++] = p.ar[i]; } } if (not found) { r.ar[j++] = m; } r.noel = j; } return r; } TPoly derivative(TPoly p) { TPoly r = { 0 }; int i = 0; while (i < p.noel and p.ar[i].deg > 0) { float coef = p.ar[i].coef; int deg = p.ar[i].deg; r = add(r, (TMono) { deg - 1, coef * deg }); ++i; } return r; } TPoly derivative2(TPoly p) { TPoly r = p; int i = 0; while (i < p.noel and p.ar[i].deg > 0) { float coef = p.ar[i].coef; int deg = p.ar[i].deg; r.ar[i] = (TMono) { deg - 1, coef * deg }; ++i; } r.noel = i; return r; } void derivative3(TPoly& p) { int i = 0; while (i < p.noel and p.ar[i].deg > 0) { float coef = p.ar[i].coef; int deg = p.ar[i].deg; p.ar[i] = (TMono) { deg - 1, coef * deg }; ++i; } p.noel = i; } void print(TPoly p) { for (int i = 0; i < p.noel; ++i) { float coef = p.ar[i].coef; int deg = p.ar[i].deg; if (coef < 0) { cout << " - "; if (coef != -1 or deg == 0) cout << -coef; } else { if (i != 0) cout << " + "; if (coef != 1 or deg == 0) cout << coef; } if (deg > 0) cout << "x"; if (deg > 1) cout << "^" << deg; } cout << endl; } float eval(TMono m, float x); float eval(TPoly p, float x) { float s = 0; for (int i = 0; i < p.noel; ++i) { s += eval(p.ar[i], x); } return s; } float horner(TPoly p, float x) { float s = p.ar[0].coef; int j = 1; for (int i = p.ar[0].deg-1; i >= 0; --i) { if (i != p.ar[j].deg or j >= p.noel) { s *= x; } else { s = s * x + p.ar[j].coef; ++j; } } return s; } float pow(float x, int deg); float eval(TMono m, float x) { return m.coef * pow(x, m.deg); } float pow(float x, int deg) { float r = 1; for (int i = 0; i < deg; ++i) { r *= x; } return r; }