Untitled

from collections import namedtuple
from typing import List

Data = namedtuple('Data', ['char', 'cnt'])
LEFT = 'LEFT'
RIGHT = 'RIGHT'


def count_substring(a):
    return a * (a + 1) // 2


memo = {}


def dp(data: List[Data], seen: List[int], idx: int, direction: str):
    inputs = (idx, direction)
    if inputs in memo:
        return memo[inputs]

    m = len(data)

    res = 0
    curr_idx = seen[idx]

    if direction == LEFT:
        if idx == len(seen) - 1:
            for j in range(curr_idx + 1, len(data)):
                res += count_substring(data[j].cnt)
        else:
            next_idx = seen[idx+1]
            for j in range(curr_idx + 1, next_idx - 1):
                res += count_substring(data[j].cnt)

            res += max(count_substring(data[next_idx-1].cnt) + dp(data, seen, idx + 1, RIGHT),
                       count_substring(data[next_idx-1].cnt + data[next_idx].cnt) + dp(data, seen, idx + 1, LEFT))

    else:
        # direction == RIGHT
        if idx == len(seen) - 1:
            res += count_substring(data[curr_idx].cnt + data[curr_idx+1].cnt)
            for j in range(curr_idx + 2, len(data)):
                res += count_substring(data[j].cnt)
        else:
            next_idx = seen[idx+1]

            if next_idx - curr_idx == 2:
                res += max(count_substring(data[curr_idx].cnt + data[curr_idx+1].cnt) + dp(data, seen, idx + 1, RIGHT),
                           count_substring(data[curr_idx].cnt + data[curr_idx+1].cnt + data[next_idx].cnt) + dp(data, seen, idx + 1, LEFT))
            else:
                res += count_substring(data[curr_idx].cnt +
                                       data[curr_idx+1].cnt)
                for j in range(curr_idx + 2, next_idx - 1):
                    res += count_substring(data[j].cnt)

                res += max(count_substring(data[next_idx-1].cnt) + dp(data, seen, idx + 1, RIGHT),
                           count_substring(data[next_idx-1].cnt + data[next_idx].cnt) + dp(data, seen, idx + 1, LEFT))

    memo[inputs] = res
    return res


def solve(color: str):
    # pre-processing
    data = []
    prev = None
    cnt = 0

    for i, v in enumerate(color):
        if v == prev:
            cnt += 1
        else:
            data.append(Data(prev, cnt))
            prev = v
            cnt = 1

    data.append(Data(color[-1], cnt))
    data.pop(0)

    # print(f'data {data}')

    # head and tail
    if len(data) == 1:
        return count_substring(data[0].cnt)

    if data[0].char == '.':
        data[1] = Data(data[1].char, data[0].cnt + data[1].cnt)
        data.pop(0)

    if data[-1][0] == '.':
        data[-2] = Data(data[-2].char, data[-1].cnt + data[-2].cnt)
        data.pop()

    # merge
    for i in range(1, len(data) - 1):
        if data[i].char == '.' and data[i-1] and data[i-1].char == data[i+1].char:
            data[i+1] = Data(data[i+1].char,
                             data[i-1].cnt + data[i].cnt + data[i+1].cnt)
            data[i] = None
            data[i-1] = None

    data = [x for x in data if x is not None]

    print(f'data {data}')

    m = len(data)
    # dp
    memo = [0] * m

    seen = []
    for i in range(len(data)):
        if data[i].char == '.':
            seen.append(i)

    res = 0
    for i in range(seen[0] - 1):
        res += count_substring(data[i].cnt)

    return res + max(count_substring(data[seen[0]-1].cnt) + dp(data, seen, 0, RIGHT),
                     count_substring(data[seen[0]-1].cnt + data[seen[0]].cnt) + dp(data, seen, 0, LEFT))


color = '.bb.a.aa.'
print(f'solve {color}: {solve(color)}')
print(f'memo {memo}')