computorv1/rendu1/main.py

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#    main.py                                            :+:      :+:    :+:    #
#                                                     +:+ +:+         +:+      #
#    By: mazimi <mazimi@student.42.fr>              +#+  +:+       +#+         #
#                                                 +#+#+#+#+#+   +#+            #
#    Created: 2015/04/22 13:13:05 by mazimi            #+#    #+#              #
#    Updated: 2015/09/29 13:06:23 by mazimi           ###   ########.fr        #
#                                                                              #
# **************************************************************************** #

import sys
import re

def ft_sqrt (n):
	a = 1
	for i in range(0, 10):
		a = 0.5 * (a + n / a)
	return (a)

def sign(a):
	if a >= 0: print("+", end = " ")

def print_d(n):
	print("{0:.3f}".format(round(n, 3)), end = " ")

def wrong_degree():
	print ("Je ne sait pas résoudre les équations de degré polynomial différent de un et deux.")
	exit()

def	cond_X0(eq, i):
	if eq[i - 1] != "^" and "0" <= eq[i] and eq[i] <= "9":
		return (1)

def parse (str):
	i = 0 
	while (i < len(str) - 2):
		if cond_X0(str, i) and str[i + 1] == " " and str[i + 2] != "*":
			a = str[:i + 1]; b = str[i + 1:]; s = "";
			seq = a, " * X^0", b; str = s.join(seq)
		i = i + 1
	if cond_X0(str, len(str) - 1):
		seq = str, " * X^0"; str = s.join(seq)
	if str[0] == "X": seq  = "1 * ", str; str = s.join(seq)
	if str[len(str) - 1] == "X":
		a = str[:len(str) - 1]; seq = a, "1 * X^1"; str = s.join(seq) 
	str = str.replace("X ", "X^1 "); str = str.replace("+ X^", "+ 1 * X^")
	str = str.replace("- X^", "- 1 * X^"); str = str.replace("= X^", "= 1 * X^")
	eq1, eq2 = str.split("=")
	eq1 = re.split('(\-*\s*[\.0-9]*)\s\*\sX\^(\-*[0-9\.]*)', eq1)
	eq2 = re.split('(\-*\s*[\.0-9]*)\s\*\sX\^(\-*[0-9\.]*)', eq2)
	eq = re.split('(\-*\s*[\.0-9]*)\s\*\sX\^(\-*[0-9\.]*)', str)
	strp = str
	return (strp, eq, eq1, eq2)

def get_degree(eq):
	degree = 1 
	for i in range(2, len(eq), 3):
		d = float(eq[i])
		if (d != 0 and d != 1 and d != 2 and d != 3): wrong_degree()
		if degree < d: degree = d
	return (degree)

def get_coef(eq1, eq2, degree):
	a, b, c, d = 0, 0, 0, 0
	if degree == 3:
		for i in range(2, len(eq1), 3):
			if eq1[i] == "3": d2 = eq1[i - 1]; d = d + float(d2.replace(" ", ""))
		for i in range(2, len(eq2), 3):
			if eq2[i] == "3": d2 = eq2[i - 1]; d = d - float(d2.replace(" ", ""))
		if d == 0: degree = 2
		else: wrong_degree()
	if degree == 2:
		for i in range(2, len(eq1), 3):
			if eq1[i] == "0": c2 = eq1[i - 1]; c = c + float(c2.replace(" ", ""))
			if eq1[i] == "1": b2 = eq1[i - 1]; b = b + float(b2.replace(" ", ""))
			if eq1[i] == "2": a2 = eq1[i - 1]; a = a + float(a2.replace(" ", ""))
		for i in range(2, len(eq2), 3):
			if eq2[i] == "0": c2 = eq2[i - 1]; c = c - float(c2.replace(" ", ""))
			if eq2[i] == "1": b2 = eq2[i - 1]; b = b - float(b2.replace(" ", ""))
			if eq2[i] == "2": a2 = eq2[i - 1]; a = a - float(a2.replace(" ", ""))
		if a == 0: return (1, b, c, 0)
		return (degree, a, b, c)
	if degree == 1:
		for i in range(2, len(eq1), 3):
			if eq1[i] == "0": b2 = eq1[i - 1]; b = b + float(b2.replace(" ", ""))
			if eq1[i] == "1": a2 = eq1[i - 1]; a = a + float(a2.replace(" ", ""))
		for i in range(2, len(eq2), 3):
			if eq2[i] == "0": b2 = eq2[i - 1]; b = b - float(b2.replace(" ", ""))
			if eq2[i] == "1": a2 = eq2[i - 1]; a = a - float(a2.replace(" ", ""))
		if a == 0: return (0, b, 0, 0)
		return (degree, a, b, 0)
	if degree == 0:
		for i in range(2, len(eq1), 3): a2 = eq1[i - 1]; a = a + float(a2.replace(" ", ""))
		for i in range(2, len(eq2), 3): a2 = eq2[i - 1]; a = a - float(a2.replace(" ", ""))
		return (0, a, 0, 0)

def display(str, a, b, c, degree):
	print("Équation :", str)
	print ("\nÉquation réduite :")
	if degree == 0: print(a, "= 0\nÉquation fausse."); exit()
	if degree == 1:
		print (a, "X", end = " "); sign(b); print(b, " = 0\naX + b = 0")
	if degree == 2:
		print (a, "X²", end = " "); sign(b); print(b, "X", end = " "); sign(c);
		print (c, "= 0\naX² + bX + c = 0")
	print ("Équation de degré polynomial", end = " "); print(int(degree), "\n")

def	solve_degree_2(a, b, c):
	delta = b**2 - 4 * a * c
	print ("Calcul du discriminant :\nΔ = b² - 4ac\nΔ =", end = " ")
	print (b, "² - 4 ×", a, "×", c, "\nΔ =", delta)
	alpha = -b / (2 * a)
	if delta > 0:
		beta = ft_sqrt(delta) / (2 * a)
		print ("Dicriminant scritement positif.\n\nCalcul des solutions :")
		print ("     -b + √Δ\nX1 = ——————— =", end = " "); print_d(alpha + beta)
		print("\n      2 × a\n\n     -b - √Δ\nX2 = ——————— =", end = " ")
		print_d(alpha - beta); print("\n      2 × a")
	if delta == 0:
		print ("Discriminant nul.\n\nCalcul des solution :")
		print ("      -b\nX = ——————— =", alpha, "\n     2 × a")
	if delta < 0:
		print ("Discriminant négatif.\n\nCalcul des solutions :")
		xi = ft_sqrt(-delta) / (2 * a)
		print ("     -b + i × √-Δ\nX1 = ————————————— =", end = " "); print_d(alpha)
		sign(a); print_d (xi); print("× i\n         2 × a\n")
		print ("     -b - i × √-Δ\nX2 = ————————————— =", end = " "); print_d(alpha)
		if a <= 0: print("+", end = " ")
		print_d (-xi); print ("× i\n         2 × a")

if __name__ == '__main__':
	if len(sys.argv) != 2: print("Entrez l’équation à résoudre."); exit()
	str = sys.argv[1]
	strp, eq, eq1, eq2 = parse(str)
	degree = get_degree(eq)
	degree, a, b, c = get_coef(eq1, eq2, degree)
	display(str, a, b, c, degree)
	if (degree == 1):
		print ("Solution :\n    -b\nX = ——— =", end = " ");
		print_d(-b / a); print("\n     a")
	if (degree == 2): solve_degree_2(a, b, c)