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#!/usr/bin/python |
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# By Danilo J. S. Bellini |
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# 2016-05-02 17:31:56 BRT |
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""" |
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Smallest quadratic equations that answers the viral math puzzle below, |
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using Sympy |
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1 + 4 = 5 |
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2 + 5 = 12 |
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3 + 6 = 21 |
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8 + 11 = ? |
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""" |
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from sympy import symbols, solve, Eq |
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from itertools import combinations |
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A, B, result, x, y, z = symbols("A B result x y z") |
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data = [(1, 4, 5), (2, 5, 12), (3, 6, 21)] |
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dict_data = [dict(zip([A, B, result], triple)) for triple in data] |
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wanted = {A: 8, B: 11} |
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base = [1, A, B, A*A, A*B, B*B] |
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unks = [x, y, z] |
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sspaces = combinations(base, len(unks)) |
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eqs = [sum(a * b for a, b in zip(dims, unks)) for dims in sspaces] |
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solvit = lambda eq: solve([Eq(eq, result).subs(d) for d in dict_data], unks) |
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eq_sol_pairs = [(eq, solvit(eq)) for eq in eqs] |
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DefaultDict = lambda miss_func: type("", (dict,), {"__missing__": miss_func}) |
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DefaultEmptyDict = DefaultDict(lambda self, k: "") |
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msg_dict = DefaultEmptyDict({0: "No solution", 2: "Free variable"}) |
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fmt = "# [{:^13}] {:36} -> {}" |
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noans = "?" |
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table = [(msg_dict[len(sol)], eq.subs(sol)) for eq, sol in eq_sol_pairs] |
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ptable = {(m, eqsol, noans if m else eqsol.subs(wanted)) for m, eqsol in table} |
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rows = sorted(fmt.format(*map(str, row)) for row in ptable) |
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for row in rows: print(row) |
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# Result: |
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# [ ] -2*A + B**2 - 9 -> 96 |
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# [ ] -A**2/3 + 4*A*B/3 -> 96 |
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# [ ] -A**2/3 + 4*B**2/3 - 4*B -> 96 |
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# [ ] 2*A*B/3 + B**2/3 - 3 -> 96 |
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# [ ] A + B**2 - 3*B -> 96 |
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# [ ] A**2 + 4*A -> 96 |
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# [ ] A**2 + 4*B - 12 -> 96 |
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# [ ] A**2/3 + 2*B**2/3 - 6 -> 96 |
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# [ ] A*B + A -> 96 |
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# [ ] A*B + B - 3 -> 96 |
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# [ ] B**2 - 2*B - 3 -> 96 |
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# [ No solution ] A*B*y + B**2*z + B*x -> ? |
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# [ No solution ] A*y + B*z + x -> ? |
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# [ Free variable ] A**2*(-z + 1) + A*B*z + A*(-3*z + 4) -> ? |
