Battle

def battle(atks, healths):
    def fight(foe: dict, ally: dict) -> bool:
        foe['health'] -= ally['atk']
        if foe['health'] > 0:
            ally['health'] -= foe['atk']
        return foe['health'] > 0

    warriors = [{"atk": atk, "health": health} for atk, health in zip(atks, healths)]
    foe = warriors[0]
    allies = sorted(warriors[1:], key=lambda a: a['atk'], reverse=True)
    allies_with_enough_health = [ally for ally in allies if ally['health'] > foe['atk']]
    allies_with_low_health = [ally for ally in allies if ally['health'] <= foe['atk']]

    while allies_with_enough_health:
        ally = allies_with_enough_health[0]
        foe_alive = fight(foe, ally)
        if not foe_alive:
            return len(allies_with_enough_health + allies_with_low_health)
        if ally['health'] <= foe['atk']:  # if health enough just fight another round
            allies_with_enough_health.pop(0)
            allies_with_low_health += [ally]

    allies_with_low_health.sort(key=lambda a: a['atk'], reverse=True)
    while allies_with_low_health:
        ally = allies_with_low_health.pop(0)
        foe_alive = fight(foe, ally)
        if not foe_alive:
            return len(allies_with_low_health) + 1  # as we already popped this ally from the list

    return 0


def test_battles():
    assert battle([1],
                  [2]) == 0
    assert battle([1, 2],
                  [2, 1]) == 1
    assert battle([2, 2],
                  [2, 1]) == 1
    assert battle([2, 2],
                  [3, 1]) == 0
    assert battle([2, 2, 1],
                  [3, 1, 1]) == 1
    assert battle([2, 2, 3],
                  [3, 1, 1]) == 2
    assert battle([3, 1, 2, 3, 4],
                  [20, 4, 2, 4, 13]) == 4
    assert battle([3, 1, 2, 3, 4],
                  [20, 4, 2, 4, 11]) == 4
    assert battle([3, 1, 2, 3, 4],
                  [21, 4, 2, 4, 11]) == 3