from matplotlib.pyplot import *
from math import *

print("Euler's Method with Slope Field")
print("Enter dy/dx explicitly")
print("Examples: 2*x/y, sqrt(x)*y, sin(x) - y")

def get_float(prompt):
    while True:
        raw = input(prompt).strip()
        try:
            return float(raw)
        except:
            print("Please enter a valid number (use decimal point).")

# allowed math functions for eval
allowed_math = {
    "sqrt": sqrt, "sin": sin, "cos": cos, "tan": tan,
    "log": log, "exp": exp, "pi": pi, "e": e,
    "asin": asin, "acos": acos, "atan": atan,
    "abs": abs, "pow": pow
}

# inputs
dydx_expression = input("dy/dx = ")
x0 = get_float("Initial x = ")
y0 = get_float("Initial y = ")
h_raw = get_float("Step size h = ")
x_end = get_float("End x = ")

# handle zero step and direction
if h_raw == 0:
    print("Step size h cannot be 0. Re-run and enter a nonzero h.")
else:
    direction = 1 if x_end > x0 else -1
    h = abs(h_raw) * direction

    def dydx(_x, _y):
        env = {"x": _x, "y": _y, "__builtins__": {}}
        env.update(allowed_math)
        try:
            return eval(dydx_expression, env)
        except Exception as e:
            print("Error in dydx:", e)
            return 0

    # Euler integration
    x_vals = [x0]
    y_vals = [y0]

    while True:
        cur_x = x_vals[-1]
        if (direction == 1 and cur_x >= x_end) or (direction == -1 and cur_x <= x_end):
            break
        step = h
        if (direction == 1 and cur_x + step > x_end) or (direction == -1 and cur_x + step < x_end):
            step = x_end - cur_x
        slope = dydx(cur_x, y_vals[-1])
        new_x = cur_x + step
        new_y = y_vals[-1] + step * slope
        x_vals.append(new_x)
        y_vals.append(new_y)
        if new_x == x_end:
            break

    # print table
    print("\nTable of values:")
    print("Step\t   x\t\t   y")
    for i in range(len(x_vals)):
        print(i, "\t", "%.5f" % x_vals[i], "\t", "%.5f" % y_vals[i])

    # Steps to do another
    print("Back out and Re-execute to do another")