Spirit Barrage

'''
Spirit Barrage Playstyle: Frame Sniping
Delay Optimization
by MarioVX
'''
from math import ceil


def average_ticks_per_frame(fpa, delay):
    '''
    Calculate average ticks per frame.

    Args:
        fpa (int): Frames per Attack of Spirit Barrage
        delay (int): The number of frames you wait after finishing
            the 3rd use of Spirit Barrage before starting the next.

    Returns:
        float: average ticks per frame.

    '''
    # total duration is 3 times FPA and the delay you wait thereafter
    duration = 3*fpa + delay
    # ticks: ticks_1 + ticks_2 + ticks_3, for each phantasm:
    # a phantasms ticks is its lifetime divided by 30 frames, rounded up,
    # but caps at 10.
    ticks = min(ceil(duration/30),10)
    return ticks/duration


def optimal_delay(fpa):
    '''
    Find the optimal delay for a given FPA.

    Args:
        fpa (int): Frames per Attack of Spirit Barrage

    Returns:
        tuple: (optimal delay, average ticks per frame at that delay)
            In case of tie, use longer delay to conserve Mana.
    '''
    # Generate tuples for all conceivable delays.
    # max delay is up to the last tick of the third phantasm
    all = [(i, average_ticks_per_frame(fpa, i)) for i in range(271-fpa)]
    # sort the tuples in the desired order, return only its first.
    return sorted(all, key=lambda x: (-x[1],-x[0]))[0]


# generate a map: fpa -> optimal_delay(fpa) for FPA from 1 to 48.
optimals = dict((i,optimal_delay(i)) for i in range(1,49))