from math import ceil

ARMOR = 0
DAMAGE = 1
RANGE = 2
TYPES = (ARMOR, DAMAGE, RANGE)

STATS = [# hp, dmg, range, cost
        (8, 2, 0, 1.00), # armor
        (6, 6, 1, 1.75), # damage
        (4, 4, 2, 2.50)] # range

def getCostFromHP(army_hp):
    return sum(STATS[t][3] * (army_hp[t] / float(STATS[t][0])) for t in TYPES)

def getDamage(att_hp, distance):
    """Compute total damage done by attacker."""
    dmg = 0
    for t in TYPES:
        units = ceil(att_hp[t] / float(STATS[t][0]))
        if STATS[t][2] >= distance:
            dmg += units * STATS[t][1]
    return dmg

def applyDamage(def_hp, dmg):
    """Apply dmg to defender's units."""
    for t in TYPES:
        if def_hp[t] >= dmg:
            def_hp[t] -= dmg
            break
        else:
            dmg -= def_hp[t]
            def_hp[t] = 0

def simulate(a_units, b_units):
    """
    Simulates battle between two armys and returns the score.
    Accepts army in this format: [armored, damage, ranged]
    """
    
    turn = 0
    
    a_hp = [STATS[t][0] * a_units[t] for t in TYPES]
    b_hp = [STATS[t][0] * b_units[t] for t in TYPES]
    a_cost = sum(STATS[t][3] * a_units[t] for t in TYPES)
    b_cost = sum(STATS[t][3] * b_units[t] for t in TYPES)
    
    while any(a_hp) and any(b_hp):
        a_dmg = getDamage(a_hp, 2 - turn)
        b_dmg = getDamage(b_hp, 2 - turn)

        applyDamage(a_hp, b_dmg)
        applyDamage(b_hp, a_dmg)
        
        turn += 1

    if any(b_hp): # if b won...
        return - getCostFromHP(b_hp) / float(b_cost)
    else:
        return getCostFromHP(a_hp) / float(a_cost)