Problem:


Score: 600 points

Problem Statement

There is a grass field that stretches infinitely.

In this field, there is a negligibly small cow. Let (x, y) denote the point that is x\ \mathrm{cm} south and y\ \mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0).

There are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).

What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead.

Constraints

All values in input are integers between -10^9 and 10^9  (inclusive).

1 \leq N, M \leq 1000

A_i < B_i\ (1 \leq i \leq N)

E_j < F_j\ (1 \leq j \leq M)

The point (0, 0) does not lie on any of the given segments.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1 C_1
:
A_N B_N C_N
D_1 E_1 F_1
:
D_M E_M F_M

Output

If the area of the region the cow can reach is infinite, print INF; otherwise, print an integer representing the area in \mathrm{cm^2}.

(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)

Sample Input 1

5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4

Sample Output 1

13

The area of the region the cow can reach is 13\ \mathrm{cm^2}.

Sample Input 2

6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4

Sample Output 2

INF

The area of the region the cow can reach is infinite.



Sample input:
5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4


Sample output:
13

Submission status: Accepted

Solution code:
from bisect import bisect_left as bl
from collections import deque
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline
n,m = map(int,input().split())
H = set([float("INF"),-float("INF")])
V = set([float("INF"),-float("INF")])
nl = []
ml = []
for i in range(n):
    a,b,c = map(int,input().split())
    H |= set([a,b])
    V.add(c)
    nl.append([a,b,c])
for i in range(m):
    c,a,b = map(int,input().split())
    V |= set([a,b])
    H.add(c)
    ml.append([a,b,c])
def compress(L):
    L2 = list(set(L))
    L2.sort()
    C = {v : k for k, v in enumerate(L2)}
    return L2, C
H ,dx = compress(H)
V, dy = compress(V)

h = len(H)+2
w = len(V)+2
d = [[0]*3001 for i in range(3001)]
checkh = [[0]*3001 for i in range(3001)]
checkv = [[0]*3001 for i in range(3001)]

for a,b,c in nl:
    s = dx[a]
    g = dx[b]
    t = dy[c]
    
    for x in range(s,g):
        checkh[x][t] = 1

for a,b,c in ml:
    s = dy[a]
    g = dy[b]
    t = dx[c]
    
    for y in range(s,g):
        checkv[t][y] = 1


def bfs(x,y):
    ans = 0
    sx = bl(H,0)-1
    sy = bl(V,0)-1
    q = deque([])
    q.append((sx,sy))
    d[sx][sy] = 1
    while q:
        h,v = q.popleft()
        ans += (H[h+1]-H[h])*(V[v+1]-V[v])
        if h != 0 and checkv[h][v] == 0 and d[h-1][v] == 0:
            d[h-1][v] = 1
            q.append((h-1,v))
        if v != 0 and checkh[h][v] == 0 and d[h][v-1] == 0:
            d[h][v-1] = 1
            q.append((h,v-1))
        if h != len(H)-2 and checkv[h+1][v] == 0 and d[h+1][v] == 0:
            d[h+1][v] = 1
            q.append((h+1,v))
        if v != len(V)-2 and checkh[h][v+1] == 0 and d[h][v+1] == 0:
            d[h][v+1] = 1
            q.append((h,v+1))
    print("INF" if ans ==float("INF") else ans)

bfs(0,0)

Submission status: Accepted

Solution code:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


n,m = map(int, input().split())

lx = [None] * n
ly = [None] * m
sx = set([-10**10, 0, 10**10])
sy = set([-10**10, 0, 10**10])
ix = 0
iy = 0
for i in range(n):
    t = tuple(map(int, input().split()))
    lx[i] = t
    sx.add(t[0])
    sx.add(t[1])
    sy.add(t[2])
        
for i in range(m):
    t = tuple(map(int, input().split()))
    ly[i] = t
    sx.add(t[0])
    sy.add(t[1])
    sy.add(t[2])
        
xs = list(sx)
ys = list(sy)
xs.sort(); ys.sort()

wx = len(xs)*2
wy = len(ys)*2
bs = [[1]*wy for _ in range(wx)]
for i, (x0, x1, y) in enumerate(lx):
    ix0 = xs.index(x0)*2
    ix1 = xs.index(x1)*2
    iy = ys.index(y)*2
    for ii in range(ix0+1, ix1, 2):
        bs[ii][iy] = -1
for i, (x, y0, y1) in enumerate(ly):
    ix = xs.index(x)*2
    iy0 = ys.index(y0)*2
    iy1 = ys.index(y1)*2
    for ii in range(iy0+1, iy1, 2):
        bs[ix][ii] = -1

xx = xs.index(0)*2+1
yy = ys.index(0)*2+1
s = [(xx,yy)]
dx = [-1,0,1,0]
dy = [0,-1,0,1]
ans = 0
end = False
while s:
    ix,iy = s.pop()
    for x, y in zip(dx,dy):
        ixx = ix + x
        iyy = iy + y
        if bs[ixx][iyy]!=1:
            continue
        ixx += x
        iyy += y
        if bs[ixx][iyy]!=1:
            continue
        if ixx<0 or ixx>=wx-1 or iyy<0 or iyy>=wy-1:
            print("INF")
            s = []
            end = True
            break
        bs[ixx][iyy] = 2
        ans += (xs[ixx//2+1] - xs[ixx//2]) * (ys[iyy//2+1] - ys[iyy//2])
        s.append((ixx, iyy))
            
if not end:
    print(ans)

Submission status: Accepted

Solution code:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


n,m = map(int, input().split())

lx = [None] * n
ly = [None] * m
sx = set([-10**10, 0, 10**10])
sy = set([-10**10, 0, 10**10])
ix = 0
iy = 0
for i in range(n):
    t = tuple(map(int, input().split()))
    lx[i] = t
    sx.add(t[0])
    sx.add(t[1])
    sy.add(t[2])
        
for i in range(m):
    t = tuple(map(int, input().split()))
    ly[i] = t
    sx.add(t[0])
    sy.add(t[1])
    sy.add(t[2])
        
xs = list(sx)
ys = list(sy)
xs.sort(); ys.sort()

wx = len(xs)*2
wy = len(ys)*2
bs = [[1]*wy for _ in range(wx)]
for i, (x0, x1, y) in enumerate(lx):
    ix0 = xs.index(x0)*2
    ix1 = xs.index(x1)*2
    iy = ys.index(y)*2
    for ii in range(ix0, ix1):
        bs[ii][iy] = -1
for i, (x, y0, y1) in enumerate(ly):
    ix = xs.index(x)*2
    iy0 = ys.index(y0)*2
    iy1 = ys.index(y1)*2
    for ii in range(iy0, iy1):
        bs[ix][ii] = -1

xx = xs.index(0)*2+1
yy = ys.index(0)*2+1
s = [(xx,yy)]
dx = [-1,0,1,0]
dy = [0,-1,0,1]
ans = 0
end = False
while s:
    ix,iy = s.pop()
    for x, y in zip(dx,dy):
        ixx = ix + x
        iyy = iy + y
        if bs[ixx][iyy]!=1:
            continue
        ixx += x
        iyy += y
        if bs[ixx][iyy]!=1:
            continue
        if ixx<0 or ixx>=wx-1 or iyy<0 or iyy>=wy-1:
            print("INF")
            s = []
            end = True
            break
        bs[ixx][iyy] = 2
        ans += (xs[ixx//2+1] - xs[ixx//2]) * (ys[iyy//2+1] - ys[iyy//2])
        s.append((ixx, iyy))
            
if not end:
    print(ans)

Submission status: Accepted

Solution code:
def f_single_dot():
    # 参考: https://atcoder.jp/contests/abc168/submissions/13368489
    import sys
    from collections import deque
    input = sys.stdin.readline
    N, M = [int(i) for i in input().split()]

    x_set, y_set = set([0]), set([0])  # 重複を除いた xy 座標の一覧 (座標圧縮に必要)

    vertical_lines = []
    for _ in range(N):
        a, b, c = [int(i) for i in input().split()]
        vertical_lines.append((a, b, c))
        x_set |= {a, b}
        y_set |= {c}

    horizontal_lines = []
    for _ in range(M):
        d, e, f = [int(i) for i in input().split()]
        horizontal_lines.append((d, e, f))
        x_set |= {d}
        y_set |= {e, f}

    x_set = sorted(x_set)
    y_set = sorted(y_set)

    # 座標圧縮 (壁も配列に格納するので、2 倍している)
    x_encoded = {n: i * 2 for i, n in enumerate(x_set)}
    y_encoded = {n: i * 2 for i, n in enumerate(y_set)}
    # 座標圧縮されたグリッドで縦横に 1 マス分進むことは実際にはどれくらい進んだことなのか
    x_length = [x_set[i // 2 + 1] - x_set[i // 2] if i %
                2 else 0 for i in range(len(x_set) * 2 - 1)]
    y_length = [y_set[i // 2 + 1] - y_set[i // 2] if i %
                2 else 0 for i in range(len(y_set) * 2 - 1)]

    # 壁を埋めていく (累積和を用いていない)
    x_size, y_size = 2 * len(x_set) - 1, 2 * len(y_set) - 1
    grid = [[0] * y_size for _ in range(x_size)]
    for a, b, c in vertical_lines:
        a, b, c = x_encoded[a], x_encoded[b], y_encoded[c]
        for x in range(a, b + 1):
            grid[x][c] = 1
    for d, e, f in horizontal_lines:
        d, e, f = x_encoded[d], y_encoded[e], y_encoded[f]
        for y in range(e, f + 1):
            grid[d][y] = 1

    queue = deque()
    is_visited = [[0] * (y_size + 1) for _ in range(x_size + 1)]

    # 一度原点から斜めに動く (壁もグリッドに入れたため、ずれが生じたことによる)
    for dx, dy in ((-1, -1), (-1, 1), (1, 1), (1, -1)):
        nx, ny = x_encoded[0] + dx, y_encoded[0] + dy
        if 0 <= nx < x_size and 0 <= ny < y_size:
            queue.append((nx, ny))
            is_visited[nx][ny] = 1

    diff = ((-1, 0), (1, 0), (0, -1), (0, 1))
    ans = 0
    while queue:
        x, y = queue.pop()
        if (x % 2) & (y % 2):
            ans += x_length[x] * y_length[y]
        # grid を 2 マスずつ動いているのは、壁をグリッドに入れたことによる
        for dx, dy in diff:
            nx, ny = x + dx, y + dy
            nnx, nny = nx + dx, ny + dy
            if grid[nx][ny] == 0:
                if not ((0 <= nnx < x_size) and (0 <= nny < y_size)):
                    return 'INF'
                if not is_visited[nnx][nny]:
                    queue.appendleft((nnx, nny))
                    is_visited[nnx][nny] = 1
    return ans

print(f_single_dot())

Submission status: Accepted

Solution code:
N,M = map(int,input().split())
ABC = [list(map(int,input().split())) for _ in [0]*N ]
DEF = [list(map(int,input().split())) for _ in [0]*M ]

X = [0]*3003
Y = [0]*3003
INF = 10**9 + 10
X[-1] = -INF
Y[-1] = -INF
X[-2] = INF
Y[-2] = INF
i = 0
j = 0
for a,b,c in ABC:
    X[i] = a
    X[i+1] = b
    Y[j] = c
    i += 2
    j += 1
for d,e,f in DEF:
    X[i] = d
    Y[j] = e
    Y[j+1] = f
    i += 1
    j += 2
X = sorted(set(X))
Y = sorted(set(Y))
Xdict = {x:i for i,x in enumerate(X)}
Ydict = {y:i for i,y in enumerate(Y)}

nx = len(X)
ny = len(Y)
nxy = nx * ny

E = [[15]*nx for _ in [0]*ny]

E[0] = [7]*nx
E[-1] = [13]*nx
for i in range(ny):
    E[i][0] -= 4
    E[i][-1] -= 1

for a,b,c in ABC:
    y1 = Ydict[c]
    y0 = y1-1
    for x in range(Xdict[a],Xdict[b]):
        E[y0][x] &= 15-2
        E[y1][x] &= 15-8

for d,e,f in DEF:
    x1 = Xdict[d]
    x0 = x1-1
    for y in range(Ydict[e],Ydict[f]):
        E[y][x0] &= 15-1
        E[y][x1] &= 15-4

dX = [x2-x for x,x2 in zip(X,X[1:])]
dY = [y2-y for y,y2 in zip(Y,Y[1:])]
burst = False
x0 = Xdict[0]
y0 = Ydict[0]
ans = dX[x0]*dY[y0]
done = [[False]*nx for _ in [0]*ny]
done[y0][x0] = True
q = [(x0,y0)]
dxy = [(1,0),(0,1),(-1,0),(0,-1)]
while q:
    qq = []
    for x,y in q:
        e = E[y][x]
        for i in range(4):
            if (e>>i)&1 == 0 : continue
            dx,dy = dxy[i]
            jx = x+dx
            jy = y+dy
            if done[jy][jx]:continue
            done[jy][jx] = True

            if jx==0 or jx==nx-1 or jy==0 or jy==ny-1:
                burst = True
                ans = "INF"
                qq = []
                break
            ans += dX[jx]*dY[jy]
            qq.append((jx,jy))
        if burst:break
    q = qq

print(ans)

Submission status: Accepted

Solution code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

n,m = map(int, readline().split())
data = list(map(int, read().split()))

point = [{0,10**9,-1*10**9} for _ in range(2)]
dic_en = [{} for _ in range(2)]
dic_de = [{} for _ in range(2)]

it = iter(data[:3*n])
for a,b,c in zip(it,it,it):
    point[0].add(a)
    point[0].add(b)
    point[1].add(c)

it = iter(data[3*n:])
for d,e,f in zip(it,it,it):
    point[0].add(d)
    point[1].add(e)
    point[1].add(f)

for i,p in enumerate(point):
    p = sorted(list(p))
    for after,before in enumerate(p):
        dic_en[i][before] = after
        dic_de[i][after] = before

len_x = len(point[0])
len_y = len(point[1])

wall_x = [[0] * (len_y-1) for _ in range(len_x)]
wall_y = [[0] * (len_y) for _ in range(len_x-1)]

it = iter(data[:3*n])
for a,b,c in zip(it,it,it):
    a,b,c = dic_en[0][a],dic_en[0][b],dic_en[1][c]
    wall_y[a][c] += 1
    if(b != len_x-1):
        wall_y[b][c] -= 1

it = iter(data[3*n:])
for d,e,f in zip(it,it,it):
    d,e,f = dic_en[0][d],dic_en[1][e],dic_en[1][f]
    wall_x[d][e] += 1
    if(f != len_y-1):
        wall_x[d][f] -= 1

for i in range(len_x):
    for j in range(1,len_y-1):
        wall_x[i][j] += wall_x[i][j-1]

for i in range(1,len_x-1):
    for j in range(len_y):
        wall_y[i][j] += wall_y[i-1][j]

start = (dic_en[0][0], dic_en[1][0])
area = [[0] * (len_y-1) for _ in range(len_x-1)]

ans = 0
stack = [start]
i,j = start
area[i][j] = 1
while(stack):
    i,j = stack.pop()
    ans += (dic_de[0][i+1] - dic_de[0][i])*(dic_de[1][j+1] - dic_de[1][j])
    #x+
    if(wall_x[i+1][j]==0):
        if(i==len_x-2):
            print('INF')
            exit()
        if(area[i+1][j] == 0):
            stack.append((i+1,j))
            area[i+1][j] = 1
    #x-
    if(wall_x[i][j]==0):
        if(i==0):
            print('INF')
            exit()
        if(area[i-1][j] == 0):
            stack.append((i-1,j))
            area[i-1][j] = 1
    #y+
    if(wall_y[i][j+1]==0):
        if(j==len_y-2):
            print('INF')
            exit()
        if(area[i][j+1] == 0):
            stack.append((i,j+1))
            area[i][j+1] = 1

    #y-
    if(wall_y[i][j]==0):
        if(j==0):
            print('INF')
            exit()
        if(area[i][j-1] == 0):
            stack.append((i,j-1))
            area[i][j-1] = 1

print(ans)

Submission status: Accepted

Solution code:
import bisect
import sys

lower_bound = bisect.bisect_left
upper_bound = bisect.bisect_right
INF = 0x3fffffff

n, m = map(int, input().split())
a = [list(map(int, input().split())) for i in range(n)]
b = [list(map(int, input().split())) for i in range(m)]

X = {-INF, INF}
Y = {-INF, INF}
for i in a:
    Y.add(i[2])
for i in b:
    X.add(i[0])

X = list(sorted(X))
Y = list(sorted(Y))
n = len(X) - 1
m = len(Y) - 1
wallx = [[False] * m for i in range(n)]
wally = [[False] * m for i in range(n)]

for x1, x2, y1 in a:
    x1 = lower_bound(X, x1)
    y1 = lower_bound(Y, y1)
    x2 = upper_bound(X, x2) - 1
    for i in range(x1, x2):
        wally[i][y1] = True

for x1, y1, y2 in b:
    x1 = lower_bound(X, x1)
    y1 = lower_bound(Y, y1)
    y2 = upper_bound(Y, y2) - 1
    for i in range(y1, y2):
        wallx[x1][i] = True

cow = [[False] * m for i in range(n)]
cx = upper_bound(X, 0) - 1
cy = upper_bound(Y, 0) - 1
cow[cx][cy] = True
q = [(cx, cy)]
ans = 0

while q:
    x, y = q.pop()
    if not x or not y:
        print("INF")
        sys.exit()
    ans += (X[x + 1] - X[x]) * (Y[y + 1] - Y[y])
    if x and not wallx[x][y] and not cow[x - 1][y]:
        cow[x - 1][y] = True
        q.append((x - 1, y))
    if y and not wally[x][y] and not cow[x][y - 1]:
        cow[x][y - 1] = True
        q.append((x, y - 1))
    if x + 1 < n and not wallx[x + 1][y] and not cow[x + 1][y]:
        cow[x + 1][y] = True
        q.append((x + 1, y))
    if y + 1 < m and not wally[x][y + 1] and not cow[x][y + 1]:
        cow[x][y + 1] = True
        q.append((x, y + 1))

print(ans)

Submission status: Accepted

Solution code:
import bisect
import sys

lower_bound = bisect.bisect_left
upper_bound = bisect.bisect_right
INF = 0x3fffffff

n, m = map(int, input().split())
a = [list(map(int, input().split())) for i in range(n)]
b = [list(map(int, input().split())) for i in range(m)]

X = {-INF, INF}
Y = {-INF, INF}
for i in a:
    Y.add(i[2])
for i in b:
    X.add(i[0])

X = list(sorted(X))
Y = list(sorted(Y))
n = len(X) - 1
m = len(Y) - 1
wallx = [[False] * m for i in range(n)]
wally = [[False] * m for i in range(n)]

for x1, x2, y1 in a:
    x1 = lower_bound(X, x1)
    y1 = lower_bound(Y, y1)
    x2 = upper_bound(X, x2) - 1
    for i in range(x1, x2):
        wally[i][y1] = True

for x1, y1, y2 in b:
    x1 = lower_bound(X, x1)
    y1 = lower_bound(Y, y1)
    y2 = upper_bound(Y, y2) - 1
    for i in range(y1, y2):
        wallx[x1][i] = True

cow = [[False] * m for i in range(n)]
cx = upper_bound(X, 0) - 1
cy = upper_bound(Y, 0) - 1
cow[cx][cy] = True
q = [(cx, cy)]
ans = 0

while q:
    x, y = q.pop()
    if not x or not y:
        print("INF")
        sys.exit()
    ans += (X[x + 1] - X[x]) * (Y[y + 1] - Y[y])
    if x and not wallx[x][y] and not cow[x - 1][y]:
        cow[x - 1][y] = True
        q.append((x - 1, y))
    if y and not wally[x][y] and not cow[x][y - 1]:
        cow[x][y - 1] = True
        q.append((x, y - 1))
    if x + 1 < n and not wallx[x + 1][y] and not cow[x + 1][y]:
        cow[x + 1][y] = True
        q.append((x + 1, y))
    if y + 1 < m and not wally[x][y + 1] and not cow[x][y + 1]:
        cow[x][y + 1] = True
        q.append((x, y + 1))

print(ans)

Submission status: Accepted

Solution code:
def f_single_dot():
    # https://atcoder.jp/contests/abc168/submissions/13368489
    import sys
    from collections import deque
    input = sys.stdin.readline
    N, M = [int(i) for i in input().split()]

    x_set, y_set = set([0]), set([0])  # 重複を除いた xy 座標の一覧 (座標圧縮に必要)

    vertical_lines = []
    for _ in range(N):
        a, b, c = map(int, input().split())
        vertical_lines.append((a, b, c))
        x_set |= {a, b}
        y_set |= {c}

    horizontal_lines = []
    for _ in range(M):
        d, e, f = map(int, input().split())
        horizontal_lines.append((d, e, f))
        x_set |= {d}
        y_set |= {e, f}

    x_set = sorted(x_set)
    y_set = sorted(y_set)

    # 座標圧縮 (壁も配列に格納するので、2 倍している)
    x_encoded = {n: i * 2 for i, n in enumerate(x_set)}
    y_encoded = {n: i * 2 for i, n in enumerate(y_set)}
    # 座標圧縮されたグリッドで縦横に 1 マス分進むことは実際にはどれくらい進んだことなのか
    x_length = [x_set[i // 2 + 1] - x_set[i // 2] if i %
                2 else 0 for i in range(len(x_set) * 2 - 1)]
    y_length = [y_set[i // 2 + 1] - y_set[i // 2] if i %
                2 else 0 for i in range(len(y_set) * 2 - 1)]

    # 壁を埋めていく (累積和を用いていない)
    x_size, y_size = 2 * len(x_set) - 1, 2 * len(y_set) - 1
    grid = [[0] * y_size for _ in range(x_size)]
    for a, b, c in vertical_lines:
        a, b, c = x_encoded[a], x_encoded[b], y_encoded[c]
        for x in range(a, b + 1):
            grid[x][c] = 1
    for d, e, f in horizontal_lines:
        d, e, f = x_encoded[d], y_encoded[e], y_encoded[f]
        for y in range(e, f + 1):
            grid[d][y] = 1

    queue = deque()
    is_visited = [[0] * (y_size + 1) for _ in range(x_size + 1)]
    dy = [1, 1, -1, -1]
    dx = [1, -1, 1, -1]
    for k in range(4):
        nnx, nny = x_encoded[0] + dx[k], y_encoded[0] + dy[k]
        if 1 <= nnx < len(x_set) * 2 - 1 and 1 <= nny < len(y_set) * 2 - 1:
            queue.append((nnx, nny))
            is_visited[nnx][nny] = 1
    ans = 0
    dy = [1, 0, -1, 0]
    dx = [0, 1, 0, -1]
    while queue:
        x, y = queue.pop()
        if (x % 2) & (y % 2):
            ans += x_length[x] * y_length[y]
        for k in range(4):
            nx, ny = x + dx[k], y + dy[k]
            nnx, nny = nx + dx[k], ny + dy[k]
            if grid[nx][ny] == 0:
                if nnx < 0 or nnx >= len(x_set) * 2 - 1 or nny < 0 or nny >= len(y_set) * 2 - 1:
                    return 'INF'
                if not is_visited[nnx][nny]:
                    queue.appendleft((nnx, nny))
                    is_visited[nnx][nny] = 1
    return ans

print(f_single_dot())

Submission status: Accepted

Solution code:
def f_single_dot():
    # https://atcoder.jp/contests/abc168/submissions/13368489
    import sys
    from collections import deque
    input = sys.stdin.readline
    N, M = [int(i) for i in input().split()]

    x_set, y_set = set([0]), set([0])  # 重複を除いた xy 座標の一覧 (座標圧縮に必要)

    vertical_lines = []
    for _ in range(N):
        a, b, c = map(int, input().split())
        vertical_lines.append((a, b, c))
        x_set |= {a, b}
        y_set |= {c}

    horizontal_lines = []
    for _ in range(M):
        d, e, f = map(int, input().split())
        horizontal_lines.append((d, e, f))
        x_set |= {d}
        y_set |= {e, f}

    x_set = sorted(x_set)
    y_set = sorted(y_set)

    # 座標圧縮 (壁も配列に格納するので、2 倍している)
    x_encoded = {n: i * 2 for i, n in enumerate(x_set)}
    y_encoded = {n: i * 2 for i, n in enumerate(y_set)}
    # 座標圧縮されたグリッドで縦横に 1 マス分進むことは実際にはどれくらい進んだことなのか
    x_length = [x_set[i // 2 + 1] - x_set[i // 2] if i %
                2 else 0 for i in range(len(x_set) * 2 - 1)]
    y_length = [y_set[i // 2 + 1] - y_set[i // 2] if i %
                2 else 0 for i in range(len(y_set) * 2 - 1)]

    grid = [[0] * (len(y_set) * 2 - 1) for _ in range(len(x_set) * 2 - 1)]
    for a, b, c in vertical_lines:
        a, b, c = x_encoded[a], x_encoded[b], y_encoded[c]
        for x in range(a, b + 1):
            grid[x][c] = 1
    for d, e, f in horizontal_lines:
        d, e, f = x_encoded[d], y_encoded[e], y_encoded[f]
        for y in range(e, f + 1):
            grid[d][y] = 1

    que = deque()
    used = [[0] * len(y_set) * 2 for _ in range(len(x_set) * 2)]
    dy = [1, 1, -1, -1]
    dx = [1, -1, 1, -1]
    for k in range(4):
        nnx, nny = x_encoded[0] + dx[k], y_encoded[0] + dy[k]
        if 1 <= nnx < len(x_set) * 2 - 1 and 1 <= nny < len(y_set) * 2 - 1:
            que.append((nnx, nny))
            used[nnx][nny] = 1
    ans = 0
    dy = [1, 0, -1, 0]
    dx = [0, 1, 0, -1]
    while que:
        x, y = que.popleft()
        if x % 2 and y % 2:
            ans += x_length[x] * y_length[y]
        for k in range(4):
            nx, ny = x + dx[k], y + dy[k]
            nnx, nny = nx + dx[k], ny + dy[k]
            if grid[nx][ny] == 0:
                if nnx < 0 or nnx >= len(x_set) * 2 - 1 or nny < 0 or nny >= len(y_set) * 2 - 1:
                    return 'INF'
                if not used[nnx][nny]:
                    que.append((nnx, nny))
                    used[nnx][nny] = 1
    return ans

print(f_single_dot())

Submission status: Accepted

Solution code:
def f_single_dot():
    # https://atcoder.jp/contests/abc168/submissions/13368489
    import sys
    from collections import deque
    input = sys.stdin.readline
    N, M = [int(i) for i in input().split()]

    x_set, y_set = set([0]), set([0])  # 重複を除いた xy 座標の一覧 (座標圧縮に必要)

    vertical_lines = []
    for _ in range(N):
        a, b, c = map(int, input().split())
        vertical_lines.append((a, b, c))
        x_set |= {a, b}
        y_set |= {c}

    horizontal_lines = []
    for _ in range(M):
        d, e, f = map(int, input().split())
        horizontal_lines.append((d, e, f))
        x_set |= {d}
        y_set |= {e, f}

    x_set = sorted(x_set)
    y_set = sorted(y_set)

    # 座標圧縮 (壁も配列に格納するので、2 倍している)
    x_encoded = {n: i * 2 for i, n in enumerate(x_set)}
    y_encoded = {n: i * 2 for i, n in enumerate(y_set)}
    # 座標圧縮されたグリッドで縦横に 1 マス分進むことは実際にはどれくらい進んだことなのか
    x_length = [x_set[i // 2 + 1] - x_set[i // 2] if i %
                2 else 0 for i in range(len(x_set) * 2 - 1)]
    y_length = [y_set[i // 2 + 1] - y_set[i // 2] if i %
                2 else 0 for i in range(len(y_set) * 2 - 1)]

    grid = [[0] * (len(x_set) * 2 - 1) for _ in range(len(y_set) * 2 - 1)]
    for a, b, c in vertical_lines:
        a, b, c = x_encoded[a], x_encoded[b], y_encoded[c]
        for x in range(a, b + 1):
            grid[c][x] = 1
    for d, e, f in horizontal_lines:
        d, e, f = x_encoded[d], y_encoded[e], y_encoded[f]
        for y in range(e, f + 1):
            grid[y][d] = 1

    que = deque()
    used = [[0] * len(x_set) * 2 for _ in range(len(y_set) * 2)]
    dy = [1, 1, -1, -1]
    dx = [1, -1, 1, -1]
    for k in range(4):
        nny, nnx = y_encoded[0] + dy[k], x_encoded[0] + dx[k]
        if 1 <= nny < len(y_set) * 2 - 1 and 1 <= nnx < len(x_set) * 2 - 1:
            que.append((nny, nnx))
            used[nny][nnx] = 1
    ans = 0
    dy = [1, 0, -1, 0]
    dx = [0, 1, 0, -1]
    while que:
        y, x = que.popleft()
        if y % 2 and x % 2:
            ans += y_length[y] * x_length[x]
        for k in range(4):
            ny, nx = y + dy[k], x + dx[k]
            nny, nnx = ny + dy[k], nx + dx[k]
            if grid[ny][nx] == 0:
                if nny < 0 or nny >= len(y_set) * 2 - 1 or nnx < 0 or nnx >= len(x_set) * 2 - 1:
                    return 'INF'
                if not used[nny][nnx]:
                    que.append((nny, nnx))
                    used[nny][nnx] = 1
    return ans

print(f_single_dot())

Submission status: Accepted

Solution code:
def f_single_dot():
    # https://atcoder.jp/contests/abc168/submissions/13368489
    import sys
    from collections import deque
    input = sys.stdin.readline
    N, M = [int(i) for i in input().split()]

    X, Y = set([0]), set([0])
    vertical_lines = []
    for _ in range(N):
        a, b, grid = map(int, input().split())
        vertical_lines.append((a, b, grid))
        X |= {a, b}
        Y |= {grid}
    horizontal_lines = []
    for _ in range(M):
        d, e, f = map(int, input().split())
        horizontal_lines.append((d, e, f))
        X |= {d}
        Y |= {e, f}
    X = sorted(X)
    Y = sorted(Y)
    dictx, dicty = {n: i * 2 for i, n in enumerate(X)}, {n: i * 2 for i, n in enumerate(Y)}
    LX = [X[i // 2 + 1] - X[i // 2] if i % 2 else 0 for i in range(len(X) * 2 - 1)]
    LY = [Y[i // 2 + 1] - Y[i // 2] if i % 2 else 0 for i in range(len(Y) * 2 - 1)]
    grid = [[0] * (len(X) * 2 - 1) for _ in range(len(Y) * 2 - 1)]
    for a, b, c in vertical_lines:
        a, b, c = dictx[a], dictx[b], dicty[c]
        for x in range(a, b + 1):
            grid[c][x] = 1
    for d, e, f in horizontal_lines:
        d, e, f = dictx[d], dicty[e], dicty[f]
        for y in range(e, f + 1):
            grid[y][d] = 1
    que = deque()
    used = [[0] * len(X) * 2 for _ in range(len(Y) * 2)]
    dy = [1, 1, -1, -1]
    dx = [1, -1, 1, -1]
    for k in range(4):
        nny, nnx = dicty[0] + dy[k], dictx[0] + dx[k]
        if 1 <= nny < len(Y) * 2 - 1 and 1 <= nnx < len(X) * 2 - 1:
            que.append((nny, nnx))
            used[nny][nnx] = 1
    ans = 0
    dy = [1, 0, -1, 0]
    dx = [0, 1, 0, -1]
    while que:
        y, x = que.popleft()
        if y % 2 and x % 2:
            ans += LY[y] * LX[x]
        for k in range(4):
            ny, nx = y + dy[k], x + dx[k]
            nny, nnx = ny + dy[k], nx + dx[k]
            if grid[ny][nx] == 0:
                if nny < 0 or nny >= len(Y) * 2 - 1 or nnx < 0 or nnx >= len(X) * 2 - 1:
                    return 'INF'
                if not used[nny][nnx]:
                    que.append((nny, nnx))
                    used[nny][nnx] = 1
    return ans

print(f_single_dot())

Submission status: Accepted

Solution code:
def f_single_dot():
    # https://atcoder.jp/contests/abc168/submissions/13368489
    import sys
    from collections import deque
    input = sys.stdin.readline
    N, M = [int(i) for i in input().split()]

    X, Y = set([0]), set([0])
    A, B, C = [0] * N, [0] * N, [0] * N
    for i in range(N):
        A[i], B[i], C[i] = map(int, input().split())
        X |= {A[i], B[i]}
        Y |= {C[i]}
    D, E, F = [0] * M, [0] * M, [0] * M
    for i in range(M):
        D[i], E[i], F[i] = map(int, input().split())
        X |= {D[i]}
        Y |= {E[i], F[i]}
    X = sorted(X)
    Y = sorted(Y)
    dictx, dicty = {n: i * 2 for i, n in enumerate(X)}, {n: i * 2 for i, n in enumerate(Y)}
    LX = [X[i // 2 + 1] - X[i // 2] if i % 2 else 0 for i in range(len(X) * 2 - 1)]
    LY = [Y[i // 2 + 1] - Y[i // 2] if i % 2 else 0 for i in range(len(Y) * 2 - 1)]
    c = [[0] * (len(X) * 2 - 1) for _ in range(len(Y) * 2 - 1)]
    for i in range(N):
        y = dicty[C[i]]
        for x in range(dictx[A[i]], dictx[B[i]] + 1):
            c[y][x] = 1
    for i in range(M):
        x = dictx[D[i]]
        for y in range(dicty[E[i]], dicty[F[i]] + 1):
            c[y][x] = 1
    que = deque()
    used = [[0] * len(X) * 2 for _ in range(len(Y) * 2)]
    dy = [1, 1, -1, -1]
    dx = [1, -1, 1, -1]
    for k in range(4):
        nny, nnx = dicty[0] + dy[k], dictx[0] + dx[k]
        if 1 <= nny < len(Y) * 2 - 1 and 1 <= nnx < len(X) * 2 - 1:
            que.append((nny, nnx))
            used[nny][nnx] = 1
    ans = 0
    dy = [1, 0, -1, 0]
    dx = [0, 1, 0, -1]
    while que:
        y, x = que.popleft()
        if y % 2 and x % 2:
            ans += LY[y] * LX[x]
        for k in range(4):
            ny, nx = y + dy[k], x + dx[k]
            nny, nnx = ny + dy[k], nx + dx[k]
            if c[ny][nx] == 0:
                if nny < 0 or nny >= len(Y) * 2 - 1 or nnx < 0 or nnx >= len(X) * 2 - 1:
                    return 'INF'
                if not used[nny][nnx]:
                    que.append((nny, nnx))
                    used[nny][nnx] = 1
    return ans

print(f_single_dot())

Submission status: Accepted

Solution code:
def f_single_dot():
    # https://atcoder.jp/contests/abc168/submissions/13368489
    import sys
    from collections import deque
    input = sys.stdin.readline
    N, M = [int(i) for i in input().split()]

    X, Y = set([0]), set([0])
    A, B, C = [0] * N, [0] * N, [0] * N
    for i in range(N):
        A[i], B[i], C[i] = map(int, input().split())
        X.add(A[i])
        X.add(B[i])
        Y.add(C[i])
    D, E, F = [0] * M, [0] * M, [0] * M
    for i in range(M):
        D[i], E[i], F[i] = map(int, input().split())
        X.add(D[i])
        Y.add(E[i])
        Y.add(F[i])
    UX = list(X)
    UY = list(Y)
    UX.sort()
    UY.sort()
    dictx, dicty = {n: i * 2 for i, n in enumerate(UX)}, {n: i * 2 for i, n in enumerate(UY)}
    LX = [UX[i // 2 + 1] - UX[i // 2] if i % 2 else 0 for i in range(len(UX) * 2 - 1)]
    LY = [UY[i // 2 + 1] - UY[i // 2] if i % 2 else 0 for i in range(len(UY) * 2 - 1)]
    c = [[0] * (len(UX) * 2 - 1) for _ in range(len(UY) * 2 - 1)]
    for i in range(N):
        y = dicty[C[i]]
        for x in range(dictx[A[i]], dictx[B[i]] + 1):
            c[y][x] = 1
    for i in range(M):
        x = dictx[D[i]]
        for y in range(dicty[E[i]], dicty[F[i]] + 1):
            c[y][x] = 1
    que = deque()
    used = [[0] * len(UX) * 2 for _ in range(len(UY) * 2)]
    dy = [1, 1, -1, -1]
    dx = [1, -1, 1, -1]
    for k in range(4):
        nny, nnx = dicty[0] + dy[k], dictx[0] + dx[k]
        if 1 <= nny < len(UY) * 2 - 1 and 1 <= nnx < len(UX) * 2 - 1:
            que.append((nny, nnx))
            used[nny][nnx] = 1
    ans = 0
    dy = [1, 0, -1, 0]
    dx = [0, 1, 0, -1]
    while que:
        y, x = que.popleft()
        if y % 2 and x % 2:
            ans += LY[y] * LX[x]
        for k in range(4):
            ny, nx = y + dy[k], x + dx[k]
            nny, nnx = ny + dy[k], nx + dx[k]
            if c[ny][nx] == 0:
                if nny < 0 or nny >= len(UY) * 2 - 1 or nnx < 0 or nnx >= len(UX) * 2 - 1:
                    return 'INF'
                if not used[nny][nnx]:
                    que.append((nny, nnx))
                    used[nny][nnx] = 1
    return ans

print(f_single_dot())