valet_parking_chapter_2-2.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((R * C + S) * logR), pass in PyPy2 but Python2
# Space: O(R * C)
#

from random import randint, seed

# Template:
# https://github.com/kamyu104/GoogleKickStart-2021/blob/master/Round%20D/final_exam.py
class SkipNode(object):
    def __init__(self, level=0, val=None):
        self.val = val
        self.nexts = [None]*level
        self.prevs = [None]*level

class SkipList(object):
    P_NUMERATOR, P_DENOMINATOR = 1, 2  # P = 1/4 in redis implementation
    MAX_LEVEL = 32  # enough for 2^32 elements

    def __init__(self, end=float("inf"), can_duplicated=True):
        seed(0)
        self.__head = SkipNode()
        self.__len = 0
        self.__can_duplicated = can_duplicated
        self.add(end)
        self.__end = self.find(end)

    def begin(self):
        return self.__head.nexts[0]

    def end(self):
        return self.__end

    def lower_bound(self, target, cmp=lambda x, y: x < y):
        return self.__lower_bound(self.__find_prev_nodes(target, cmp))

    def find(self, target):
        return self.__find(target, self.__find_prev_nodes(target))

    def add(self, val):
        if not self.__can_duplicated and self.find(val):
            return self.find(val), False
        node = SkipNode(self.__random_level(), val)
        if len(self.__head.nexts) < len(node.nexts):
            self.__head.nexts.extend([None]*(len(node.nexts)-len(self.__head.nexts)))
        prevs = self.__find_prev_nodes(val)
        for i in xrange(len(node.nexts)):
            node.nexts[i] = prevs[i].nexts[i]
            if prevs[i].nexts[i]:
                prevs[i].nexts[i].prevs[i] = node
            prevs[i].nexts[i] = node
            node.prevs[i] = prevs[i]
        self.__len += 1
        return node if self.__can_duplicated else (node, True)

    def remove(self, it):
        prevs = it.prevs
        curr = self.__find(it.val, prevs)
        if not curr:
            return self.__end
        self.__len -= 1
        for i in reversed(xrange(len(curr.nexts))):
            prevs[i].nexts[i] = curr.nexts[i]
            if curr.nexts[i]:
                curr.nexts[i].prevs[i] = prevs[i]
            if not self.__head.nexts[i]:
                self.__head.nexts.pop()
        return curr.nexts[0]

    def __lower_bound(self, prevs):
        if prevs:
            candidate = prevs[0].nexts[0]
            if candidate:
                return candidate
        return None

    def __find(self, val, prevs):
        candidate = self.__lower_bound(prevs)
        if candidate and candidate.val == val:
            return candidate
        return None

    def __find_prev_nodes(self, val, cmp=lambda x, y: x < y):
        prevs = [None]*len(self.__head.nexts)
        curr = self.__head
        for i in reversed(xrange(len(self.__head.nexts))):
            while curr.nexts[i] and cmp(curr.nexts[i].val, val):
                curr = curr.nexts[i]
            prevs[i] = curr
        return prevs

    def __random_level(self):
        level = 1
        while randint(1, SkipList.P_DENOMINATOR) <= SkipList.P_NUMERATOR and \
              level < SkipList.MAX_LEVEL:
            level += 1
        return level

    def __iter__(self):
        it = self.begin()
        while it != self.end():
            yield it.val
            it = it.nexts[0]

    def __len__(self):
        return self.__len-1  # excluding end node

    def __str__(self):
        result = []
        for i in reversed(xrange(len(self.__head.nexts))):
            result.append([])
            curr = self.__head.nexts[i]
            while curr:
                result[-1].append(str(curr.val))
                curr = curr.nexts[i]
        return "\n".join(map(lambda x: "->".join(x), result))

# Template:
# https://github.com/kamyu104/GoogleCodeJam-2020/blob/master/Virtual%20World%20Finals/pack_the_slopes.py
class SegmentTree(object):  # 0-based index
    def __init__(self, N,
                 build_fn=lambda x, y: [y]*(2*x),
                 query_fn=lambda x, y: y if x is None else min(x, y),
                 update_fn=lambda x, y: y if x is None else x+y,
                 default_val=float("inf")):
        self.N = N
        self.H = (N-1).bit_length()
        self.query_fn = query_fn
        self.update_fn = update_fn
        self.tree = build_fn(N, default_val)
        self.lazy = [None]*N
        for i in reversed(xrange(1, N)):
            self.tree[i] = query_fn(self.tree[2*i], self.tree[2*i+1])

    def __apply(self, x, val):
        self.tree[x] = self.update_fn(self.tree[x], val)
        if x < self.N:
            self.lazy[x] = self.update_fn(self.lazy[x], val)

    def update(self, L, R, h):  # Time: O(logN), Space: O(N)
        def pull(x):
            while x > 1:
                x //= 2
                self.tree[x] = self.query_fn(self.tree[x*2], self.tree[x*2+1])
                if self.lazy[x] is not None:
                    self.tree[x] = self.update_fn(self.tree[x], self.lazy[x])

        if L > R:
            return
        L += self.N
        R += self.N
        L0, R0 = L, R
        while L <= R:
            if L & 1:  # is right child
                self.__apply(L, h)
                L += 1
            if R & 1 == 0:  # is left child
                self.__apply(R, h)
                R -= 1
            L //= 2
            R //= 2
        pull(L0)
        pull(R0)

    def query(self, L, R):  # Time: O(logN), Space: O(N)
        def push(x):
            n = 2**self.H
            while n != 1:
                y = x // n
                if self.lazy[y] is not None:
                    self.__apply(y*2, self.lazy[y])
                    self.__apply(y*2 + 1, self.lazy[y])
                    self.lazy[y] = None
                n //= 2

        result = None
        if L > R:
            return result

        L += self.N
        R += self.N
        push(L)
        push(R)
        while L <= R:
            if L & 1:  # is right child
                result = self.query_fn(result, self.tree[L])
                L += 1
            if R & 1 == 0:  # is left child
                result = self.query_fn(result, self.tree[R])
                R -= 1
            L //= 2
            R //= 2
        return result

    def __str__(self):
        showList = []
        for i in xrange(self.N):
            showList.append(self.query(i, i))
        return ",".join(map(str, showList))

# Template:
# https://github.com/kamyu104/GoogleKickStart-2021/blob/main/Round%20F/festival2.py
def update_skip_lists(K, c, r, sl):
    if c == 1:
        sl[0].add(-r)
        if len(sl[0]) <= K:
            sl[1] = sl[0].end().prevs[0]
        elif r >= -sl[1].val:
            sl[1] = sl[1].prevs[0]
    else:
        sl[0].remove(sl[0].find(-r))
        if len(sl[0]) < K:
            sl[1] = sl[0].end().prevs[0]
        elif r >= -sl[1].val:
            sl[1] = sl[1].nexts[0]

def update(R, K, r, sls, st, diff):
    s1, s2 = sls
    A = -s1[1].val if R-K+1 <= len(s1[0]) else -1
    B = s2[1].val if K <= len(s2[0]) else R+2
    update_skip_lists(R-K+1, diff, r, s1)
    update_skip_lists(K, diff, -r, s2)
    if r >= A:
        new_A = -s1[1].val if R-K+1 <= len(s1[0]) else -1
        st.update(A+1, new_A-1, diff) if diff == 1 else st.update(new_A+1, A-1, diff)
        A = new_A
    if r <= B:
        new_B = s2[1].val if K <= len(s2[0]) else R+2
        st.update(new_B+1, B-1, diff) if diff == 1 else st.update(B+1, new_B-1, diff)
        B = new_B
    if not (r < A or r > B):
        st.update(r, r, 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)]

    sls = [[[SkipList(), None] for _ in xrange(2)] for _ in xrange(C)]
    st = SegmentTree(R+2, build_fn=lambda x, y: [abs((i-x)-K) if i >= x else y for i in xrange(2*x)])
    for j in xrange(C):
        for i in xrange(R):
            if G[i][j] == 'X':
                update(R, K, i+1, sls[j], st, 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, sls[j], st, 1 if G[i][j] == 'X' else -1)
        result += st.query(0, R+1)
    return result

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