#function to return coefficient of degree k term of product of two polynomials def poly_prod(P, Q): prod=[] for k in range(0, max(len(P), len(Q))+1): coef=0 for i in range(0, k+1): if i<len(P) and k-i<len(Q): coef = coef + P[i]*Q[k-i] prod.append(coef) return prod #generating functions for 5 distinct scorings plays def safety(points): P=[] for i in range(0, points+1): if i % 2 == 0: P[len(P):]=[1] else: P[len(P):]=[0] return P def fg(points): P=[] for i in range(0, points+1): if i % 3 == 0: P[len(P):]=[1] else: P[len(P):]=[0] return P def td(points): P=[] for i in range(0, points+1): if i % 6 == 0: P[len(P):]=[1] else: P[len(P):]=[0] return P def td_fg(points): P=[] for i in range(0, points+1): if i % 7 == 0: P[len(P):]=[1] else: P[len(P):]=[0] return P def td_conv(points): P=[] for i in range(0, points+1): if i % 8 == 0: P[len(P):]=[1] else: P[len(P):]=[0] return P def ways_to_score(points): return poly_prod( safety(points), poly_prod(fg(points), poly_prod(td(points), poly_prod(td_fg(points), td_conv(points)))))[points]
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