Problem: 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.

Submission attempts (in order):
import sys
H, W, M = map(int, input().split())
hList = {i+1: 0 for i in range(H)}
wList = {i+1: 0 for i in range(W)}
pList = set()
#print(hList, wList, pList)
for _ in range(M):
  h, w = list(map(int, input().split()))
  #print(h, w)
  hList[h] += 1
  wList[w] += 1
  pList.add((h, w))
#print(hList, wList, pList)

maxCount = max(hList.values())
maxHList = [h for h, count in hList.items() if count==maxCount]


maxCount = max(wList.values())
maxWList = [w for w, count in wList.items() if count==maxCount]

#counterList = []
#for maxH in maxHList:
#  for maxW in maxWList:
#    counterList.append(hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0))
#print(max(counterList))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
for maxH in maxHList:
  for maxW in maxWList:
    if (maxH, maxW) in pList:
      print(hList[maxH] + wList[maxW] - 1)
      sys.exit(0)

print(hList[maxH] + wList[maxW])


import sys
H, W, M = map(int, input().split())
hList = {i+1: 0 for i in range(H)}
wList = {i+1: 0 for i in range(W)}
pList = set()
#print(hList, wList, pList)
for _ in range(M):
  h, w = list(map(int, input().split()))
  #print(h, w)
  hList[h] += 1
  wList[w] += 1
  pList.add((h, w))
#print(hList, wList, pList)

maxHCount = max(hList.values())
maxHList = [h for h, count in hList.items() if count==maxHCount]


maxWCount = max(wList.values())
maxWList = [w for w, count in wList.items() if count==maxWCount]

#counterList = []
#for maxH in maxHList:
#  for maxW in maxWList:
#    counterList.append(hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0))
#print(max(counterList))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))

for maxH in maxHList:
  for maxW in maxWList:
    if (maxH, maxW) in pList:
      print(maxHCount + maxWList - 1)
      sys.exit(0)

print(maxHCount + maxWList)


import sys
H, W, M = map(int, input().split())
hList = {i+1: 0 for i in range(H)}
wList = {i+1: 0 for i in range(W)}
pList = set()
#print(hList, wList, pList)
for _ in range(M):
  h, w = list(map(int, input().split()))
  #print(h, w)
  hList[h] += 1
  wList[w] += 1
  pList.add((h, w))
#print(hList, wList, pList)

maxCount = max(hList.values())
maxHList = [h for h, count in hList.items() if count==maxCount]
if maxCount==0:
  print(0)
  sys.exit(0)


maxCount = max(wList.values())
maxWList = [w for w, count in wList.items() if count==maxCount]

#counterList = []
#for maxH in maxHList:
#  for maxW in maxWList:
#    counterList.append(hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0))
#print(max(counterList))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
for maxH, maxW in (maxH, maxW for maxH in maxHList for maxW in maxWList):
	if (maxH, maxW) in pList:
		print(hList[maxH] + wList[maxW] - 1)
		sys.exit(0)

print(hList[maxH] + wList[maxW])


import sys
H, W, M = map(int, input().split())
hList = {i+1: 0 for i in range(H)}
wList = {i+1: 0 for i in range(W)}
pList = set()
#print(hList, wList, pList)
for _ in range(M):
  h, w = list(map(int, input().split()))
  #print(h, w)
  hList[h] += 1
  wList[w] += 1
  pList.add((h, w))
#print(hList, wList, pList)

maxHCount = max(hList.values())
maxHList = [h for h, count in hList.items() if count==maxHCount]


maxWCount = max(wList.values())
maxWList = [w for w, count in wList.items() if count==maxWCount]

#counterList = []
#for maxH in maxHList:
#  for maxW in maxWList:
#    counterList.append(hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0))
#print(max(counterList))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))

for maxH in maxHList:
  for maxW in maxWList:
    if (maxH, maxW) in pList:
      print(maxHCount + maxWList - 1)
      sys.exit(0)

print(maxHCount + maxWList])


import sys
H, W, M = map(int, input().split())
hList = {i+1: 0 for i in range(H)}
wList = {i+1: 0 for i in range(W)}
pList = set()
#print(hList, wList, pList)
for _ in range(M):
  h, w = list(map(int, input().split()))
  #print(h, w)
  hList[h] += 1
  wList[w] += 1
  pList.add((h, w))
#print(hList, wList, pList)

maxCount = max(hList.values())
maxHList = [h for h, count in hList.items() if count==maxCount]
if maxCount==0:
  print(0)
  sys.exit(0)


maxCount = max(wList.values())
maxWList = [w for w, count in wList.items() if count==maxCount]

#counterList = []
#for maxH in maxHList:
#  for maxW in maxWList:
#    counterList.append(hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0))
#print(max(counterList))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
for maxH, maxW in ((maxH, maxW) for maxH in maxHList for maxW in maxWList):
	if (maxH, maxW) in pList:
		print(hList[maxH] + wList[maxW] - 1)
		sys.exit(0)

print(hList[maxH] + wList[maxW])


import sys
H, W, M = map(int, input().split())
hList = {i+1: 0 for i in range(H)}
wList = {i+1: 0 for i in range(W)}
pList = set()
#print(hList, wList, pList)
for _ in range(M):
  h, w = list(map(int, input().split()))
  #print(h, w)
  hList[h] += 1
  wList[w] += 1
  pList.add((h, w))
#print(hList, wList, pList)

maxHCount = max(hList.values())
maxHList = [h for h, count in hList.items() if count==maxHCount]


maxWCount = max(wList.values())
maxWList = [w for w, count in wList.items() if count==maxWCount]

#counterList = []
#for maxH in maxHList:
#  for maxW in maxWList:
#    counterList.append(hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0))
#print(max(counterList))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))

if M < len(maxHList)*len(maxWList):
	print(maxHCount + maxWList)
	sys.exit(0)

for maxH in maxHList:
  for maxW in maxWList:
    if (maxH, maxW) in pList:
      print(maxHCount + maxWList - 1)
      sys.exit(0)

print(maxHCount + maxWList)


import sys
H, W, M = map(int, input().split())
hList = {i+1: 0 for i in range(H)}
wList = {i+1: 0 for i in range(W)}
pList = set()
#print(hList, wList, pList)
for _ in range(M):
  h, w = list(map(int, input().split()))
  #print(h, w)
  hList[h] += 1
  wList[w] += 1
  pList.add((h, w))
#print(hList, wList, pList)

maxHCount = max(hList.values())
maxHList = [h for h, count in hList.items() if count==maxHCount]


maxWCount = max(wList.values())
maxWList = [w for w, count in wList.items() if count==maxWCount]

#counterList = []
#for maxH in maxHList:
#  for maxW in maxWList:
#    counterList.append(hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0))
#print(max(counterList))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))

if M < len(maxHList)*len(maxWList):
	print(maxHCount + maxWCount)
	sys.exit(0)

for maxH in maxHList:
  for maxW in maxWList:
    if (maxH, maxW) in pList:
      print(maxHCount + maxWCount - 1)
      sys.exit(0)

print(maxHCount + maxWCount)


import sys
H, W, M = map(int, input().split())
hList = {i+1: 0 for i in range(H)}
wList = {i+1: 0 for i in range(W)}
pList = set()
#print(hList, wList, pList)
for _ in range(M):
  h, w = list(map(int, input().split()))
  #print(h, w)
  hList[h] += 1
  wList[w] += 1
  pList.add((h, w))
#print(hList, wList, pList)

maxHCount = max(hList.values())
maxHList = [h for h, count in hList.items() if count==maxHCount]


maxWCount = max(wList.values())
maxWList = [w for w, count in wList.items() if count==maxWCount]

#counterList = []
#for maxH in maxHList:
#  for maxW in maxWList:
#    counterList.append(hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0))
#print(max(counterList))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))
#print(max(((hList[maxH] + wList[maxW] - (1 if ((maxH, maxW) in pList) else 0)) for maxH in maxHList for maxW in maxWList)))

#if M < len(maxHList)*len(maxWList):
#	print(maxHCount + maxWCount)
#	sys.exit(0)

for maxH in maxHList:
  for maxW in maxWList:
    if (maxH, maxW) not in pList:
      print(maxHCount + maxWCount)
      sys.exit(0)

print(maxHCount + maxWCount - 1)


Verdicts: Wrong Answer

Runtime Error

Runtime Error

Runtime Error

Wrong Answer

Runtime Error

Wrong Answer

Accepted