valet_parking_chapter_2-5.py

# Copyright (c) 2021 kamyu. All rights reserved.
#
# Facebook Hacker Cup 2021 Round 2 - Problem C. Valet Parking - Chapter 2
# https://www.facebook.com/codingcompetitions/hacker-cup/2021/round-2/problems/C2
#
# Time:  O(S * min(R, C) + (R * C + S) * logR)
# Space: O(R * C)
#

# Template:
# https://github.com/kamyu104/GoogleKickStart-2021/blob/main/Round%20F/festival.py
class BIT(object):  # 0-indexed.
    def __init__(self, n):
        self.__bit = [0]*(n+1)  # Extra one for dummy node.

    def add(self, i, val):
        i += 1  # Extra one for dummy node.
        while i < len(self.__bit):
            self.__bit[i] += val
            i += (i & -i)

    def query(self, i):
        i += 1  # Extra one for dummy node.
        ret = 0
        while i > 0:
            ret += self.__bit[i]
            i -= (i & -i)
        return ret

    def kth_element(self, k):
        floor_log2_n = (len(self.__bit)-1).bit_length()-1
        pow_i = 2**floor_log2_n
        total = pos = 0  # 1-indexed
        for _ in reversed(xrange(floor_log2_n+1)):  # O(logN)
            if pos+pow_i < len(self.__bit) and total+self.__bit[pos+pow_i] < k:  # find max pos s.t. total < k
                total += self.__bit[pos+pow_i]
                pos += pow_i
            pow_i >>= 1
        return (pos+1)-1  # 0-indexed, return min pos s.t. total >= k if pos exists else n

def update(R, K, r, bit, cnts, left, right, diff):
    total = bit.query(R-1)
    A = bit.kth_element(total-(R-K+1)+1)+1 if R-K+1 <= total else -1
    B = bit.kth_element(K)+1 if K <= total else R+2
    bit.add(r-1, diff)
    total += diff
    if r >= A:
        new_A = bit.kth_element(total-(R-K+1)+1)+1 if R-K+1 <= total else -1
        nl, nr = (max(left, A+1), min(right, new_A-1)) if diff == 1 else (max(left, new_A+1), min(right, A-1))
        for i in xrange(nl, nr+1):
            cnts[i-left] += diff
        A = new_A
    if r <= B:
        new_B = bit.kth_element(K)+1 if K <= total else R+2
        nl, nr = (max(left, new_B+1), min(right, B-1)) if diff == 1 else (max(left, B+1), min(right, new_B-1))
        for i in xrange(nl, nr+1):
            cnts[i-left] += diff
        B = new_B
    if not (r < A or r > B):
        if left <= r <= right:
            cnts[r-left] += diff

def valet_parking_chapter_2():
    R, C, K, S = map(int, raw_input().strip().split())
    G = [list(raw_input().strip()) for _ in xrange(R)]

    bits = [BIT(R) for _ in xrange(C)]
    left, right = max(K-(C-1), 0), min(K+(C-1), R+1)
    cnts = [abs(i-K) for i in xrange(left, right+1)]
    for j in xrange(C):
        for i in xrange(R):
            if G[i][j] == 'X':
                update(R, K, i+1, bits[j], cnts, left, right, 1)
    result = 0
    for _ in xrange(S):
        i, j = map(lambda x: int(x)-1, raw_input().strip().split())
        G[i][j] = 'X' if G[i][j] == '.' else '.'
        update(R, K, i+1, bits[j], cnts, left, right, 1 if G[i][j] == 'X' else -1)
        result += min(cnts)
    return result

for case in xrange(input()):
    print 'Case #%d: %s' % (case+1, valet_parking_chapter_2())