Problem:


Problem D: Futon

The sales department of Japanese Ancient Giant Corp. is visiting a hot spring resort for their
recreational trip. For deepening their friendships, they are staying in one large room of a
Japanese-style hotel called a ryokan.

In the ryokan, people sleep in Japanese-style beds called futons. They all have put their futons
on the floor just as they like. Now they are ready for sleeping but they have one concern: they
don’t like to go into their futons with their legs toward heads — this is regarded as a bad custom
in Japanese tradition. However, it is not obvious whether they can follow a good custom. You
are requested to write a program answering their question, as a talented programmer.

Here let's model the situation. The room is considered to be a grid on an xy-plane. As usual,
x-axis points toward right and y-axis points toward up. Each futon occupies two adjacent cells.
People put their pillows on either of the two cells. Their heads come to the pillows; their foots
come to the other cells. If the cell of some person's foot becomes adjacent to the cell of another
person's head, regardless their directions, then it is considered as a bad case. Otherwise people
are all right.

Input

The input is a sequence of datasets. Each dataset is given in the following format:

       n

       x1 y1 dir1

       ...

       xn yn dirn

n is the number of futons (1 ≤ n ≤ 20,000); (xi, yi) denotes the coordinates of the left-bottom
corner of the i-th futon; diri is either 'x' or  'y' and denotes the direction of the i-th futon,
where 'x' means the futon is put horizontally and 'y' means vertically. All coordinate values are
non-negative integers not greater than 109 .

It is guaranteed that no two futons in the input overlap each other.

The input is terminated by a line with a single zero. This is not part of any dataset and thus
should not be processed.

Output

For each dataset, print "Yes" in a line if it is possible to avoid a bad case, or "No" otherwise.

Sample Input

4
0 0 x
2 0 x
0 1 x
2 1 x
4
1 0 x
0 1 x
2 1 x
1 2 x
4
0 0 x
2 0 y
0 1 y
1 2 x
0

Output for the Sample Input

Yes
No
Yes



Sample input:
4
0 0 x
2 0 x
0 1 x
2 1 x
4
1 0 x
0 1 x
2 1 x
1 2 x
4
0 0 x
2 0 y
0 1 y
1 2 x
0


Sample output:
Yes
No
Yes

Submission status: Wrong Answer

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    rr = []

    while True:
        n = I()
        if n == 0:
            break

        a = [LS() for _ in range(n)]
        d = collections.defaultdict(int)
        for i in range(n):
            x, y, di = a[i]
            x = int(x)
            y = int(y)
            d[(x,y)] = i + 1
            if di == 'x':
                d[(x+1,y)] = i + 1
            else:
                d[(x,y+1)] = i + 1

        v = collections.defaultdict(bool)
        f = True
        for k in list(d.keys()):
            if v[k]:
                continue
            s1 = set()
            s2 = set()
            ns1 = set([k])
            ns2 = set()
            while ns1 or ns2:
                for ak in list(ns1):
                    for di,dj in dd:
                        nk = (ak[0]+di, ak[1]+dj)
                        if d[nk] == 0:
                            continue
                        if d[nk] == d[ak]:
                            ns1.add(nk)
                        else:
                            ns2.add(nk)
                ns2 -= s2
                for ak in list(ns2):
                    for di,dj in dd:
                        nk = (ak[0]+di, ak[1]+dj)
                        if d[nk] == 0:
                            continue
                        if d[nk] == d[ak]:
                            ns2.add(nk)
                        else:
                            ns1.add(nk)

                ns2 -= s2
                ns1 -= s1
                s2 |= ns2
                s1 |= ns1
                if s1 & s2:
                    f = False
                    break

            if not f:
                break

            for c in s1:
                v[c] = 1
            for c in s2:
                v[c] = 1

        if f:
            rr.append('Yes')
        else:
            rr.append('No')



    return '\n'.join(map(str,rr))


print(main())

Submission status: Wrong Answer

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    rr = []

    while True:
        n = I()
        if n == 0:
            break

        a = [LS() for _ in range(n)]
        d = collections.defaultdict(int)
        for i in range(n):
            x, y, di = a[i]
            x = int(x)
            y = int(y)
            d[(x,y)] = i + 1
            if di == 'x':
                d[(x+1,y)] = i + 1
            else:
                d[(x,y+1)] = i + 1

        v = collections.defaultdict(bool)
        f = True
        for k in list(d.keys()):
            if v[k]:
                continue
            s1 = set()
            s2 = set()
            ns1 = set([k])
            ns2 = set()
            while ns1 or ns2:
                for ak in list(ns1):
                    for di,dj in dd:
                        nk = (ak[0]+di, ak[1]+dj)
                        if d[nk] == 0:
                            continue
                        if d[nk] == d[ak]:
                            ns2.add(nk)
                        else:
                            ns1.add(nk)
                ns2 -= s2
                for ak in list(ns2):
                    for di,dj in dd:
                        nk = (ak[0]+di, ak[1]+dj)
                        if d[nk] == 0:
                            continue
                        if d[nk] == d[ak]:
                            ns1.add(nk)
                        else:
                            ns2.add(nk)

                ns2 -= s2
                ns1 -= s1
                s2 |= ns2
                s1 |= ns1
                if s1 & s2:
                    f = False
                    break

            if not f:
                break

            for c in s1:
                v[c] = 1
            for c in s2:
                v[c] = 1

        if f:
            rr.append('Yes')
        else:
            rr.append('No')



    return '\n'.join(map(str,rr))


print(main())

Submission status: Wrong Answer

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    rr = []

    while True:
        n = I()
        if n == 0:
            break

        a = [LS() for _ in range(n)]
        d = collections.defaultdict(int)
        ed = collections.defaultdict(lambda: None)
        for i in range(n):
            x, y, di = a[i]
            x = int(x)
            y = int(y)
            d[(x,y)] = i + 1
            if di == 'x':
                d[(x+1,y)] = i + 1
                ed[(x,y)] = (x+1,y)
                ed[(x+1,y)] = (x,y)
            else:
                d[(x,y+1)] = i + 1
                ed[(x,y)] = (x,y+1)
                ed[(x,y+1)] = (x,y)

        ee = collections.defaultdict(set)
        dka = list(d.keys())
        for x,y in list(d.keys()):
            dt = d[(x,y)]
            for di,dj in dd:
                ni = x + di
                nj = y + dj
                if d[(ni,nj)] > 0 and d[(ni,nj)] != dt:
                    ee[(x,y)].add((ni,nj))

        v = collections.defaultdict(bool)
        f = True
        for k in dka:
            if v[k]:
                continue
            s1 = set()
            s2 = set()
            ns1 = set([k])
            ns2 = set()
            while ns1 or ns2:
                s1 |= ns1
                na = list(ns1)
                ns1 = set()
                for k in na:
                    ns1 |= ee[k]
                    ns2.add(ed[k])

                ns2 -= s2
                na = list(ns2)
                s2 |= ns2
                ns2 = set()
                for k in na:
                    ns2 |= ee[k]
                    ns1.add(ed[k])

                ns1 -= s1
                ns2 -= s2
                s1 |= ns1
                s2 |= ns2
                if s1 & s2:
                    f = False
                    break
            # print('k', k)
            # print('s1', s1)
            # print('s2', s2)

            if f:
                for k in s1:
                    v[k] = 1
                for k in s2:
                    v[k] = 1
            else:
                break

        if f:
            rr.append('Yes')
        else:
            rr.append('No')


    return '\n'.join(map(str,rr))


print(main())

Submission status: Wrong Answer

Solution code:
def check(x,y,d):
    if d == "x":
        for i in xrange(6):
            dx,dy = dxy1[i]
            if not (x+dx,y+dy) in futon: continue
            if futon[(x+i/3,y)] != futon[(x+dx,y+dy)]:
                return False
    else:
        for i in xrange(6):
            dx,dy = dxy2[i]
            if not (x+dx,y+dy) in futon: continue
            if futon[(x,y+i/3)] != futon[(x+dx,y+dy)]:
                return False
    return True

dxy1 = zip([-1,0,0,1,1,2],[0,1,-1,1,-1,0])
dxy2 = zip([0,1,-1,1,-1,0],[-1,0,0,1,1,2])
while 1:
    futon = {}
    n = int(raw_input())
    if n == 0: break
    valid = True
    for loop in xrange(n):
        x,y,d = raw_input().split()
        x,y = int(x),int(y)
        if not valid: continue
        if d == "x":
            for dx,dy in dxy1:
                if (x+dx,y+dy) in futon:
                    v = futon[(x+dx,y+dy)]
                    futon[(x  ,y)] = (v   if dx < 1 else 1-v)
                    futon[(x+1,y)] = (1-v if dx < 1 else v  )
                    valid = check(x,y,d)
                    break
            else:
                futon[(x  ,y)] = 1
                futon[(x+1,y)] = 0
        else:
            for dx,dy in dxy2:
                if (x+dx,y+dy) in futon:
                    v = futon[(x+dx,y+dy)]
                    futon[(x  ,y)] = (v   if dy < 1 else 1-v)
                    futon[(x,y+1)] = (1-v if dy < 1 else v  )
                    valid = check(x,y,d)
                    break
            else:
                futon[(x,y  )] = 1
                futon[(x,y+1)] = 0
    
    print "Yes" if valid else "No"

Submission status: Accepted

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    rr = []

    while True:
        n = I()
        if n == 0:
            break

        a = [LS() for _ in range(n)]
        d = collections.defaultdict(int)
        ed = collections.defaultdict(lambda: None)
        for i in range(n):
            x, y, di = a[i]
            x = int(x)
            y = int(y)
            d[(x,y)] = i + 1
            if di == 'x':
                d[(x+1,y)] = i + 1
                ed[(x,y)] = (x+1,y)
                ed[(x+1,y)] = (x,y)
            else:
                d[(x,y+1)] = i + 1
                ed[(x,y)] = (x,y+1)
                ed[(x,y+1)] = (x,y)

        ee = collections.defaultdict(set)
        dka = list(d.keys())
        for x,y in list(d.keys()):
            dt = d[(x,y)]
            for di,dj in dd:
                ni = x + di
                nj = y + dj
                if d[(ni,nj)] > 0 and d[(ni,nj)] != dt:
                    ee[(x,y)].add((ni,nj))

        v = collections.defaultdict(bool)
        f = True
        for k in dka:
            if v[k]:
                continue
            s1 = set()
            s2 = set()
            ns1 = set([k])
            ns2 = set()
            while ns1:
                na = list(ns1)
                s1 |= ns1
                ns1 = set()
                for k in na:
                    ns1 |= ee[k]
                    ns2.add(ed[k])
                ns2 -= s2

                while ns2:
                    na = list(ns2)
                    s2 |= ns2
                    ns2 = set()
                    for k in na:
                        ns2 |= ee[k]
                        ns1.add(ed[k])
                    ns2 -= s2

                ns1 -= s1

            if s1 & s2:
                f = False
            # print('k', k)
            # print('s1', s1)
            # print('s2', s2)

            if f:
                for k in s1:
                    v[k] = 1
                for k in s2:
                    v[k] = 1
            else:
                break

        if f:
            rr.append('Yes')
        else:
            rr.append('No')


    return '\n'.join(map(str,rr))


print(main())

Submission status: Accepted

Solution code:
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

move = [(0,1),(1,0)]
def solve(n):
    f = defaultdict(lambda : 0)
    v = defaultdict(list)
    l = []
    for i in range(n):
        a,b,dir = input().split()
        a = int(a)
        b = int(b)
        f[(a,b)] = 1
        dir = 0 if dir == "x" else 1
        na,nb = a+1-dir,b+dir
        f[(na,nb)] = 1
        l.append((a,b,na,nb))
        l.append((na,nb,a,b))
        v[(a,b)].append(((na,nb),1))
        v[(na,nb)].append(((a,b),1))
    for a,b,c,d in l:
        for dx,dy in move:
            na,nb = a+dx,b+dy
            if f[(na,nb)] and (c,d) != (na,nb):
                v[(a,b)].append(((na,nb),0))
                v[(na,nb)].append(((a,b),0))
    bfs = defaultdict(lambda : -1)
    q = deque()
    for a,b,c,d in l:
        if bfs[(a,b)] < 0:
            q.append((a,b))
            bfs[(a,b)] = 0
            while q:
                x,y = q.popleft()
                for node,k in v[(x,y)]:
                    nx,ny = node
                    if k:
                        nb = 1-bfs[(x,y)]
                    else:
                        nb = bfs[(x,y)]
                    if bfs[(nx,ny)] >= 0:
                        if bfs[(nx,ny)] != nb:
                            print("No")
                            return
                    else:
                        bfs[(nx,ny)] = nb
                        q.append((nx,ny))
    print("Yes")
    return

#Solve
if __name__ == "__main__":
    while 1:
        n = I()
        if n == 0:
            break
        solve(n)

Submission status: Runtime Error

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    rr = []

    while True:
        n = I()
        if n == 0:
            break

        a = [LS() for _ in range(n)]
        d = collections.defaultdict(int)
        for i in range(n):
            x, y, di = a[i]
            x = int(x)
            y = int(y)
            d[(x,y)] = i + 1
            if di == 'x':
                d[(x+1,y)] = i + 1
            else:
                d[(x,y+1)] = i + 1

        v = collections.defaultdict(bool)
        f = True
        for k in list(d.keys()):
            if v[k]:
                continue
            s1 = set()
            s2 = set()
            ns1 = set([k])
            ns2 = set()
            while ns1:
                while ns1:
                    ns1 -= s1
                    s1 |= ns1
                    for ak in list(ns1):
                        for di,dj in dd:
                            nk = (ak[0]+di, ak[1]+dj)
                            if d[nk] == 0:
                                continue
                            if d[nk] == d[ak]:
                                ns2.add(nk)
                            else:
                                ns1.add(nk)
                    if s1 & s2:
                        f = False
                        break

                while ns2:
                    ns2 -= s2
                    s2 |= ns2
                    for ak in list(ns2):
                        for di,dj in dd:
                            nk = (ak[0]+di, ak[1]+dj)
                            if d[nk] == 0:
                                continue
                            if d[nk] == d[ak]:
                                ns1.add(nk)
                            else:
                                ns2.add(nk)

                    if s1 & s2:
                        f = False
                        break

                if s1 & s2:
                    f = False
                    break

            if not f:
                break

            for c in s1:
                v[c] = 1
            for c in s2:
                v[c] = 2

        if f:
            rr.append('Yes')
        else:
            rr.append('No')


    return '\n'.join(map(str,rr))


print(main())

Submission status: Runtime Error

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    rr = []

    while True:
        n = I()
        if n == 0:
            break

        a = [LS() for _ in range(n)]
        d = collections.defaultdict(int)
        ed = collections.defaultdict(lambda: None)
        for i in range(n):
            x, y, di = a[i]
            x = int(x)
            y = int(y)
            d[(x,y)] = i + 1
            if di == 'x':
                d[(x+1,y)] = i + 1
                ed[(x,y)] = (x+1,y)
                ed[(x+1,y)] = (x,y)
            else:
                d[(x,y+1)] = i + 1
                ed[(x,y)] = (x,y+1)
                ed[(x,y+1)] = (x,y)

        ee = collections.defaultdict(set)
        dka = list(d.keys())
        for x,y in list(d.keys()):
            dt = d[(x,y)]
            for di,dj in dd:
                ni = x + di
                nj = y + dj
                if d[(ni,nj)] > 0 and d[(ni,nj)] != dt:
                    ee[(x,y)].add((ni,nj))

        v = collections.defaultdict(bool)
        f = True
        for k in dka:
            if v[k]:
                continue
            s1 = set()
            s2 = set()
            ns1 = set([k])
            ns2 = set()
            while ns1:
                na = list(ns1)
                s1 |= ns1
                ns1 = set()
                for k in na:
                    ns1 |= ee[k]
                    ns2.add(ed[k])
                ns2 -= s2

                while ns2:
                    na = list(ns2)
                    s2 |= ns2
                    ns2 = set()
                    for k in na:
                        ns2 |= ee[k]
                        ns1.add(ed[k])
                    ns2 -= s2

                ns1 -= s1
                if s1 & s2:
                    f = False
                    break
            # print('k', k)
            # print('s1', s1)
            # print('s2', s2)

            if f:
                for k in s1:
                    v[k] = 1
                for k in s2:
                    v[k] = 1
            else:
                break

        if f:
            rr.append('Yes')
        else:
            rr.append('No')


    return '\n'.join(map(str,rr))


print(main())