Problem:


Score : 500 points

Problem Statement

There are K items placed on a grid of squares with R rows and C columns. Let (i, j) denote the square at the i-th row (1 \leq i \leq R) and the j-th column (1 \leq j \leq C). The i-th item is at (r_i, c_i) and has the value v_i.

Takahashi will begin at (1, 1), the start, and get to (R, C), the goal. When he is at (i, j), he can move to (i + 1, j) or (i, j + 1) (but cannot move to a non-existent square).

He can pick up items on the squares he visits, including the start and the goal, but at most three for each row. It is allowed to ignore the item on a square he visits.

Find the maximum possible sum of the values of items he picks up.

Constraints

1 \leq R, C \leq 3000

1 \leq K \leq \min(2 \times 10^5, R \times C)

1 \leq r_i \leq R

1 \leq c_i \leq C

(r_i, c_i) \neq (r_j, c_j) (i \neq j)

1 \leq v_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

R C K
r_1 c_1 v_1
r_2 c_2 v_2
:
r_K c_K v_K

Output

Print the maximum possible sum of the values of items Takahashi picks up.

Sample Input 1

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

Sample Output 1

8

He has two ways to get to the goal:

Visit (1, 1), (1, 2), and (2, 2), in this order. In this case, the total value of the items he can pick up is 3 + 5 = 8.

Visit (1, 1), (2, 1), and (2, 2), in this order. In this case, the total value of the items he can pick up is 3 + 4 = 7.

Thus, the maximum possible sum of the values of items he picks up is 8.

Sample Input 2

2 5 5
1 1 3
2 4 20
1 2 1
1 3 4
1 4 2

Sample Output 2

29

We have four items in the 1-st row. The optimal choices are as follows:

Visit (1, 1) (1, 2), (1, 3), (1, 4), (2, 4), and (2, 5), in this order, and pick up all items except the one on (1, 2). Then, the total value of the items he picks up will be 3 + 4 + 2 + 20 = 29.

Sample Input 3

4 5 10
2 5 12
1 5 12
2 3 15
1 2 20
1 1 28
2 4 26
3 2 27
4 5 21
3 5 10
1 3 10

Sample Output 3

142



Sample input:
2 2 3
1 1 3
2 1 4
1 2 5


Sample output:
8

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

#############
# Libraries #
#############

import sys
input = sys.stdin.readline

import math
#from math import gcd
import bisect
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache

#############
# Constants #
#############

MOD = 10**9+7
INF = float('inf')
AZ = "abcdefghijklmnopqrstuvwxyz"

#############
# Functions #
#############

######INPUT######
def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]


#####Shorten#####
def DD(arg): return defaultdict(arg)

#####Inverse#####
def inv(n): return pow(n, MOD-2, MOD)

######Combination######
kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n): return kaijo_memo[n]
  if(len(kaijo_memo) == 0): kaijo_memo.append(1)
  while(len(kaijo_memo) <= n): kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n): return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0): gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n): gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if n == r: return 1
  if n < r or r < 0: return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret

######Factorization######
def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0: 
        cnt+=1 
        temp //= i
      arr.append([i, cnt])
  if temp!=1: arr.append([temp, 1])
  if arr==[]: arr.append([n, 1])
  return arr

#####MakeDivisors######
def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i: 
        divisors.append(n//i)
  return divisors

#####MakePrimes######
def make_primes(N):
  max = int(math.sqrt(N))
  seachList = [i for i in range(2,N+1)]
  primeNum = []
  while seachList[0] <= max:
    primeNum.append(seachList[0])
    tmp = seachList[0]
    seachList = [i for i in seachList if i % tmp != 0]
  primeNum.extend(seachList)
  return primeNum

#####GCD#####
def gcd(a, b):
    while b: a, b = b, a % b
    return a

#####LCM#####
def lcm(a, b):
    return a * b // gcd (a, b)

#####BitCount#####
def count_bit(n):
  count = 0
  while n:
    n &= n-1
    count += 1
  return count

#####ChangeBase#####
def base_10_to_n(X, n):
  if X//n: return base_10_to_n(X//n, n)+[X%n]
  return [X%n]

def base_n_to_10(X, n):
  return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))

def base_10_to_n_without_0(X, n):
  X -= 1
  if X//n: return base_10_to_n_without_0(X//n, n)+[X%n]
  return [X%n]

#####IntLog#####
def int_log(n, a):
  count = 0
  while n>=a:
    n //= a
    count += 1
  return count

#############
# Main Code #
#############

R,C,K = IL()
data = [[0 for i in range(C)] for j in range(R)]
for _ in range(K):
  j,i,v = IL()
  data[j-1][i-1] = v

dp = [[0,0,0,0] for i in range(C+1)]
for j in range(R):
  dpprev = dp[:]
  for i in range(C):
    v = data[j][i]
    m = max(dpprev[i+1])
    if v == 0:
      dp[i+1][0] = max(dp[i][0],m)
      dp[i+1][1] = max(dp[i][1],m)
      dp[i+1][2] = max(dp[i][2],m)
      dp[i+1][3] = max(dp[i][3],m)
    else:
      dp[i+1][0] = max(dp[i][0],m)
      dp[i+1][1] = max(dp[i][1],dp[i][0]+v,m+v)
      dp[i+1][2] = max(dp[i][2],dp[i][1]+v)
      dp[i+1][3] = max(dp[i][3],dp[i][2]+v)
print(max(dp[-1]))

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

#############
# Libraries #
#############

import sys
input = sys.stdin.readline

import math
#from math import gcd
import bisect
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache

#############
# Constants #
#############

MOD = 10**9+7
INF = float('inf')
AZ = "abcdefghijklmnopqrstuvwxyz"

#############
# Functions #
#############

######INPUT######
def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]


#####Shorten#####
def DD(arg): return defaultdict(arg)

#####Inverse#####
def inv(n): return pow(n, MOD-2, MOD)

######Combination######
kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n): return kaijo_memo[n]
  if(len(kaijo_memo) == 0): kaijo_memo.append(1)
  while(len(kaijo_memo) <= n): kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n): return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0): gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n): gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if n == r: return 1
  if n < r or r < 0: return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret

######Factorization######
def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0: 
        cnt+=1 
        temp //= i
      arr.append([i, cnt])
  if temp!=1: arr.append([temp, 1])
  if arr==[]: arr.append([n, 1])
  return arr

#####MakeDivisors######
def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i: 
        divisors.append(n//i)
  return divisors

#####MakePrimes######
def make_primes(N):
  max = int(math.sqrt(N))
  seachList = [i for i in range(2,N+1)]
  primeNum = []
  while seachList[0] <= max:
    primeNum.append(seachList[0])
    tmp = seachList[0]
    seachList = [i for i in seachList if i % tmp != 0]
  primeNum.extend(seachList)
  return primeNum

#####GCD#####
def gcd(a, b):
    while b: a, b = b, a % b
    return a

#####LCM#####
def lcm(a, b):
    return a * b // gcd (a, b)

#####BitCount#####
def count_bit(n):
  count = 0
  while n:
    n &= n-1
    count += 1
  return count

#####ChangeBase#####
def base_10_to_n(X, n):
  if X//n: return base_10_to_n(X//n, n)+[X%n]
  return [X%n]

def base_n_to_10(X, n):
  return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))

def base_10_to_n_without_0(X, n):
  X -= 1
  if X//n: return base_10_to_n_without_0(X//n, n)+[X%n]
  return [X%n]

#####IntLog#####
def int_log(n, a):
  count = 0
  while n>=a:
    n //= a
    count += 1
  return count

#############
# Main Code #
#############

R,C,K = IL()
data = [[0 for i in range(C)] for j in range(R)]
for _ in range(K):
  j,i,v = IL()
  data[j-1][i-1] = v

dp = [[0,0,0,0] for i in range(C+1)]
for j in range(R):
  dpprev = dp[:]
  for i in range(C):
    v = data[j][i] 
    if v == 0:
      dp[i+1][0] = max(dp[i][0],max(dpprev[i+1]))
      dp[i+1][1] = max(dp[i][1],max(dpprev[i+1]))
      dp[i+1][2] = max(dp[i][2],max(dpprev[i+1]))
      dp[i+1][3] = max(dp[i][3],max(dpprev[i+1]))
    else:
      dp[i+1][0] = max(dp[i][0],max(dpprev[i+1]))
      dp[i+1][1] = max(dp[i][1],dp[i][0]+v,max(dpprev[i+1])+v)
      dp[i+1][2] = max(dp[i][2],dp[i][1]+v)
      dp[i+1][3] = max(dp[i][3],dp[i][2]+v)
print(max(dp[-1]))

Submission status: Accepted

Solution code:
R,C,K = map(int,input().split())
dp0 = [[0 for _ in range(C+1)] for f in range(R+1)]
dp1 = [[0 for _ in range(C+1)] for f in range(R+1)]
dp2 = [[0 for _ in range(C+1)] for f in range(R+1)]
dp3 = [[0 for _ in range(C+1)] for f in range(R+1)]
vl = [[0 for _ in range(C+1)] for f in range(R+1)]

for i in range(K):
	r,c,v = map(int,input().split())
	vl[r][c] = v

for i in range(1, R+1):
	for j in range(1, C+1):
		dp0[i][j] = max(dp0[i][j], dp0[i-1][j], dp1[i-1][j], dp2[i-1][j], dp3[i-1][j])
		dp3[i][j] = max(dp3[i][j], dp3[i][j-1], dp2[i][j-1]+vl[i][j], dp2[i][j]+vl[i][j])
		dp2[i][j] = max(dp2[i][j], dp2[i][j-1], dp1[i][j-1]+vl[i][j], dp1[i][j]+vl[i][j])
		dp1[i][j] = max(dp1[i][j], dp1[i][j-1], dp0[i][j-1]+vl[i][j], dp0[i][j]+vl[i][j])

print(max(dp0[R][C], dp1[R][C], dp2[R][C], dp3[R][C]))

Submission status: Accepted

Solution code:
import sys

inp = [int(x) for x in sys.stdin.read().split()]; ii = 0

class SegmentTree:
    def __init__(self, data, default=0, func=max):
        """initialize the segment tree with data"""
        self._default = default
        self._func = func
        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()

        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])

    def __delitem__(self, idx):
        self[idx] = self._default

    def __getitem__(self, idx):
        return self.data[idx + self._size]

    def __setitem__(self, idx, value):
        idx += self._size
        self.data[idx] = value
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
            idx >>= 1

    def __len__(self):
        return self._len

    def query(self, start, stop):
        """func of data[start, stop)"""
        start += self._size
        stop += self._size

        res_left = res_right = self._default
        while start < stop:
            if start & 1:
                res_left = self._func(res_left, self.data[start])
                start += 1
            if stop & 1:
                stop -= 1
                res_right = self._func(self.data[stop], res_right)
            start >>= 1
            stop >>= 1

        return self._func(res_left, res_right)

    def __repr__(self):
        return "SegmentTree({0})".format(self.data)

shift = int(10**9 + 1)
rows, cols, k = inp[ii:ii+3]; ii += 3
items = [[] for _ in range(rows+1)]
best = [0]*(cols+1)
for _ in range(k):
	r, c, v = inp[ii:ii+3]; ii += 3
	items[r].append(c*shift+v)
for i in range(rows+1):
	items[i].sort()
S = SegmentTree(best)
ans = 0
for r in range(1, rows+1):
	dp = []
	best1, best2 = 0, 0
	Row = items[r]
	for X in Row:
		c, v = X//shift, X%shift
		v1 = S.query(1, c+1) + v
		v2 = best1 + v
		v3 = best2 + v
		V = v1
		if V < v2:
			V = v2
		if V < v3:
			V = v3
		dp.append(V)
		if v1 > best1:
			best1 = v1
		if v2 > best2:
			best2 = v2
		if ans < V:
			ans = V
	for j in range(len(dp)):
		c = Row[j]//shift
		if S[c] < dp[j]:
			S[c] = dp[j]
print(ans)

Submission status: Accepted

Solution code:
import sys
input=sys.stdin.readline
def main():
	R,C,K=map(int,input().split())
	lis=[[0]*(C) for i in range(R)]
	for i in range(K):
		a,b,c=map(int,input().split())
		lis[a-1][b-1]=c
	dp0=[[0]*(C+1) for i in range(R+1)]
	dp1=[[0]*(C+1) for i in range(R+1)]
	dp2=[[0]*(C+1) for i in range(R+1)]
	dp3=[[0]*(C+1) for i in range(R+1)]
	for i in range(1,R+1):
		for j in range(1,C+1):
			for x,y in ((dp0,0),(dp1,dp0),(dp2,dp1),(dp3,dp2)):
				t=lis[i-1][j-1]
				x[i][j]=max(x[i-1][j],x[i][j])
				x[i][j]=max(x[i][j-1],x[i][j])
				if t!=0:
					dp1[i][j]=max(dp1[i][j],x[i-1][j]+t)
					if y!=0:
						x[i][j]=max(x[i][j],y[i][j-1]+t)
	print(max(dp0[-1][-1],dp1[-1][-1],dp2[-1][-1],dp3[-1][-1]))
if __name__ == '__main__':
	main()

Submission status: Accepted

Solution code:
R,C,k = map(int,input().split())
dp1 = [[0]*(C+1) for i in range(R+1)]
dp2 = [[0]*(C+1) for i in range(R+1)]
dp3 = [[0]*(C+1) for i in range(R+1)]
for i in range(k):
    r,c,v = map(int,input().split())
    dp1[r][c] = v
for i in range(1,R+1):
    for j in range(1,C+1):
        a = dp1[i][j]
        dp3[i][j] = max(dp2[i][j-1]+a,dp3[i][j-1])
        dp2[i][j] = max(dp1[i][j-1]+a,dp2[i][j-1])
        dp1[i][j] = max(dp1[i-1][j]+a,dp2[i-1][j]+a,dp3[i-1][j]+a,dp1[i][j-1],a)
print(max(dp1[R][C],dp2[R][C],dp3[R][C]))

Submission status: Accepted

Solution code:
import sys
input=sys.stdin.readline

def main():
    r,c,k=map(int,input().split())

    item=[[0]*c for i in range(r)]
    for i in range(k):
        R,C,v=map(int,input().split())
        item[R-1][C-1]=v

    dp0=[[-10**10]*c  for i in range(r)]
    dp1 = [[-10 ** 10] * c for i in range(r)]
    dp2 = [[-10 ** 10] * c for i in range(r)]
    dp3 = [[-10 ** 10] * c for i in range(r)]

    if item[0][0]==0:
        dp0[0][0]=0
    else:
        dp0[0][0]=0
        dp1[0][0]=item[0][0]

    for i in range(r):
        for j in range(c):
            if j!=c-1:
                v=item[i][j+1]
                if v==0:
                    dp0[i][j+1]=max(dp0[i][j],dp0[i][j+1])
                    dp1[i][j + 1] = max(dp1[i][j], dp1[i][j + 1])
                    dp2[i][j + 1] = max(dp2[i][j], dp2[i][j + 1])
                    dp3[i][j + 1] = max(dp3[i][j], dp3[i][j + 1])
                else:
                    dp0[i][j+1]=max(dp0[i][j],dp0[i][j+1])
                    dp1[i][j+1]=max(dp0[i][j]+v,dp1[i][j],dp1[i][j+1])
                    dp2[i][j + 1] = max(dp1[i][j] + v, dp2[i][j], dp2[i][j + 1])
                    dp3[i][j + 1] = max(dp2[i][j] + v, dp3[i][j], dp3[i][j + 1])
            if i!=r-1:
                v=item[i+1][j]
                if v==0:
                    dp0[i+1][j]=max(dp0[i][j],dp1[i][j],dp2[i][j],dp3[i][j],dp0[i+1][j])
                else:
                    dp0[i+1][j]=max(dp0[i][j],dp1[i][j],dp2[i][j],dp3[i][j],dp0[i+1][j])
                    dp1[i + 1][j] = max(dp0[i][j]+v, dp1[i][j]+v, dp2[i][j]+v, dp3[i][j]+v, dp1[i + 1][j])

    ans=max(dp0[r-1][c-1],dp1[r-1][c-1],dp2[r-1][c-1],dp3[r-1][c-1])
    print(ans)

if __name__=='__main__':
    main()

Submission status: Accepted

Solution code:
R,C,k = map(int,input().split())
dp1 = [[0]*(C+1) for i in range(R+1)]
dp2 = [[0]*(C+1) for i in range(R+1)]
dp3 = [[0]*(C+1) for i in range(R+1)]
item = [[0]*(C+1) for i in range(R+1)]
for i in range(k):
    r,c,v = map(int,input().split())
    dp1[r][c] = v

for i in range(1,R+1):
    for j in range(1,C+1):
        a = dp1[i][j]
        dp3[i][j] = max(dp2[i][j-1]+a,dp3[i][j-1])
        dp2[i][j] = max(dp1[i][j-1]+a,dp2[i][j-1])
        dp1[i][j] = max(dp1[i-1][j]+a,dp2[i-1][j]+a,dp3[i-1][j]+a,dp1[i][j-1],a)

print(max(dp1[R][C],dp2[R][C],dp3[R][C]))

Submission status: Accepted

Solution code:
R,C,k = map(int,input().split())
dp0 = [[0]*(C+1) for i in range(R+1)]
dp1 = [[0]*(C+1) for i in range(R+1)]
dp2 = [[0]*(C+1) for i in range(R+1)]
dp3 = [[0]*(C+1) for i in range(R+1)]
item = [[0]*(C+1) for i in range(R+1)]
for i in range(k):
    r,c,v = map(int,input().split())
    # item[r][c] = v
    dp1[r][c] = v
# for i in range(R+1):
    # print(item[i])

for i in range(1,R+1):
    for j in range(1,C+1):
        # a = item[i][j]
        # dp0[i][j] = max(dp0[i-1][j],dp1[i-1][j],dp2[i-1][j],dp3[i-1][j],dp0[i][j-1])
        # dp1[i][j] = max(dp0[i][j-1]+a,dp1[i][j-1])
        # dp2[i][j] = max(dp1[i][j-1]+a,dp2[i][j-1])
        # dp3[i][j] = max(dp2[i][j-1]+a,dp3[i][j-1])
        # dp0[i][j] = max(dp0[i-1][j],dp1[i-1][j],dp2[i-1][j],dp3[i-1][j],dp0[i][j-1],dp0[i][j])
        dp3[i][j] = max(dp2[i][j-1]+dp1[i][j],dp3[i][j-1])
        dp2[i][j] = max(dp1[i][j-1]+dp1[i][j],dp2[i][j-1])
        dp1[i][j] = max(dp1[i-1][j]+dp1[i][j],dp2[i-1][j]+dp1[i][j],dp3[i-1][j]+dp1[i][j],dp1[i][j-1],dp1[i][j])
        
        

# for i in range(R+1):
#     print(dp2[i])
print(max(dp0[R][C],dp1[R][C],dp2[R][C],dp3[R][C]))

Submission status: Accepted

Solution code:
import sys


def input():
    return sys.stdin.readline().rstrip()


def main():
    R, C, K = map(int, input().split())

    field = [[0 for j in range(C)] for i in range(R)]

    for _ in range(K):
        r, c, v = map(int, input().split())
        field[r - 1][c - 1] += v

    dp = [[0] * 4 for j in range(C)]

    for i in range(R):
        for j in range(C):
            ct = field[i][j]
            premax = max(dp[j])

            if ct == 0:
                if j>0:
                    dp[j][0] = max(dp[j - 1][0], premax)
                else:
                    dp[j][0] = premax

                for k in range(1, 4):
                    if j > 0:
                        dp[j][k] = dp[j - 1][k]
            else:
                if j>0:
                    dp[j][0] = max(dp[j - 1][0], premax)
                    dp[j][1] = max(ct + max(dp[j - 1][0], premax), dp[j - 1][1])
                else:
                    dp[j][0] = premax
                    dp[j][1] = premax +ct
                for k in range(2, 4):
                    if j > 0:
                        dp[j][k] = max(dp[j - 1][k - 1] + ct, dp[j - 1][k])

    print(max(dp[C - 1]))


if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
import sys

input = sys.stdin.readline
R, C, K = map(int, input().split())
values = [[0]*C for _ in range(R)]
for _ in range(K):
    r, c, v = map(int, input().split())
    values[r-1][c-1] = v

dp = [[[0 for _ in range(C+1)] for _ in range(R+1)] for _ in range(4)]

for r in range(R-1, -1, -1):
    # dp[0][r][C - 1] = dp[3][r + 1][C - 1]
    # for i in range(1, 4):
    #    dp[i][r][C-1] = dp[3][r + 1][C-1][3]+values[r][C-1]
    for c in range(C-1, -1, -1):
        v = values[r][c]
        for i in range(4):
            if i == 0 or v == 0:
                dp[i][r][c] = max(dp[3][r+1][c], dp[i][r][c+1])
            else:
                dp[i][r][c] = max(dp[3][r + 1][c]+v, dp[i][r][c + 1], dp[i-1][r][c + 1] + v)

print(dp[3][0][0])

Submission status: Accepted

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

import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(2147483647)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

r, c, k = LI()
maze = [[0] * c for _ in range(r)]
for _ in range(k):
    R, C, V = LI()
    maze[R-1][C-1] = V

dp1 = [[0] * (c+1) for _ in range(r+1)]
dp2 = [[0] * (c+1) for _ in range(r+1)]
dp3 = [[0] * (c+1) for _ in range(r+1)]

for i in range(1, r+1):
    for j in range(1, c+1):
        dp1[i][j] = max(dp1[i][j-1], dp1[i-1][j] + maze[i-1][j-1], maze[i-1][j-1], dp2[i-1][j] + maze[i-1][j-1], dp3[i-1][j] + maze[i-1][j-1])
        dp2[i][j] = max(dp2[i][j-1], dp2[i-1][j], dp1[i][j-1] + maze[i-1][j-1])
        dp3[i][j] = max(dp3[i][j-1], dp3[i-1][j], dp2[i][j-1] + maze[i-1][j-1])
ans = max(dp1[-1][-1], dp2[-1][-1], dp3[-1][-1])
print(ans)

Submission status: Accepted

Solution code:
# pypy
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines

R, C, K = map(int, readline().split())
rcv = list(map(int, read().split()))
rr = rcv[::3]
cc = rcv[1::3]
vv = rcv[2::3]
rc2v = {}
for _r, _c, _v in zip(rr, cc, vv):
    rc2v[(_r-1, _c-1)] = _v

dp = [[0]*4 for c in range(C)]

for r in range(R):
    for c in range(C):
        if(c!=0):
            dp[c][0] = max(dp[c-1][0], max(dp[c]))
        else:
            dp[c][0] = max(dp[c])

        v = 0
        if (r, c) in rc2v:
            v = rc2v[(r, c)]
        for k in range(1,4):
            if(c!=0):
                dp[c][k] = max(dp[c-1][k], dp[c-1][k-1] + v, dp[c][0] + v)
            else:
                dp[c][k] = dp[c][0] + v

print(max(dp[-1]))

Submission status: Accepted

Solution code:
def main():

    R, C, K = map(int, input().split())
    a = dict()
    for _ in range(K):
        r, c, v = map(int, input().split())
        a[(r-1, c-1)] = v

    dp = [[[0]*4 for _ in range(C+1)] for _ in range(2)]

    for i in range(R):
        for j in range(C):
            v = max(dp[0][j+1])
            u = 0
            if (i, j) in a: u = a[(i, j)]
            dp[1][j+1][0] = max(dp[1][j+1][0], v)
            dp[1][j+1][1] = max(dp[1][j+1][1], dp[1][j][1], dp[1][j][0] + u,  v + u)
            dp[1][j+1][2] = max(dp[1][j+1][2], dp[1][j][2], dp[1][j][1] + u )
            dp[1][j+1][3] = max(dp[1][j+1][3], dp[1][j][3], dp[1][j][2] + u )
        dp[1], dp[0] = dp[0], dp[1]

    return max(dp[0][C])

if __name__ == '__main__':
    print(main())

Submission status: Accepted

Solution code:
R,C,K = map(int,input().split())
J=[0] * K
for i in range(K):
  J[i] = list(map(int,input().split()))

#DP0 = [[0]*(C+2) for i in range(R+2)]
DP1 = [[0]*(C+2) for i in range(R+2)]
DP2 = [[0]*(C+2) for i in range(R+2)]
DP3 = [[0]*(C+2) for i in range(R+2)]

MAP = [[0]*C for i in range(R)]

for x,y,v in J:
    MAP[x-1][y-1] = v
#print(MAP)
for i in range(R):
    for j in range(C):
        DP1[i][j] = max(DP1[i][j-1],DP1[i-1][j]+MAP[i][j],DP2[i-1][j]+MAP[i][j],DP3[i-1][j]+MAP[i][j])
        DP2[i][j] = max(DP2[i][j-1],DP1[i][j-1]+MAP[i][j])
        DP3[i][j] = max(DP3[i][j-1],DP2[i][j-1]+MAP[i][j])

#print(DP1)
#print(DP2)
#print(DP3)
ANS=0
for i in range(R):
    for j in range(C):
        ANS=max(ANS,DP1[i][j],DP2[i][j],DP3[i][j])
print(ANS)

Submission status: Accepted

Solution code:
import sys

input=sys.stdin.readline

R,C,K=map(int,input().split())
item=[[0 for i in range(C)] for j in range(R)]
for i in range(K):
    r,c,v=map(int,input().split())
    item[r-1][c-1]=v

dp=[[0 for i in range(3)] for j in range(C)]
dp[C-1][0]=item[R-1][C-1]
dp[C-1][1]=item[R-1][C-1]
dp[C-1][2]=item[R-1][C-1]

for j in range(C-2,-1,-1):
    dp[j][0]=max(dp[j+1][1]+item[R-1][j],dp[j+1][0])
    dp[j][1]=max(dp[j+1][2]+item[R-1][j],dp[j+1][1])
    dp[j][2]=max(item[R-1][j],dp[j+1][2])


for i in range(R-2,-1,-1):
    ndp=[[0 for i in range(3)] for j in range(C)]
    ndp[C-1][0]=dp[C-1][0]+item[i][C-1]
    ndp[C-1][1]=dp[C-1][0]+item[i][C-1]
    ndp[C-1][2]=dp[C-1][0]+item[i][C-1]
    for j in range(C-2,-1,-1):
        ndp[j][0]=max(max(dp[j][0],ndp[j+1][1])+item[i][j],ndp[j+1][0])
        ndp[j][1]=max(max(dp[j][0],ndp[j+1][2])+item[i][j],ndp[j+1][1])
        ndp[j][2]=max(dp[j][0]+item[i][j],ndp[j+1][2])
    dp=ndp

print(dp[0][0])

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
def solve():
  R, C, K = map(int, input().split())
  item = [[0]*C for _ in range(R)]
  for i in range(K):
    r,c,v = map(int, input().split())
    item[r-1][c-1] = v
  dp = [[[0]*(C+1) for _ in range(R+1)] for _ in range(4)]
  for i in range(1,R+1):
    for j in range(1,C+1):
      for k in range(4): #横から取らない
        dp[k][i][j] = dp[k][i][j-1]
      #上から取らない
      dp[0][i][j] = max(dp[0][i][j],dp[-1][i-1][j])
      if item[i-1][j-1]>0:
        #上からとる
        dp[1][i][j] = max(dp[1][i][j],dp[-1][i-1][j]+item[i-1][j-1])
        for k in range(1,4): #横から取る
          dp[k][i][j] = max(dp[k][i][j],dp[k-1][i][j-1]+item[i-1][j-1])
      for k in range(1,4):
        dp[k][i][j] = max(dp[k-1][i][j],dp[k][i][j])
  ans = 0
  for k in range(4):
    ans = max(ans,dp[k][-1][-1])
  return ans
print(solve())

Submission status: Accepted

Solution code:
import sys
def MI(): return map(int,sys.stdin.readline().rstrip().split())

R,C,K = MI()
item = [[0]*(C+1) for _ in range(R+1)]
for i in range(K):
    r,c,v = MI()
    item[r][c] = v

dp = [[[0]*(C+1) for j in range(4)] for i in range(R+1)]  # dp[i][j][k] = (i,k)に至るまでに拾ったアイテムの価値の合計の最大値、但しi列目からアイテムをj個拾う

for i in range(1,R+1):
    for j in range(4):
        for k in range(1,C+1):
            if item[i][k] == 0:
                if j == 0:
                    dp[i][j][k] = max(dp[i][j][k-1],dp[i-1][0][k],dp[i-1][1][k],dp[i-1][2][k],dp[i-1][3][k])
                else:
                    dp[i][j][k] = dp[i][j][k-1]
            else:
                if j == 0:
                    dp[i][j][k] = max(dp[i][j][k-1],dp[i-1][0][k],dp[i-1][1][k],dp[i-1][2][k],dp[i-1][3][k])
                elif j == 1:
                    dp[i][j][k] = max(dp[i][j][k-1]-item[i][k],dp[i][j-1][k-1],dp[i-1][0][k],dp[i-1][1][k],dp[i-1][2][k],dp[i-1][3][k]) + item[i][k]
                else:
                    dp[i][j][k] = max(dp[i][j][k-1],dp[i][j-1][k-1] + item[i][k])

ans = 0
for j in range(4):
    ans = max(ans,dp[R][j][C])

print(ans)

Submission status: Accepted

Solution code:
import sys
input=lambda: sys.stdin.readline().rstrip()
r,c,k=map(int,input().split())
D=[[0]*c for _ in range(r)] 
for _ in range(k):
	ri,ci,v=map(int,input().split())
	ri-=1
	ci-=1
	D[ri][ci]=v

DP=[[[0]*(c+1) for _ in range(r+1)] for i in range(4)]
for i in range(r):
	for j in range(c):
		v=D[i][j]

		for ii in range(4):
			DP[0][i][j]=max(DP[0][i][j],DP[ii][i-1][j])
			if v!=0:
				DP[1][i][j]=max(DP[1][i][j],DP[ii][i-1][j]+v)

			DP[ii][i][j]=max(DP[ii][i][j],DP[ii][i][j-1])
			if v!=0 and ii!=0:
				DP[ii][i][j]=max(DP[ii][i][j],DP[ii-1][i][j-1]+v)
ans=0
for i in range(4):
	ans=max(ans,DP[i][r-1][c-1])
print(ans)

Submission status: Accepted

Solution code:
R, C, K = map(int, input().split())
V = [[0]*C for _ in range(R)]
for _ in range(K):
    r, c, v = map(int, input().split())
    V[r-1][c-1] = v
dp = [[0]*4 for _ in range(C+1)]
for j in range(C):
    for k in range(1, 4):
        dp[j+1][k] = max(dp[j][k-1]+V[0][j], dp[j][k])
for i in range(1, R):
    newdp = [[0]*4 for _ in range(C+1)]
    for j in range(C):
        newdp[j+1][0] = max(max(dp[j+1]), newdp[j][0])
        newdp[j+1][1] = max(max(max(dp[j+1]), newdp[j][0])+V[i][j], newdp[j][1])
        for k in range(2, 4):
            newdp[j+1][k] = max(newdp[j][k-1]+V[i][j], newdp[j][k])
    dp = newdp
print(max(dp[-1]))

Submission status: Accepted

Solution code:
import sys

inp = [int(x) for x in sys.stdin.read().split()]; ii = 0
shift = int(10**9 + 1)
rows, cols, k = inp[ii:ii+3]; ii += 3
items = [[] for _ in range(rows+1)]
best = [0]*(cols+1)
for _ in range(k):
	r, c, v = inp[ii:ii+3]; ii += 3
	items[r].append(c*shift+v)
for i in range(rows+1):
	items[i].sort()
ans = 0
for r in range(1, rows+1):
	dp = []
	best1, best2 = 0, 0
	Row = items[r]
	for X in Row:
		c, v = X//shift, X%shift
		v1 = best[c] + v
		v2 = best1 + v
		v3 = best2 + v
		V = v1
		if V < v2:
			V = v2
		if V < v3:
			V = v3
		dp.append(V)
		if v1 > best1:
			best1 = v1
		if v2 > best2:
			best2 = v2
		if ans < V:
			ans = V
	for j in range(len(dp)):
		c = Row[j]//shift
		if best[c] < dp[j]:
			best[c] = dp[j]
	for j in range(2, cols+1):
		if best[j] < best[j-1]:
			best[j] = best[j-1]
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

R, C, K = map(int, input().split())
items = [[0] * (C+1) for _ in range(R+1)]
for _ in range(K):
    r, c, v = map(int, input().split())
    items[r][c] = v
dp = [[0] * 4 for _ in range(C+1)]
for i in range(1, R+1):
    ndp = [[0] * 4 for _ in range(C+1)]
    for j in range(1, C+1):
        for k in range(4):
            ndp[j][0] = max(ndp[j][0], dp[j][k])
            ndp[j][k] = max(ndp[j][k], ndp[j-1][k])
        if items[i][j]:
            for k in range(3, 0, -1):
                ndp[j][k] = max(ndp[j][k], ndp[j][k-1] + items[i][j])
    dp = ndp
print(max(dp[C]))

Submission status: Accepted

Solution code:
import sys
read = sys.stdin.buffer.read
readlines = sys.stdin.buffer.readlines
input = sys.stdin.buffer.readline
H, W, K = map(int, input().split())
B = {}

for _ in range(K):
    r, c, v = map(int, input().split())
    B[(r-1,c-1)] = v

dp = [[0]*(W+1) for _ in range(4)]
 
for i in range(H):
    for j in range(W):
        if (i, j) in B:
            v = B[(i, j)]
            dp[0][j+1] = max(dp[0][j], dp[0][j+1], dp[1][j+1], dp[2][j+1], dp[3][j+1])
            dp[1][j+1] = max(dp[1][j], dp[0][j+1]+v)
            dp[2][j+1] = max(dp[2][j], dp[1][j]+v)
            dp[3][j+1] = max(dp[3][j], dp[2][j]+v)
        else:
            dp[0][j+1] = max(dp[0][j], dp[0][j+1], dp[1][j+1], dp[2][j+1], dp[3][j+1])
            dp[1][j+1] = dp[1][j]
            dp[2][j+1] = dp[2][j]
            dp[3][j+1] = dp[3][j]
print(max(dp[i][-1] for i in range(4)))

Submission status: Accepted

Solution code:
import bisect, copy, heapq, math, sys
from collections import *
from functools import lru_cache
from itertools import accumulate, combinations, permutations, product
def input():
    return sys.stdin.readline()[:-1]
def ruiseki(lst):
    return [0]+list(accumulate(lst))
def celi(a,b):
    return -(-a//b)
sys.setrecursionlimit(5000000)
mod=pow(10,9)+7
al=[chr(ord('a') + i) for i in range(26)]
direction=[[1,0],[0,1],[-1,0],[0,-1]]

def main():
    r,c,k=map(int,input().split())
    rcv=[list(map(int,input().split())) for i in range(k)]

    dpn=[[0]*4 for i in range(c+1)]

    dic={}
    for i in range(k):
        r1,c1,v=rcv[i]
        dic[(r1,c1)]=v

    for i in range(r):
        for j in range(c):
            dpn[j+1][0]=max(dpn[j+1][0],max(dpn[j+1]))
            if (i+1,j+1) in dic:
                for k in range(3)[::-1]:
                    dpn[j+1][k+1]=max(dpn[j+1][k]+dic[(i+1,j+1)],dpn[j][k]+dic[(i+1,j+1)])
            for k in range(4):
                dpn[j+1][k]=max(dpn[j+1][k],dpn[j][k])
        # print(dpn)
    print(max(dpn[-1]))

main()