Problem 101

p101.py

def PolynomialInterpolator(sequence):
    if len(sequence) == 1: #Basic case
        return sequence[0][1]
    elif len(sequence) == 2: #Still basic
        return sequence[1][1] + (sequence[1][1] - sequence[0][1])
    else: #Using Lagrange's Formula
        length = len(sequence)
        goal = length + 1
        total = 0
        for x in range(length):
            temp_total_multiple = sequence[x][1] #Set up a multiple and divisor variable to avoid precision errors
            temp_total_divisor = 1
            for y in range(1,goal+1):
                if (x+1) - y != 0 and goal - y != 0:
                    temp_total_multiple *= (goal - y)
                    temp_total_divisor *= ((x+1)-y)         
            total += temp_total_multiple/temp_total_divisor
    return total

def compute():
    terms = [(1,1),(2,683),(3,44287),(4,838861),(5,8138021),(6,51828151),(7,247165843),(8,954437177),(9,3138105961),(10,9090909091)]
    total = 0
    for x in range(1,len(terms)+1):
        temp = PolynomialInterpolator(terms[:x])
        total += temp
    return total