Problem:


Score : 500 points

Problem Statement

We have a two-dimensional grid with H \times W squares. There are M targets to destroy in this grid - the position of the i-th target is \left(h_i, w_i \right).

Takahashi will choose one square in this grid, place a bomb there, and ignite it. The bomb will destroy all targets that are in the row or the column where the bomb is placed. It is possible to place the bomb at a square with a target.

Takahashi is trying to maximize the number of targets to destroy. Find the maximum number of targets that can be destroyed.

Constraints

All values in input are integers.

1 \leq H, W \leq 3 \times 10^5

1 \leq M \leq \min\left(H\times W, 3 \times 10^5\right)

1 \leq h_i \leq H

1 \leq w_i \leq W

\left(h_i, w_i\right) \neq \left(h_j, w_j\right) \left(i \neq j\right)

Input

Input is given from Standard Input in the following format:

H W M
h_1 w_1
\vdots
h_M w_M

Output

Print the answer.

Sample Input 1

2 3 3
2 2
1 1
1 3

Sample Output 1

3

We can destroy all the targets by placing the bomb at \left(1, 2\right).

Sample Input 2

3 3 4
3 3
3 1
1 1
1 2

Sample Output 2

3

Sample Input 3

5 5 10
2 5
4 3
2 3
5 5
2 2
5 4
5 3
5 1
3 5
1 4

Sample Output 3

6



Sample input:
2 3 3
2 2
1 1
1 3


Sample output:
3

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
from collections import Counter, defaultdict


def read():
    H, W, M = map(int, input().strip().split())
    HW = []
    for i in range(M):
        h, w = map(int, input().strip().split())
        HW.append((h, w))
    return H, W, M, HW


def solve(H, W, M, HW):
    hcount = Counter()
    wcount = Counter()
    for h, w in HW:
        hcount[h] += 1
        wcount[w] += 1
    hm = hcount.most_common()
    wm = wcount.most_common()
    hmax = hm[0][1]
    wmax = wm[0][1]
    hn = len([1 for k, v in hcount.items() if v == hmax])
    wn = len([1 for k, v in wcount.items() if v == wmax])
    m = hn * wn
    for h, w in HW:
        if hcount[h] == hmax and wcount[w] == wmax:
            m -= 1
    if m == 0:
        return hmax + wmax - 1
    return hmax + wmax


if __name__ == '__main__':
    inputs = read()
    outputs = solve(*inputs)
    if outputs is not None:
        print("%s" % str(outputs))

Submission status: Accepted

Solution code:
h,w,m=map(int,input().split())

st=set()
h_b=[0 for i in range(h)]
w_b=[0 for i in range(w)]
for i in range(m):
  th,tw=map(int,input().split())
  th-=1
  tw-=1
  st.add((th,tw))
  h_b[th]+=1
  w_b[tw]+=1

h_max=max(h_b)
w_max=max(w_b)

h_cand=[i for i in range(h) if h_b[i]==h_max]
w_cand=[i for i in range(w) if w_b[i]==w_max]

for i in h_cand:
  for j in w_cand:
    if (i,j) not in st:
      print(h_max+w_max)
      exit()

print(h_max+w_max-1)

Submission status: Accepted

Solution code:
H, W, M = map(int, input().split())
h_list = [0] * H
w_list = [0] * W
target = []
for _ in range(M):
  h, w = map(int, input().split())
  h_list[h-1] += 1
  w_list[w-1] += 1
  target += [[h-1,w-1]]

h_max = max(h_list)
w_max = max(w_list)
h_max_list = set([i for i, v in enumerate(h_list) if v == h_max])
w_max_list = set([i for i, v in enumerate(w_list) if v == w_max])

place = len(h_max_list) * len(w_max_list)
candidate = 0
for h,w in target:
  if (h in h_max_list) and (w in w_max_list):
    candidate +=1

print(h_max+w_max-(place == candidate))

Submission status: Accepted

Solution code:
H,W,M = map(int, input().split())

hs = [0] * H
ws = [0] * W
s = set()

for i in range(M):
  h,w = map(int, input().split())
  h -= 1
  w -= 1
  hs[h] += 1
  ws[w] += 1
  s.add((h,w))

mh = 0
mw = 0
for i in range(H):
  mh = max(mh,hs[i])
for j in range(W):
  mw = max(mw,ws[j])
i_s = list()
j_s = list()
for i in range(H):
  if mh == hs[i]:
    i_s.append(i)
for j in range(W):
  if mw == ws[j]:
    j_s.append(j)
ans = mh + mw
for i in i_s:
  for j in j_s:
    if (i,j) in s:
      continue
    print(ans)
    exit()
ans -= 1
print(ans)

Submission status: Accepted

Solution code:
H,W,M = map(int,input().split())
hs = [0] * H
ws = [0] * W
s = set()

for i in range(M):
  r,c = map(int,input().split())
  r -= 1
  c -= 1
  hs[r] += 1
  ws[c] += 1
  s.add((r,c))
mh = 0
mw = 0
for i in range(H):
  mh = max(mh, hs[i])
for j in range(W):
  mw = max(mw, ws[j])

i_s = list()
j_s = list()
for i in range(H):
  if mh == hs[i]:
    i_s.append(i)
for j in range(W):
  if mw == ws[j]:
    j_s.append(j)
ans = mh + mw
for i in i_s:
  for j in j_s:
    if (i,j) in s:
      continue
    print(ans)
    exit()
ans -= 1
print(ans)

Submission status: Accepted

Solution code:

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

grid=[]

row=[0]*n
col=[0]*m

for _ in range(t):
    x,y=map(int,input().split())
    grid.append((x-1,y-1))
    row[x-1]+=1
    col[y-1]+=1

prow=[]
pcol=[]
qr=max(row)
for i in range(n):
    if row[i]==qr :
        prow.append(i)

qc=max(col)
for i in range(m):
    if col[i]==qc :
        pcol.append(i)

num=len(prow)*len(pcol)
ans=qr+qc
for i in grid:
    if row[i[0]]==qr and col[i[1]]==qc :
        num-=1
if num>0:
    print(ans)
else:
    print(ans-1)

Submission status: Accepted

Solution code:
import sys
from collections import deque
H, W, M = map(int, input().split())
S = list(tuple(map(int, input().split())) for _ in range(M))
hh = dict()
ww = dict()
for i in range(M):
    h, w = S[i]
    if h in hh.keys():
        hh[h] += 1
    else:
        hh[h] = 1
    if w in ww.keys():
        ww[w] += 1
    else:
        ww[w] = 1
hhh = sorted(hh.items(), key=lambda x:x[1], reverse=True)
www = sorted(ww.items(), key=lambda x:x[1], reverse=True)
h = hhh[0][1]
w = www[0][1]
ans = h+w
Nh = 0
Nw = 0
for i in range(len(hhh)):
    if h == hhh[i][1]:
        Nh += 1
    else:
        break
for i in range(len(www)):
    if w == www[i][1]:
        Nw += 1
    else:
        break
tt = Nh*Nw
if tt > M:
    print(ans)
    sys.exit()

for tmp in S:
    if hh[tmp[0]] == h and ww[tmp[1]] == w:
        tt -= 1
if tt > 0:
    print(ans)
else:
    print(ans-1)

Submission status: Accepted

Solution code:
def main():
    H, W, M = map(int, input().split())
    hw = [tuple(list(map(int, input().split()))) for _ in [0]*M]
    hw_set = set(hw)
    h_count = [0 for i in range(H+1)]
    w_count = [0 for i in range(W+1)]
    for h, w in hw:
        h_count[h] += 1
        w_count[w] += 1
    h_m = max(h_count)
    w_m = max(w_count)
    h_list = []
    w_list = []
    for i in range(H+1):
        if h_count[i] == h_m:
            h_list.append(i)
    for i in range(W+1):
        if w_count[i] == w_m:
            w_list.append(i)
    #print(h_list, w_list)
    for i in h_list:
        for j in w_list:
            if (i, j) not in hw_set:
                print(h_m+w_m)
                return
    print(h_m+w_m-1)


main()

Submission status: Accepted

Solution code:
H, W, M = map(int, input().split())
row=[0]*H #x座標を入れるっちゅうかカウント
col=[0]*W #y座標を入れる
 
mat=[] #座標を入れる
 
for i in range(M):
    h, w = map(int, input().split())
    row[h-1]+=1
    col[w-1]+=1
    mat.append((h-1,w-1))
r=max(row)
c=max(col)
 
rr=[1 if row[i]==r else 0 for i in range(H)] #maxな列のインデックス
cc=[1 if col[i]==c else 0 for i in range(W)] #maxな行のインデックス
 
x=0 #maxな列と行の交差点にある爆弾の個数をカウント
for k in mat:
    if rr[k[0]]==1 and cc[k[1]]==1:
        x+=1
        
if sum(rr)*sum(cc)==x: #行と列の全ての交差点に爆弾があれば-1する
    print(r+c-1)
else:
    print(r+c)

Submission status: Accepted

Solution code:
h,w,m=map(int,input().split())

H,W=[0]*h,[0]*w
P=set()

for i in range(m):
  y,x=map(int,input().split())
  H[~-y]+=1
  W[~-x]+=1
  P.add(~-y*w+~-x)

mh,mw=max(H),max(W)
MH=[i for i,h in enumerate(H) if h==mh]
MW=[i for i,v in enumerate(W) if v==mw]
for y in MH:
  for x in MW:
    if y*w+x not in P:
      print(mh+mw)
      exit()

print(mh+mw-1)

Submission status: Accepted

Solution code:
# E - Bomber

from collections import Counter

h, w, m = map(int, input().split())
hw = [tuple(map(int, input().split())) for i in range(m)]

ys, xs = zip(*hw)
ymax, = Counter(ys).most_common(1)
xmax, = Counter(xs).most_common(1)

bombed = max(ymax[1], xmax[1])

if bombed < m:
    if ymax[1] > xmax[1]:
        xs = [b for a, b in hw if a != ymax[0]]
        xmax, = Counter(xs).most_common(1)
        bombed += xmax[1]
    else:
        ys = [a for a, b in hw if b != xmax[0]]
        ymax, = Counter(ys).most_common(1)
        bombed += ymax[1]

print(bombed)

Submission status: Accepted

Solution code:
H, W, M = map(int, input().split())
row=[0]*H
col=[0]*W

mat=[]

for i in range(M):
  h, w = map(int, input().split())
  row[h-1]+=1
  col[w-1]+=1
  mat.append((h-1,w-1))
  
r=max(row)
c=max(col)

rr=[1 if row[i]==r else 0 for i in range(H)]
cc=[1 if col[i]==c else 0 for i in range(W)]

x=0
for k in mat:
  if rr[k[0]]==1 and cc[k[1]]==1:
    x+=1

if sum(rr)*sum(cc)==x:
  print(r+c-1)
else:
  print(r+c)

Submission status: Accepted

Solution code:
# E - Bomber

from collections import Counter

h, w, m = map(int, input().split())
hw = [tuple(map(int, input().split())) for i in range(m)]

ys, xs = zip(*hw)
ymax, = Counter(ys).most_common(1)
xmax, = Counter(xs).most_common(1)

bombed = max(ymax[1], xmax[1])

if bombed < m:
    if ymax[1] > xmax[1]:
        hw2 = [(a, b) for a, b in hw if a != ymax[0]]
        _, xs = zip(*hw2)
        xmax, = Counter(xs).most_common(1)
        bombed += xmax[1]
    else:
        hw2 = [(a, b) for a, b in hw if b != xmax[0]]
        ys, _ = zip(*hw2)
        ymax, = Counter(ys).most_common(1)
        bombed += ymax[1]

print(bombed)

Submission status: Accepted

Solution code:
import numpy as np
import numba
import sys
from numba import njit, b1, i4, i8, f8

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines


@njit((i8, i8, i8[:]), cache=True)
def main(Height, Width, XY):
    UP = 300010
    row = np.zeros(UP, np.int64)
    col = np.zeros(UP, np.int64)
    
    for i in range(0, len(XY), 2):
        x, y = XY[i:i + 2] - 1
        row[x] += 1
        col[y] += 1
    
    row_max = row.max()
    col_max = col.max()

    judge = np.sum(row == row_max) * np.sum(col == col_max)

    for i in range(0, len(XY), 2):
        x, y = XY[i:i + 2] - 1
        
        if (row[x] == row_max and col[y] == col_max):
            judge -= 1
    
    summ = row_max + col_max
    
    return (summ if judge else summ - 1)


Height, Width, M_ko = map(int, readline().split())
XY = np.array(read().split(), np.int64)

ans = main(Height, Width, XY)
print(ans)

Submission status: Accepted

Solution code:
h, w, m = map(int, input().split())
r = [0] * (h+1)
c = [0] * (w+1)
bomb = []
for _ in range(m):
    hi, wi = map(int, input().split())
    r[hi] += 1
    c[wi] += 1
    bomb.append([hi, wi])

hmax = max(r)
wmax = max(c)

cnt = 0
ret = 1
for i in range(1, h+1):
    if r[i] == hmax:
        cnt += 1
ret *= cnt

cnt = 0
for i in range(1, w+1):
    if c[i] == wmax:
        cnt += 1

ret *= cnt

for i in range(m):
    hi, wi = bomb[i]
    if r[hi] == hmax and c[wi] == wmax:
        ret -= 1

if ret == 0:
    print(hmax + wmax - 1)
else:
    print(hmax + wmax)

Submission status: Accepted

Solution code:
#!usr/bin/env python3
from collections import defaultdict, deque, Counter, OrderedDict
from bisect import bisect_left, bisect_right
from functools import reduce, lru_cache
from heapq import heappush, heappop, heapify

import itertools
import math, fractions
import sys, copy

def L(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline().rstrip())
def SL(): return list(sys.stdin.readline().rstrip())
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI1(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LS(): return [list(x) for x in sys.stdin.readline().split()]
def R(n): return [sys.stdin.readline().strip() for _ in range(n)]
def LR(n): return [L() for _ in range(n)]
def IR(n): return [I() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def LIR1(n): return [LI1() for _ in range(n)]
def SR(n): return [SL() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]

def perm(n, r): return math.factorial(n) // math.factorial(r)
def comb(n, r): return math.factorial(n) // (math.factorial(r) * math.factorial(n-r))

def make_list(n, *args, default=0): return [make_list(*args, default=default) for _ in range(n)] if len(args) > 0 else [default for _ in range(n)]

dire = [[1, 0], [0, 1], [-1, 0], [0, -1]]
dire8 = [[1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]]
alphabets = "abcdefghijklmnopqrstuvwxyz"
ALPHABETS = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
MOD = 1000000007
INF = float("inf")

sys.setrecursionlimit(1000000)

def main():
    H, W, M = LI()
    hw = LIR(M)

    s = set(h + w * (10 ** 6) for h, w in hw)

    ch = Counter(i for i, _ in hw)
    cw = Counter(j for _, j in hw)
    _, maxcy = ch.most_common(1)[0]
    _, maxcx = cw.most_common(1)[0]

    ans = maxcy + maxcx - 1

    lh = [k for k, v in ch.items() if v == maxcy]
    lw = [k for k, v in cw.items() if v == maxcx]

    for h in lh:
        for w in lw:
            if not h + w * (10 ** 6) in s:
                print(ans + 1)
                return
    print(ans)




if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys

read = sys.stdin.read
readline = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 8)
INF = float('inf')
MOD = 10 ** 9 + 7


def main():
    H, W, M = map(int, readline().split())
    row = [0] * H
    column = [0] * W
    grid = set()

    for _ in range(M):
        h, w = map(int, readline().split())
        row[h-1] += 1
        column[w-1] += 1
        grid.add((h-1,w-1))

    max_row = max(row)
    max_column = max(column)

    idx_row = [i for i,x in enumerate(row) if x == max_row]
    idx_column = [i for i,x in enumerate(column) if x == max_column]

    ans = max_row+max_column
    flag = False

    for h in idx_row:
        for w in idx_column:
            if not (h,w) in grid:
                flag = True
                break

    if flag:
        print(ans)
    else:
        print(ans-1)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
from itertools import chain
from bisect import bisect_left, bisect_right

H, W, M = map(int, input().split())
YX = [list(map(int, input().split())) for _ in range(M)]
# H, W, M = 3*10**5, 3*10**5, 3*10**5
# YX = [[(i*100)//W, (i*100)%W] for i in range(M)]

X_sets = [[] for _ in range(W+1)]
Y_sets = [[] for _ in range(H+1)]
for y, x in YX:
    X_sets[x].append(y)
    Y_sets[y].append(x)

[s.sort() for s in X_sets]
[s.sort() for s in Y_sets]

# print(X_sets, Y_sets)

X_set_max_len = max(map(len, X_sets))
Y_set_max_len = max(map(len, Y_sets))

# print("ppp", X_set_max_len, Y_set_max_len)

# for s in X_sets:
#     print(s)

X_list = set(i for i, s in enumerate(X_sets) if len(s) == X_set_max_len)
Y_list = set(i for i, s in enumerate(Y_sets) if len(s) == Y_set_max_len)

score = X_set_max_len + Y_set_max_len - 1
# print("b", score, X_list, Y_list)
for x in X_list:
    for y in Y_list:
        c = bisect_right(X_sets[x], y) - bisect_left(X_sets[x], y)
        # print(x, y, c)
        if c == 0:
            score += 1
            print(score)
            exit()

print(score)

Submission status: Accepted

Solution code:
H,W,M = map(int, input().split())
width = [0]*W
height = [0]*H

st = set()
for i in range(M):
  y, x = map(int, input().split())
  st.add((x - 1,y - 1))
  width[x-1] += 1
  height[y-1] += 1

maxW = max(width)
maxH = max(height)

indexW = [i for i, v in enumerate(width) if v == maxW]
indexH = [i for i, v in enumerate(height) if v == maxH]

ans = maxW + maxH 

#それぞれ列と行の最大値の中から適当に１つずつ列と行を選ぶ
tmpX = indexW[0]
tmpY = indexH[0]

#HeightとWidthのそれぞれの最大値の点(x, y)に爆弾がない場合があるかどうか
flag = 0

#print(f"indexH {indexH}")
#print(f"indexW {indexW}")

#Heightの最大値と、widthのそれぞれを全探索
for x in indexW:
  y = tmpY
  if not (x, y) in st:
    flag = 1
    break


for y in indexH:
  x = tmpX
  if not (x, y) in st:
    flag = 1
    break

if flag == 1:
  print(ans)
else:
  print(ans - 1)

Submission status: Accepted

Solution code:
h,w,m = map(int,input().split())
row = [0]*(h+1)
col = [0]*(w+1)
bombs = set([])
for i in range(m):
  a,b = map(int,input().split())
  row[a] += 1
  col[b] += 1
  bombs.add((a,b))
r,c = max(row),max(col)
rcnt,ccnt = 0,0
for v in row:
  if v==r:
    rcnt += 1
for v in col:
  if v==c:
    ccnt += 1
doubled = 0
for i,j in bombs:
  if row[i]==r and col[j]==c:
    doubled += 1
if doubled==rcnt*ccnt:
  print(r+c-1)
else:
  print(r+c)

Submission status: Accepted

Solution code:
H, W, M = map(int, input().split())
bombs = {}
rows = []
cols = []
for i in range(H):
    rows.append([i, 0])
for i in range(W):
    cols.append([i, 0])
for i in range(M):
    y, x = map(lambda x: x - 1, map(int, input().split()))
    bombs[(y,x)] = True
    rows[y][1] += 1
    cols[x][1] += 1


rows = sorted(rows, key=lambda x: x[1], reverse=True)
cols = sorted(cols, key=lambda x: x[1], reverse=True)
answer = 0
for row in rows:
    a = cols[0][1] + row[1] - (1 if (row[0], cols[0][0]) in bombs else 0)
    if a > answer:
        answer = a
for col in cols:
    a = rows[0][1] + col[1] - (1 if (rows[0][0], col[0]) in bombs else 0)
    if a > answer:
        answer = a
print(answer)

Submission status: Accepted

Solution code:
H, W, M = map(int,input().split())
Bomb = []
for _ in range(M):
    hi, wi = map(lambda x: int(x) - 1, input().split())
    Bomb.append((hi, wi))

counterH = [0] * H
counterW = [0] * W

for (hi, wi) in Bomb:
    counterH[hi] += 1
    counterW[wi] += 1

# 最大のところを選ぶ
max_h = max(counterH)
max_w = max(counterW)

count = 0
for (hi, wi) in Bomb:
    if counterH[hi] == max_h and counterW[wi] == max_w:
        count += 1

# 共通部分を確認 (-1)
ans = max_h + max_w
if count == counterH.count(max_h) * counterW.count(max_w):
    ans -= 1
print(ans)

Submission status: Accepted

Solution code:
h, w, m = map(int, input().split())
b = []
for i in range(m):
    hh, ww = map(int,input().split())
    hh -= 1
    ww -= 1
    b.append([hh, ww])
    
cnth = [0] * h
cntw = [0] * w
          
for i in range(m):
    hh, ww = b[i][0], b[i][1]
    cnth[hh] += 1
    cntw[ww] += 1
    
mh = max(cnth)
mw = max(cntw)

cnt_mh = 0
for i in range(h):
    if cnth[i] == mh:
        cnt_mh += 1
cnt_mw = 0
for i in range(w):
    if cntw[i] == mw:
        cnt_mw += 1

cnt_m = 0
for i in range(m):
    hh, ww = b[i][0], b[i][1]
    if cnth[hh] == mh and cntw[ww] == mw:
        cnt_m += 1
print(mh+mw) if cnt_mh*cnt_mw > cnt_m else print(mh+mw-1)

Submission status: Accepted

Solution code:
H, W, M = map(int, input().split())

Hc = [0 for i in range(H)]
Wc = [0 for i in range(W)]
B = []

for m in range(M):
  h, w = map(int, input().split())
  Hc[h - 1] += 1
  Wc[w - 1] += 1
  B.append((h - 1, w - 1))
Hcmax = max(Hc)
Hcmax_idx = [i for i, x in enumerate(Hc) if x == Hcmax] 
Wcmax = max(Wc)
Wcmax_idx = [i for i, x in enumerate(Wc) if x == Wcmax] 

ans = Hcmax + Wcmax - 1
B = set(B)
f = False
for i in Hcmax_idx:
  if f:
    break
  for j in Wcmax_idx:
    if (i, j) not in B:
      ans = Hcmax + Wcmax
      f = True
      break
print(ans)

Submission status: Accepted

Solution code:
from collections import defaultdict
h, w, m = map(int, input().split())
target = []
point = defaultdict(int)
count_target_of_y = defaultdict(int)
count_target_of_x = defaultdict(int)
for i in range(m):
    x, y = map(int, input().split())
    count_target_of_y[y] += 1
    count_target_of_x[x] += 1
    point[(x,y)] += 1
max_x_count = max(list(count_target_of_x.items()), key=lambda x:x[1])[1]
max_y_count = max(list(count_target_of_y.items()), key=lambda x:x[1])[1]
max_x_count_list = [i for i in count_target_of_x.items() if i[1] == max_x_count]
max_y_count_list = [i for i in count_target_of_y.items() if i[1] == max_y_count]
for x in max_x_count_list:
    for y in max_y_count_list:
        if point[(x[0], y[0])] == 0:
            print(max_x_count + max_y_count)
            exit()
print(max_x_count + max_y_count - 1)

Submission status: Accepted

Solution code:
def solve():
    H, W, M = map(int, input().split())
    N = 3 * 10 ** 5
    cnth = [0] * N
    cntw = [0] * N
    st = set()
    for i in range(M):
        h, w = map(lambda x: int(x) - 1, input().split())
        cnth[h] += 1
        cntw[w] += 1
        st.add((h, w))
    mh = max(cnth)
    mw = max(cntw)
    Y = []
    X = []
    for i in range(H):
        if cnth[i] == mh:
            Y.append(i)
    for i in range(W):
        if cntw[i] == mw:
            X.append(i)
    for y in Y:
        for x in X:
            if not (y, x) in st:
                return mh + mw
    return mh + mw - 1

print(solve())

Submission status: Accepted

Solution code:
def solve():
    H, W, M = map(int, input().split())
    N = 3 * 10 ** 5
    cnth = [0] * N
    cntw = [0] * N
    dic = dict()
    for i in range(M):
        h, w = map(lambda x: int(x) - 1, input().split())
        cnth[h] += 1
        cntw[w] += 1
        dic[(h, w)] = 1
    mh = max(cnth)
    mw = max(cntw)
    Y = []
    X = []
    for i in range(H):
        if cnth[i] == mh:
            Y.append(i)
    for i in range(W):
        if cntw[i] == mw:
            X.append(i)
    for y in Y:
        for x in X:
            if not (y, x) in dic:
                return mh + mw
    return mh + mw - 1

print(solve())

Submission status: Accepted

Solution code:

H, W, M = list(map(int, input().split()))

h = [0] * H
w = [0] * W

hw = {}

for _ in range(M):
    a, b = list(map(int, input().split()))
    h[a - 1] += 1
    w[b - 1] += 1
    temp = "x" + str(a - 1) + "y" + str(b - 1)
    hw[temp] = 1

hm = max(h)
wm = max(w)

hp = [i for i, v in enumerate(h) if v == hm]
wp = [i for i, v in enumerate(w) if v == wm]

for x in hp:
    for y in wp:
        temp = "x" + str(x) + "y" + str(y)
        if temp not in hw:
            print(hm + wm)
            exit()
else:
    print(hm + wm - 1)

Submission status: Accepted

Solution code:
h, w, m = map(int, input().split())
bord_x, bord_y = [0]*h, [0]*w
 
hw = []
for _i in range(m):
    s, t = map(int, input().split())
    s -= 1
    t -= 1
    bord_x[s] += 1
    bord_y[t] += 1
    hw.append([s, t])
 
x_max, y_max = max(bord_x), max(bord_y)
 
cnt = 0
for i, j in hw:
    if bord_x[i] == x_max and bord_y[j] == y_max:
        cnt += 1
 
if cnt == bord_x.count(x_max)*bord_y.count(y_max):
    x_max -= 1
 
print(x_max+y_max)

Submission status: Accepted

Solution code:
def main():
    h, w, m, *BOM = map(int, open(0).read().split())
    row = [0] * h
    col = [0] * w
    for i, j in zip(BOM[::2], BOM[1::2]):
        i -= 1
        j -= 1
        row[i] += 1
        col[j] += 1

    p, q = max(row), max(col)
    rr = sum(1 for i in range(h) if row[i] == p)
    rl = sum(1 for i in range(w) if col[i] == q)

    cnd = rr * rl

    for i, j in zip(BOM[::2], BOM[1::2]):
        i -= 1
        j -= 1
        if (row[i], col[j]) == (p, q):
            cnd -= 1

    if cnd > 0:
        ans = p + q
    else:
        ans = p + q - 1

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
H, W, M = map(int,input().split())
P = [list(map(int, input().split())) for i in range(M)]
for p in P:
    p[0] -= 1
    p[1] -= 1
cnth = [0]*H
cntw = [0]*W
ans = 0
for p in P:
    cnth[p[0]] += 1
for p in P:
    cntw[p[1]] += 1
mxh = max(cnth)
mxw = max(cntw)
cntx = 0
for p in P:
    if cnth[p[0]] == mxh and cntw[p[1]] == mxw:
        cntx += 1
if cntx == cnth.count(mxh) * cntw.count(mxw):
    ans = mxh + mxw -1
else:
    ans = mxh + mxw
print(ans)

Submission status: Accepted

Solution code:

h, w, m = map(int, input().split())

h_b_list = [0 for i in range(h)]
w_b_list = [0 for i in range(w)]

targets = set()
for i in range(m):
  bh, bw = map(int, input().split())
  targets.add((bh, bw))
  h_b_list[bh-1] += 1
  w_b_list[bw-1] += 1
  
h_max = max(h_b_list)
w_max = max(w_b_list)

h_cans = []
w_cans = []
for i in range(h):
  if h_b_list[i] == h_max:
    h_cans.append(i)
    
for i in range(w):
  if w_b_list[i] == w_max:
    w_cans.append(i)

for hi in h_cans:
  for wi in w_cans:
    if (hi+1, wi+1) not in targets:
      print(h_max+w_max)
      exit()
else:
  print(h_max+w_max-1)

Submission status: Accepted

Solution code:
def main():
    H,W,M = map(int,input().split())
    row = [0 for i in range(H)]
    col = [0 for i in range(W)]
    target  = set()

    for _ in range(M):
        h,w = map(lambda x: int(x)-1,input().split())
        row[h] += 1
        col[w] += 1
        target.add((h,w))
    max_r = max(row)
    max_w = max(col)

    candidate_r = []
    for i,r in enumerate(row):
        if r == max_r:
            candidate_r.append(i)
    candidate_c = []
    for i,c in enumerate(col):
        if c == max_w:
            candidate_c.append(i)

    for idx_r in candidate_r:
        for idx_c in candidate_c:
            if (idx_r,idx_c) not in target:
                print(max_r+max_w)
                return
    print(max_r+max_w-1)
    return

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
H,W,M=map(int,input().split())
l = [ list(map(int,input().split(" "))) for i in range(M)]
h=[0]*H
w=[0]*W
for i in range(M):
    h[l[i][0]-1]+=1
    w[l[i][1]-1]+=1
maxh=max(h)
maxw=max(w)
hlist=[]
wlist=[]
for i in range(H):
    if h[i]==maxh:
        hlist.append(i)
for i in range(W):
    if w[i]==maxw:
        wlist.append(i)
c=0
for i in range(M):
  if h[l[i][0]-1]==maxh and w[l[i][1]-1]==maxw:
    c+=1
if len(hlist)*len(wlist)==c:
  print(maxh+maxw-1)
else:
  print(maxh+maxw)

Submission status: Accepted

Solution code:
H,W,M=map(int,input().split())
row=[0]*H
col=[0]*W
target=set()
for i in range(M):
    h,w=map(int,input().split())
    row[h-1]+=1
    col[w-1]+=1
    target.add((h-1,w-1))
A=max(row)
B=max(col)
a=[x for x in range(H) if row[x]==A]
b=[x for x in range(W) if col[x]==B]
for i in a:
    for j in b:
        if (i,j) not in target:
            print(A+B)
            exit(0)
print(A+B-1)

Submission status: Accepted

Solution code:
H,W,M=map(int,input().split())
row=[0]*H
col=[0]*W
target=set()
for i in range(M):
    h,w=map(int,input().split())
    row[h-1]+=1
    col[w-1]+=1
    target.add((h-1,w-1))
A=max(row)
B=max(col)
a=[x for x in range(H) if row[x]==A]
b=[x for x in range(W) if col[x]==B]
cnt=0
for i in a:
    for j in b:
        cnt+=1
        if (i,j) not in target:
            print(A+B)
            exit(0)
        if cnt>M:
            print(A+B-1)
            exit(0)
print(A+B-1)

Submission status: Accepted

Solution code:
#!/usr/bin/env python3

from pprint import pprint
import sys

sys.setrecursionlimit(10 ** 6)


H, W, M = map(int, input().split())

num_bombs_each_row = [0] * H
num_bombs_each_col = [0] * W
bombs = set()

for _ in range(M):
    h, w = map(int, input().split())
    # 0-index
    h -= 1
    w -= 1

    bombs.add((h, w))
    num_bombs_each_row[h] += 1
    num_bombs_each_col[w] += 1

max_bombs_in_row = max(num_bombs_each_row)
max_bombs_in_col = max(num_bombs_each_col)

rows_with_max_bombs = []
for row in range(H):
    if num_bombs_each_row[row] == max_bombs_in_row:
        rows_with_max_bombs.append(row)

cols_with_max_bombs = []
for col in range(W):
    if num_bombs_each_col[col] == max_bombs_in_col:
        cols_with_max_bombs.append(col)

found = False
for row in rows_with_max_bombs:
    for col in cols_with_max_bombs:
        if (row, col) not in bombs:
            found = True
            break

ans = max_bombs_in_row + max_bombs_in_col
if found:
    print(ans)
else:
    print(ans - 1)

Submission status: Accepted

Solution code:
#!/usr/bin/env python3

from pprint import pprint
import sys

sys.setrecursionlimit(10 ** 6)


H, W, M = map(int, input().split())

num_bombs_each_row = [0] * H
num_bombs_each_col = [0] * W
bombs = set()

for _ in range(M):
    h, w = map(int, input().split())
    # 0-index
    h -= 1
    w -= 1

    bombs.add((h, w))
    num_bombs_each_row[h] += 1
    num_bombs_each_col[w] += 1

max_bombs_in_row = max(num_bombs_each_row)
max_bombs_in_col = max(num_bombs_each_col)

rows_with_max_bombs = []
for row in range(H):
    if num_bombs_each_row[row] == max_bombs_in_row:
        rows_with_max_bombs.append(row)

cols_with_max_bombs = []
for col in range(W):
    if num_bombs_each_col[col] == max_bombs_in_col:
        cols_with_max_bombs.append(col)

found = False
for row in rows_with_max_bombs:
    for col in cols_with_max_bombs:
        if not (row, col) in bombs:
            found = True
            break

ans = max_bombs_in_row + max_bombs_in_col
if found:
    print(ans)
else:
    print(ans - 1)

Submission status: Accepted

Solution code:
H, W, M = map(int, input().split())

countW = [0]*(W+1)
countH = [0]*(H+1)
bomb = []
for i in range(M):
    h, w = map(int, input().split())
    bomb.append((h, w))
    countH[h] += 1
    countW[w] += 1

maxW = max(countW)
maxH = max(countH)
ans = maxW + maxH - 1
countMaxW = countW.count(maxW)
countMaxH = countH.count(maxH)

sumz = 0
for i in range(M):
    h, w = bomb[i]
    if countH[h] == maxH and countW[w] == maxW:
        sumz += 1

if countMaxW*countMaxH > sumz:
    ans += 1
print(ans)

Submission status: Accepted

Solution code:
H,W,M = map(int, input().split())
# grid = [[0 for _ in range(W)] for _ in range(H)]
bombs = set()

hc = [0 for h in range(H)]
wc = [0 for w in range(W)]

for _ in range(M):
    h,w = map(int, input().split())
    h-=1
    w-=1
    bombs.add((h, w))
    hc[h] += 1
    wc[w] += 1

hmax = max(hc)
wmax = max(wc)

htable = []
for h in range(H):
    if hc[h] == hmax:
        htable.append(h)

wtable = []
for w in range(W):
    if wc[w] == wmax:
        wtable.append(w)

# print(uw, uh)
#print(grid)
#print(wc, uw)
#print(hc, uh)

found = False
for h in htable:
    for w in wtable:
        if (h,w) not in bombs:
            print(hmax + wmax)
            exit(0)

print(hmax + wmax - 1)

Submission status: Accepted

Solution code:
import sys

H, W, M = map(int, input().split())
A = [list(map(lambda x: int(x) - 1, input().split())) for i in range(M)]

cnth = [0] * H
cntw = [0] * W
st = set()

for y, x in A:
    cnth[y] += 1
    cntw[x] += 1
    st.add((y, x))

my = max(cnth)
mx = max(cntw)

Y = []
X = []

for i in range(H):
    if cnth[i] == my:
        Y.append(i)

for i in range(W):
    if cntw[i] == mx:
        X.append(i)

for y in Y:
    for x in X:
        if not (y, x) in st:
            print(my + mx)
            exit(0)

print(my + mx - 1)

Submission status: Accepted

Solution code:
h, w, k = map(int, input().split())

r_n = [0] * h
c_n = [0] * w
bomb_table = set()
for i in range(k):
    hi, wi = map(int, input().split())
    hi -= 1
    wi -= 1
    r_n[hi] += 1
    c_n[wi] += 1
    bomb_table.add((hi, wi))

max_x = max(c_n)
max_y = max(r_n)
ans = max_x + max_y

max_x_table = set()
max_y_table = set()

for i in range(h):
    if r_n[i] == max_y:
        max_y_table.add(i)

for i in range(w):
    if c_n[i] == max_x:
        max_x_table.add(i)

for i in max_y_table:
    for j in max_x_table:
        if (i, j) not in bomb_table:
            print(ans)
            exit(0)
print(ans - 1)

Submission status: Accepted

Solution code:
import collections

h,w,m = map(int,input().split())

gyou = [0 for i in range(h)]
retu = [0 for i in range(w)]
l = []

for i in range(m):
    y,x = map(int,input().split())
    gyou[y-1] += 1
    retu[x-1] += 1
    l.append((y-1,x-1))

ymax = max(gyou)
xmax = max(retu)
c_ymax = gyou.count(ymax)
c_xmax = retu.count(xmax)
ans = ymax + xmax

c = 0
for y,x in l:
    if gyou[y] == ymax and retu[x] == xmax:
        c += 1

if c == c_ymax*c_xmax:
    print(ans-1)
else:
    print(ans)