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:
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians, gcd
from itertools import accumulate, permutations, combinations, product, groupby, combinations_with_replacement
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from heapq import heappush, heappop
from functools import reduce
from decimal import Decimal, ROUND_CEILING
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

R, C, K = MAP()

dp1 = [[0]*4 for _ in range(C+1)]
dp2 = [[0]*4 for _ in range(C+1)]

field = [[0]*(C+1)] + [[0]*(C+1) for _ in range(R)]

for _ in range(K):
    r, c, v = MAP()
    field[r][c] = v

for i in range(1, R+1):
    for j in range(1, C+1):
        if i%2 == 0:       
            up_max = max(dp1[j])
            p = field[i][j]
            dp2[j][0] = max(up_max, dp1[j-1][0])
            dp2[j][1] = max(up_max+p, dp2[j-1][1], dp2[j-1][0]+p)
            dp2[j][2] = max(dp2[j-1][2], dp2[j-1][1]+p)
            dp2[j][3] = max(dp2[j-1][3], dp2[j-1][2]+p)
        else:
            up_max = max(dp2[j])
            p = field[i][j]
            dp1[j][0] = max(up_max, dp2[j-1][0])
            dp1[j][1] = max(up_max+p, dp1[j-1][1], dp1[j-1][0]+p)
            dp1[j][2] = max(dp1[j-1][2], dp1[j-1][1]+p)
            dp1[j][3] = max(dp1[j-1][3], dp1[j-1][2]+p)

a = max(dp1[-1])
b = max(dp2[-1])
print(max(a, b))

Submission status: Accepted

Solution code:
import sys
input=sys.stdin.readline
def main():
    r,c,k=map(int,input().split())
    v=[[0]*c for _ in range(r)]
    for _ in range(k):
        ri,ci,a=map(int,input().split())
        ri-=1
        ci-=1
        v[ri][ci]=a
    dp=[[[0]*c for _ in range(r)] for i in range(4)]
    #print(dp)
    if v[0][0]>0:
        dp[1][0][0]=v[0][0]

    for i in range(r):
        for j in range(c):
            if i>0:
                dp[1][i][j]=max(dp[1][i][j],dp[0][i-1][j]+v[i][j])
                dp[0][i][j]=max(dp[0][i][j],dp[0][i-1][j])
                dp[1][i][j]=max(dp[1][i][j],dp[1][i-1][j]+v[i][j])
                dp[0][i][j]=max(dp[0][i][j],dp[1][i-1][j])
                dp[1][i][j]=max(dp[1][i][j],dp[2][i-1][j]+v[i][j])
                dp[0][i][j]=max(dp[0][i][j],dp[2][i-1][j])
                dp[1][i][j]=max(dp[1][i][j],dp[3][i-1][j]+v[i][j])
                dp[0][i][j]=max(dp[0][i][j],dp[3][i-1][j])
            if j>0:
                dp[1][i][j]=max(dp[1][i][j],dp[0][i][j-1]+v[i][j])
                dp[2][i][j]=max(dp[2][i][j],dp[1][i][j-1]+v[i][j])
                dp[3][i][j]=max(dp[3][i][j],dp[2][i][j-1]+v[i][j])
                dp[0][i][j]=max(dp[0][i][j],dp[0][i][j-1])
                dp[1][i][j]=max(dp[1][i][j],dp[1][i][j-1])
                dp[2][i][j]=max(dp[2][i][j],dp[2][i][j-1])
                dp[3][i][j]=max(dp[3][i][j],dp[3][i][j-1])
    #print(dp)
    ans=0
    for i in range(4):
        ans=max(dp[i][r-1][c-1],ans)
    return print(ans)
if __name__=="__main__":
    main()

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**7)

readline = sys.stdin.buffer.readline
def readstr():return readline().rstrip().decode()
def readstrs():return list(readline().decode().split())
def readint():return int(readline())
def readints():return list(map(int,readline().split()))
def printrows(x):print('\n'.join(map(str,x)))
def printline(x):print(' '.join(map(str,x)))


r,c,k = readints()
a = [[0]*(c+1) for i in range(r+1)]

for i in range(k):
    R,C,V = readints()
    a[R][C] = V

dp = [0]*(r+1)*(c+1)*4

for x in range((r+1)*(c+1)*4):
    i = x//((c+1)*4)
    l = x%((c+1)*4)
    j = l//4
    l %= 4
    if i==0 or j==0:
        continue
    if l==0:
        dp[x] = max(dp[i*(c+1)*4 + (j-1)*4], dp[(i-1)*(c+1)*4 + j*4 + 3])
    else:
        dp[x] = max(dp[i*(c+1)*4 + (j-1)*4 + l], dp[(i-1)*(c+1)*4 + j*4 + 3]+a[i][j], dp[i*(c+1)*4 + (j-1)*4 + l-1]+a[i][j])

print(dp[-1])

Submission status: Accepted

Solution code:
R, C, K = map(int, input().split())
inf = float('inf')
v_list = [[0 for _ in range(C)] for _ in range(R)]
for _ in range(K):
    r, c, v = map(int, input().split())
    v_list[r - 1][c - 1] = v

dp = [[0, 0, 0, 0] for _ in range(C)]
for r in range(R):
    for c in range(C):
        if c > 0:
            dp[c][0] = max(dp[c])
            dp[c][1] = dp[c - 1][1]
            dp[c][2] = dp[c - 1][2]
            dp[c][3] = dp[c - 1][3]
        else:
            dp[c][0] = max(dp[c])
            dp[c][1] = 0
            dp[c][2] = 0
            dp[c][3] = 0
        if v_list[r][c] > 0:
            v = v_list[r][c]
            dp[c][3] = max(dp[c][2] + v, dp[c][3])
            dp[c][2] = max(dp[c][1] + v, dp[c][2])
            dp[c][1] = max(dp[c][0] + v, dp[c][1])            
print(max(dp[-1]))

Submission status: Accepted

Solution code:
import sys,heapq
input = sys.stdin.buffer.readline
 
R,C,k = map(int,input().split())
 
 
val = dict()
for _ in range(k):
    rr,cc,vv = map(int,input().split())
    rr -= 1
    cc -= 1
    val[rr*C + cc] = vv
 
dp = [[0,0,0,0] for i in range(C)]
dp2 = [[0,0,0,0] for i in range(C)]

for i in range(R):
    for j in range(C):
        idx  = j
        if i*C + j in val:
            v = val[i*C + j]
        else:
            v = 0
        if i%2 == 0:
            if i == 0:
                if j == 0:
                    dp[idx][1] = v
                else:
                    dp[idx][1] = max(dp[idx-1][1],v)
                    dp[idx][2] = max(dp[idx-1][2],dp[idx-1][1] + v)
                    dp[idx][3] = max(dp[idx-1][3],dp[idx-1][2] + v)
            else:
                if j == 0:
                    dp[idx][0] = max(dp2[idx][0],dp2[idx][1],dp2[idx][2],dp2[idx][3])
                    dp[idx][1] = dp[idx][0] + v
                else:
                    dp[idx][0] = max(dp2[idx][0],dp2[idx][1],dp2[idx][2],dp2[idx][3],dp[idx-1][0])
                    dp[idx][1] = max(dp[idx-1][1],dp[idx][0] + v)
                    dp[idx][2] = max(dp[idx-1][2],dp[idx-1][1] + v)
                    dp[idx][3] = max(dp[idx-1][3],dp[idx-1][2] + v)
        else:
            if i == 0:
                if j == 0:
                    dp2[idx][1] = v
                else:
                    dp2[idx][1] = max(dp2[idx-1][1],v)
                    dp2[idx][2] = max(dp2[idx-1][2],dp2[idx-1][1] + v)
                    dp2[idx][3] = max(dp2[idx-1][3],dp2[idx-1][2] + v)
            else:
                if j == 0:
                    dp2[idx][0] = max(dp[idx][0],dp[idx][1],dp[idx][2],dp[idx][3])
                    dp2[idx][1] = dp2[idx][0] + v
                else:
                    dp2[idx][0] = max(dp[idx][0],dp[idx][1],dp[idx][2],dp[idx][3],dp2[idx-1][0])
                    dp2[idx][1] = max(dp2[idx-1][1],dp2[idx][0] + v)
                    dp2[idx][2] = max(dp2[idx-1][2],dp2[idx-1][1] + v)
                    dp2[idx][3] = max(dp2[idx-1][3],dp2[idx-1][2] + v)
 
print(max(max(dp[-1]),max(dp2[-1])))

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
def main(R,C,K,rcv):
  inf=float('inf')
  dp0=[[-inf,-inf,-inf,0] for _ in range(C)]
  item=[[0]*C for _ in range(R)]
  for r,c,v in rcv:
    item[r-1][c-1]=v
  # dp0[c][j]:c列目の時点で残りちょうどj個取れる時の最大値
  for i in range(R):
    # i+1行目に対する操作
    # 遷移
    for j in range(C):
      if j>0:
        dp0[j][3]=max(dp0[j])
        dp0[j][0]=dp0[j-1][0]
        dp0[j][1]=dp0[j-1][1]
        dp0[j][2]=dp0[j-1][2]
      else:
        dp0[0][3]=max(dp0[0])
        dp0[0][2]=-inf
        dp0[0][1]=-inf
        dp0[0][0]=-inf 
      if item[i][j]>0:
        v=item[i][j]
        dp0[j][0]=max(dp0[j][0],dp0[j][1]+v)
        dp0[j][1]=max(dp0[j][1],dp0[j][2]+v)
        dp0[j][2]=max(dp0[j][2],dp0[j][3]+v)
  print(max(dp0[-1]))
if __name__=='__main__':
  R,C,K=map(int,input().split())
  rcv=[list(map(int,input().split())) for _ in range(K)]
  main(R,C,K,rcv)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
def main(R,C,K,rcv):
  inf=float('inf')
  dp0=[[-inf,-inf,-inf,0] for _ in range(C)]
  item=[[0]*C for _ in range(R)]
  for r,c,v in rcv:
    item[r-1][c-1]=v
  # dp0[c][j]:c列目の時点で残りちょうどj個取れる時の最大値
  for i in range(R):
    # i+1行目に対する操作
    # 初期化
    for j in range(C):
      dp0[j][3]=max(dp0[j])
      dp0[j][2]=-inf
      dp0[j][1]=-inf
      dp0[j][0]=-inf
    for j in range(C):
      if j>0:
        dp0[j][0]=max(dp0[j][0],dp0[j-1][0])
        dp0[j][1]=dp0[j-1][1]
        dp0[j][2]=dp0[j-1][2]
      if item[i][j]>0:
        v=item[i][j]
        dp0[j][0]=max(dp0[j][0],dp0[j][1]+v)
        dp0[j][1]=max(dp0[j][1],dp0[j][2]+v)
        dp0[j][2]=max(dp0[j][2],dp0[j][3]+v)
  print(max(dp0[-1]))
if __name__=='__main__':
  R,C,K=map(int,input().split())
  rcv=[list(map(int,input().split())) for _ in range(K)]
  main(R,C,K,rcv)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
# 文字列をinput()した場合、末尾に改行が入るので注意
def main(R,C,K,rcv):
  inf=float('inf')
  dp0=[[-inf,-inf,-inf,0] for _ in range(C)]
  dp1=[[-inf]*4 for _ in range(C)]
  dp0[0][3]=0
  rcv.sort(key=lambda x:C*R*x[0]+x[1])
  i=0
  nowc=0
  while i<K and rcv[i][0]==1:
    nextc=rcv[i][1]-1
    for j in range(nowc+1,nextc+1):
      dp0[j][0]=dp0[nowc][0]
      dp0[j][1]=dp0[nowc][1]
      dp0[j][2]=dp0[nowc][2]
    v=rcv[i][2]
    dp0[nextc][0]=max(dp0[nextc][0],dp0[nextc][1]+v)
    dp0[nextc][1]=max(dp0[nextc][1],dp0[nextc][2]+v)
    dp0[nextc][2]=max(dp0[nextc][2],dp0[nextc][3]+v)
    i+=1
    nowc=nextc
    for j in range(nowc+1,C):
      dp0[j][0]=dp0[nowc][0]
      dp0[j][1]=dp0[nowc][1]
      dp0[j][2]=dp0[nowc][2]
  for j in range(1,R):
    for c in range(C):
      dp0[c][3]=max(dp0[c])
      dp0[c][2]=-inf
      dp0[c][1]=-inf
      dp0[c][0]=-inf
    nowc=0
    while i<K and rcv[i][0]==j+1:
      nextc=rcv[i][1]-1
      for k in range(nowc+1,nextc+1):
        dp0[k][0]=dp0[nowc][0]
        dp0[k][1]=dp0[nowc][1]
        dp0[k][2]=dp0[nowc][2]
      v=rcv[i][2]
      dp0[nextc][0]=max(dp0[nextc][0],dp0[nextc][1]+v)
      dp0[nextc][1]=max(dp0[nextc][1],dp0[nextc][2]+v)
      dp0[nextc][2]=max(dp0[nextc][2],dp0[nextc][3]+v)
      i+=1
      nowc=nextc
    for j in range(nowc+1,C):
      dp0[j][0]=dp0[nowc][0]
      dp0[j][1]=dp0[nowc][1]
      dp0[j][2]=dp0[nowc][2]
    #print(dp0)

  print(max(dp0[-1]))


if __name__=='__main__':
  R,C,K=map(int,input().split())
  rcv=[list(map(int,input().split())) for _ in range(K)]
  #import datetime
  #print(datetime.datetime.now())
  main(R,C,K,rcv)
  #print(datetime.datetime.now())

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
def main(R,C,K,rcv):
  inf=float('inf')
  dp0=[[-inf,-inf,-inf,0] for _ in range(C)]
  # dp0[i][j]:i列目の時点で残りちょうどj個取れる時の最大値
  rcv.sort(key=lambda x:C*R*x[0]+x[1])
  i=0
  nowc=0
  for j in range(R):
    # j+1行目に対する操作
    # 初期化
    for c in range(C):
      dp0[c][3]=max(dp0[c])
      dp0[c][2]=-inf
      dp0[c][1]=-inf
      dp0[c][0]=-inf
    nowc=0
    while i<K and rcv[i][0]==j+1:
      nextc=rcv[i][1]-1
      for k in range(nowc+1,nextc+1):
        dp0[k][0]=max(dp0[k][0],dp0[nowc][0])
        dp0[k][1]=max(dp0[k][1],dp0[nowc][1])
        dp0[k][2]=max(dp0[k][2],dp0[nowc][2])
      v=rcv[i][2]
      dp0[nextc][0]=max(dp0[nextc][0],dp0[nextc][1]+v)
      dp0[nextc][1]=max(dp0[nextc][1],dp0[nextc][2]+v)
      dp0[nextc][2]=max(dp0[nextc][2],dp0[nextc][3]+v)
      i+=1
      nowc=nextc
    for k in range(nowc+1,C):
      dp0[k][0]=max(dp0[k][0],dp0[nowc][0])
      dp0[k][1]=max(dp0[k][1],dp0[nowc][1])
      dp0[k][2]=max(dp0[k][2],dp0[nowc][2])
    #print(dp0)
  print(max(dp0[-1]))
if __name__=='__main__':
  R,C,K=map(int,input().split())
  rcv=[list(map(int,input().split())) for _ in range(K)]
  main(R,C,K,rcv)

Submission status: Accepted

Solution code:
f=lambda:map(int,input().split())
R,C,K=f()
g=[[0]*(C+1) for _ in range(R+1)]
for _ in range(K):
  r,c,v=f()
  g[r][c]=v
dp=[[[0]*(C+2) for _ in range(R+2)] for _ in range(4)]
for i in range(1,R+1):
  for j in range(1,C+1):
    for k in range(3,-1,-1):
      if k: dp[k][i][j]=max(dp[k][i][j],dp[k-1][i][j]+g[i][j])
      dp[0][i+1][j]=max(dp[0][i+1][j],dp[k][i][j])
      dp[k][i][j+1]=max(dp[k][i][j+1],dp[k][i][j])
print(max(dp[k][R][C] for k in range(4)))

Submission status: Accepted

Solution code:
f=lambda:map(int,input().split())
R,C,K=f()
g=[[0]*(C+1) for _ in range(R+1)]
for _ in range(K):
  r,c,v=f()
  g[r][c]=v
dp=[[[0]*(C+2) for _ in range(R+2)] for _ in range(4)]
for i in range(1,R+1):
  for j in range(1,C+1):
    for k in range(3,-1,-1):
      if k: dp[k][i][j]=max(dp[k][i][j],dp[k-1][i][j]+g[i][j])
      dp[0][i+1][j]=max(dp[0][i+1][j],dp[k][i][j])
      dp[k][i][j+1]=max(dp[k][i][j+1],dp[k][i][j])
print(max(dp[i][R][C] for i in range(4)))

Submission status: Accepted

Solution code:
def solve():
    R,C,K = map(int, input().split())
    #value = [[0 for _ in range(C)] for _ in range(R)]
    dp = [[[0 for _ in range(C+1)] for _ in range (R+1)] for _ in range(5)]
    for _ in range(K):
        r,c,v = map(int, input().split())
        dp[4][r][c] = v

    #print(value)
    #print(dp)

    for r in range(1, R+1):
        for c in range(1, C+1):
            v = dp[4][r][c]
            prow = max(dp[0][r-1][c], dp[1][r-1][c], dp[2][r-1][c], dp[3][r-1][c])
            if v == 0: # no item
                dp[0][r][c] = max(prow, dp[0][r][c-1])
                dp[1][r][c] = dp[1][r][c-1]
                dp[2][r][c] = dp[2][r][c-1]
                dp[3][r][c] = dp[3][r][c-1]
            else:
                dp[0][r][c] = max(prow, dp[0][r][c-1])
                dp[1][r][c] = max(dp[1][r][c-1], dp[0][r][c-1] + v, prow + v)
                dp[2][r][c] = max(dp[2][r][c-1], dp[1][r][c-1] + v)
                dp[3][r][c] = max(dp[3][r][c-1], dp[2][r][c-1] + v)

    #print(dp)
    print(max(dp[0][R][C], dp[1][R][C], dp[2][R][C], dp[3][R][C]))

solve()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
R,C,K = map(int,input().split())
lis = [[0] * (C+1) for i in range(R+1)]
for _ in range(K):
    r,c,v = map(int,input().split())
    lis[r][c] = v

dp = [[[0] * (C+1) for _ in range(R+1)] for _ in range(4)]
#print(dp)
for i in range(1,R+1):
    for j in range(1,C+1):
        for k in range(4):
            dp[0][i][j] = max(dp[0][i][j],dp[k][i-1][j])
            dp[1][i][j] = max(dp[1][i][j],dp[k][i-1][j] + lis[i][j])

            dp[k][i][j] = max(dp[k][i][j],dp[k][i][j-1])
            if k > 0:
                dp[k][i][j] = max(dp[k][i][j],dp[k-1][i][j-1] + lis[i][j])
# print(dp[0])
# print(dp[1])
# print(dp[2])
# print(dp[3])
print(max(dp[0][R][C],dp[1][R][C],dp[2][R][C],dp[3][R][C]))

Submission status: Accepted

Solution code:
import numpy as np
from numba import jit


def test():
    R, C, K = map(int, input().split())
    rcv = [list(map(int, input().split())) for _ in range(K)]

    items = np.zeros((R+1, C+1), dtype='int64')
    for item in rcv:
        items[item[0]][item[1]] = item[2]

    dp = np.zeros((R+1, C+1), dtype='int64')

    # まずは3個の制約がない場合での実装
    for j in range(1, R+1):
        for i in range(1, C+1):
            # 下に行く遷移
            dp[j][i] = max(dp[j][i], dp[j-1][i] + items[j][i])

            # 右に行く遷移
            dp[j][i] = max(dp[j][i], dp[j][i-1] + items[j][i])

    print(dp[R][C])


@jit
def main(R, C, items):

    dp = np.zeros((4, R+1, C+1), dtype=np.int64)

    # 3個の制約がある場合の実装
    for i in range(1, R+1):
        for j in range(1, C+1):
            for k in range(4):
                # 下に行く遷移
                # 取らない場合
                dp[0][i][j] = max(dp[0][i][j], dp[k][i-1][j])
                # 取る場合
                dp[1][i][j] = max(dp[1][i][j], dp[k][i-1][j] + items[i][j])

                # 右に行く遷移
                # 取らない場合
                dp[k][i][j] = max(dp[k][i][j], dp[k][i][j-1])
                # 取る場合
                if k > 0:
                    dp[k][i][j] = max(dp[k][i][j], dp[k-1]
                                      [i][j-1] + items[i][j])

    ans = 0
    for k in range(4):
        if ans < dp[k][R][C]:
            ans = dp[k][R][C]

    print(ans)


if __name__ == "__main__":
    R, C, K = map(int, input().split())
    rcv = [list(map(int, input().split())) for _ in range(K)]
    items = np.zeros((R+1, C+1), dtype=np.int64)
    for item in rcv:
        items[item[0]][item[1]] = item[2]
    main(R, C, items)

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] * C for j in range(R)] for i in range(4)]

    for i in range(R):
        for j in range(C):
            ct = field[i ][j ]
            pm = max(dp[0][i-1][j],dp[1][i-1][j],dp[2][i-1][j],dp[3][i-1][j])
            if ct == 0:
                dp[0][i][j] = max(dp[0][i][j-1],pm)

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

    print(max(dp[0][R-1][C-1],dp[1][R-1][C-1],dp[2][R-1][C-1],dp[3][R-1][C-1]))

if __name__ == "__main__":
    main()

Submission status: Accepted

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

r, c, k = map(int, input().split())
v = [[0 for _ in range(c)] for _ in range(r)]

for i in range(k):
    rr, cc, vv = map(int, input().split())
    rr, cc = rr - 1, cc - 1
    v[rr][cc] = vv

dp = [[0 for _ in range(c + 1)] for _ in range(4)]
for y in range(r):
    tmp = [[0 for _ in range(c + 1)] for _ in range(4)]
    for x in range(c):
        for i in range(2, -1, -1):
            dp[i + 1][x] = max(dp[i + 1][x], dp[i][x] + v[y][x])
        for i in range(4):
            tmp[0][x] = max(tmp[0][x], dp[i][x])
            dp[i][x + 1] = max(dp[i][x + 1], dp[i][x])
    dp = tmp
print(dp[0][c - 1])

Submission status: Accepted

Solution code:
import sys
from itertools import product
input = lambda:sys.stdin.buffer.readline().rstrip()

m, n, k = map(int, input().split())
grid = [[0] * n for _ in range(m)]
for _ in range(k):
    i, j, v = map(int, input().split())
    i -= 1; j -= 1
    grid[i][j] = v

dp = [[0] * 4 for _ in range(n)]
for i in range(m):
    ndp = [[0] * 4 for _ in range(n)]
    for j, k in product(range(n), range(4)):
        # from top
        ndp[j][0] = max(ndp[j][0], dp[j][k])
        ndp[j][1] = max(ndp[j][1], dp[j][k] + grid[i][j])
        # from left
        if j > 0:
            ndp[j][k] = max(ndp[j][k], ndp[j - 1][k])
            if k > 0:
                ndp[j][k] = max(ndp[j][k], ndp[j - 1][k - 1] + grid[i][j])
    dp = ndp

print(max(dp[-1]))

Submission status: Accepted

Solution code:
# Date [ 2020-08-15 21:54:45 ]
# Problem [ e.py ]
# Author Koki_tkg

import sys;      from decimal import Decimal
import math;     from itertools import combinations, product
import bisect;   from collections import Counter, deque, defaultdict

# sys.setrecursionlimit(10 ** 6)
MOD = 10 ** 6 + 7
INF = 10 ** 9
PI = 3.14159265358979323846

def read_str():      return sys.stdin.readline().strip()
def read_int():      return int(sys.stdin.readline().strip())
def read_ints():     return map(int, sys.stdin.readline().strip().split())
def read_str_list(): return list(sys.stdin.readline().strip().split())
def read_int_list(): return list(map(int, sys.stdin.readline().strip().split()))
def lcm(a: int, b: int) -> int: return (a * b) // math.gcd(a, b)

from numba import njit, i8
import numpy as np

@njit(i8(i8, i8, i8[:,:]))
def dp(R, C, grid):
    dp = np.zeros((R+1, C+1, 4), np.int64)
    for y in range(1, R+1):
        for x in range(1, C+1):
            for i in range(4):
                dp[y][x][i] = max(dp[y][x - 1][i], dp[y - 1][x][3])
            for i in range(3, 0, -1):
                dp[y][x][i] = max(dp[y][x][i], dp[y][x][i - 1] + grid[y-1][x-1])
    return dp[R][C][3]

def Main():
    R, C, k = read_ints()
    item = [read_int_list() for _ in range(k)]
    grid = np.zeros((R, C), np.int64)
    for r, c, v in item:
        grid[r - 1][c - 1] = v
    print(dp(R, C, grid))

if __name__ ==  '__main__':
    Main()

Submission status: Accepted

Solution code:
R, C, K = map(int, input().split())
goods = [[0] * C for _ in range(R)]
for _ in range(K):
    r, c, v = map(int, input().split())
    goods[r-1][c-1] = v

dp = [[[0] * C for _ in range(4)] for _ in range(R)]
dp[0][1][0] = goods[0][0]
for i in range(R):
    for j in range(4):
        for k in range(C):
            if i < R - 1:
                dp[i+1][0][k] = max(dp[i+1][0][k], dp[i][j][k])
                dp[i+1][1][k] = max(dp[i+1][1][k], dp[i][j][k] + goods[i+1][k])
        
            if k < C - 1:
                dp[i][j][k+1] = max(dp[i][j][k+1], dp[i][j][k])
                if j < 3:
                    dp[i][j+1][k+1] = max(dp[i][j+1][k+1], dp[i][j][k] + goods[i][k+1])

res = 0
for i in range(4):
    res = max(res, dp[R-1][i][C-1])

print(res)

Submission status: Accepted

Solution code:
R, C, K = map(int, input().split())
goods = [[0] * C for _ in range(R)]
for _ in range(K):
    r, c, v = map(int, input().split())
    goods[r-1][c-1] = v

dp = [[[0] * C for _ in range(4)] for _ in range(R)]
dp[0][1][0] = goods[0][0]
for i in range(R):
    for j in range(4):
        for k in range(C):
            if i < R - 1:
                dp[i+1][0][k] = max(dp[i+1][0][k], dp[i][j][k])
                dp[i+1][1][k] = max(dp[i+1][1][k], dp[i][j][k] + goods[i+1][k])
        
            if k < C - 1:
                dp[i][j][k+1] = max(dp[i][j][k+1], dp[i][j][k])
                if j < 3:
                    dp[i][j+1][k+1] = max(dp[i][j+1][k+1], dp[i][j][k] + goods[i][k+1])

res = 0
for i in range(4):
    res = max(res, dp[R-1][i][C-1])
print(res)

Submission status: Accepted

Solution code:
R, C, K = map(int,input().split())
MAP = [[0 for i in range(C)] for j in range(R)]
DP = [[[0 for i in range(C+1)] for j in range(4)] for k in range(R+1)]
 
for _ in range(K):
    r, c, v = map(int,input().split())
    MAP[r-1][c-1] = v
 
for i in range(R):
    for j in range(4):
        for k in range(C):
            DP[i+1][j][k+1] = max(DP[i][3][k+1], DP[i+1][j][k])
            if j == 0:
                continue
            v = MAP[i][k]
            if v == 0:
                continue
            DP[i+1][j][k+1] = max(DP[i+1][j][k+1], max(DP[i][3][k+1], DP[i+1][j-1][k]) + v)

print(DP[R][3][C])

Submission status: Accepted

Solution code:
from numpy import zeros, int64
from numba import njit

R, C, K, *RCV = map(int64, open(0).read().split())
V = zeros((R + 1, C + 1), int64)
for r, c, v in zip(*[iter(RCV)] * 3):
    V[r][c] = v

@njit
def main():
    dp = zeros((R + 1, C + 1, 4), int64)
    for i in range(1, R + 1):
        for j in range(1, C + 1):

            vij = V[i][j]

            for k in range(4):
                dp[i][j][k] = max(
                    dp[i][j - 1][k],
                    dp[i - 1][j][3]
                )
            for k in range(3, 0, -1):
                dp[i][j][k] = max(
                    dp[i][j][k],
                    vij + dp[i][j][k - 1]
                )

    print(dp[R][C][3])

main()

Submission status: Accepted

Solution code:
import os
import sys

import numpy as np


def solve(inp):
    r, c, k = inp[:3]
    items = np.zeros((r + 1, c + 1), dtype=np.int64)
    rrr = inp[3::3]
    ccc = inp[4::3]
    vvv = inp[5::3]
    for r_, c_, v in zip(rrr, ccc, vvv):
        items[r_][c_] = v

    dp = np.zeros((r + 1, c + 1, 4), dtype=np.int64)

    for i in range(1, r + 1):
        for j in range(1, c + 1):
            for w in range(4):
                dp[i][j][w] = max(dp[i][j - 1][w], dp[i - 1][j][3])
            if items[i][j] > 0:
                for w in range(2, -1, -1):
                    dp[i][j][w + 1] = max(dp[i][j][w + 1], dp[i][j][w] + items[i][j])

    return dp[r][c][3]


if sys.argv[-1] == 'ONLINE_JUDGE':
    from numba.pycc import CC

    cc = CC('my_module')
    cc.export('solve', '(i8[:],)')(solve)
    cc.compile()
    exit()

if os.name == 'posix':
    # noinspection PyUnresolvedReferences
    from my_module import solve
else:
    from numba import njit

    solve = njit('(i8[:],)', cache=True)(solve)
    print('compiled', file=sys.stderr)

inp = np.fromstring(sys.stdin.read(), dtype=np.int64, sep=' ')
ans = solve(inp)
print(ans)

Submission status: Accepted

Solution code:
import os
import sys

import numpy as np


def solve(inp):
    r, c, k = inp[:3]
    items = np.zeros((r + 1, c + 1), dtype=np.int64)
    rrr = inp[3::3]
    ccc = inp[4::3]
    vvv = inp[5::3]
    for r_, c_, v in zip(rrr, ccc, vvv):
        items[r_, c_] = v

    dp = np.zeros((r + 1, c + 1, 4), dtype=np.int64)

    for i in range(1, r + 1):
        for j in range(1, c + 1):
            for w in range(4):
                dp[i, j, w] = max(dp[i, j - 1, w], dp[i - 1, j, 3])
            if items[i, j] > 0:
                for w in range(2, -1, -1):
                    dp[i, j, w + 1] = max(dp[i, j, w + 1], dp[i, j, w] + items[i, j])

    return dp[-1, -1, -1]


if sys.argv[-1] == 'ONLINE_JUDGE':
    from numba.pycc import CC

    cc = CC('my_module')
    cc.export('solve', '(i8[:],)')(solve)
    cc.compile()
    exit()

if os.name == 'posix':
    # noinspection PyUnresolvedReferences
    from my_module import solve
else:
    from numba import njit

    solve = njit('(i8[:],)', cache=True)(solve)
    print('compiled', file=sys.stderr)

inp = np.fromstring(sys.stdin.read(), dtype=np.int64, sep=' ')
ans = solve(inp)
print(ans)

Submission status: Accepted

Solution code:
import os
import sys

import numpy as np


def solve(inp):
    r, c, k = inp[:3]
    items = np.zeros((r + 1, c + 1), dtype=np.int64)
    rrr = inp[3::3]
    ccc = inp[4::3]
    vvv = inp[5::3]
    for r_, c_, v in zip(rrr, ccc, vvv):
        items[r_][c_] = v

    dp = np.zeros((r + 1, c + 1, 4), dtype=np.int64)

    for i in range(1, r + 1):
        for j in range(1, c + 1):
            up = dp[i - 1][j][3]
            for w in range(4):
                dp[i][j][w] = max(dp[i][j - 1][w], up)
            v = items[i][j]
            if v == 0:
                continue
            for w in range(2, -1, -1):
                dp[i][j][w + 1] = max(dp[i][j][w + 1], dp[i][j][w] + v)

    return dp[-1][-1][3]


if sys.argv[-1] == 'ONLINE_JUDGE':
    from numba.pycc import CC

    cc = CC('my_module')
    cc.export('solve', '(i8[:],)')(solve)
    cc.compile()
    exit()

if os.name == 'posix':
    # noinspection PyUnresolvedReferences
    from my_module import solve
else:
    from numba import njit

    solve = njit('(i8[:],)', cache=True)(solve)
    print('compiled', file=sys.stderr)

inp = np.fromstring(sys.stdin.read(), dtype=np.int64, sep=' ')
ans = solve(inp)
print(ans)

Submission status: Accepted

Solution code:
import os
import sys

import numpy as np


def solve(inp):
    r, c, k = inp[:3]
    items = np.zeros((r + 1, c + 1), dtype=np.int64)
    rrr = inp[3::3]
    ccc = inp[4::3]
    vvv = inp[5::3]
    for r_, c_, v in zip(rrr, ccc, vvv):
        items[r_, c_] = v

    dp = np.zeros((r + 1, c + 1, 4), dtype=np.int64)

    for i in range(1, r + 1):
        for j in range(1, c + 1):
            v = items[i, j]
            dp[i, j] = np.maximum(dp[i, j - 1], dp[i - 1, j, 3])
            if v > 0:
                dp[i, j, 1:] = np.maximum(dp[i, j, 1:], dp[i, j, :-1] + v)

    return dp[-1, -1, -1]


if sys.argv[-1] == 'ONLINE_JUDGE':
    from numba.pycc import CC

    cc = CC('my_module')
    cc.export('solve', '(i8[:],)')(solve)
    cc.compile()
    exit()

if os.name == 'posix':
    # noinspection PyUnresolvedReferences
    from my_module import solve
else:
    from numba import njit

    solve = njit('(i8[:],)', cache=True)(solve)
    print('compiled', file=sys.stderr)

inp = np.fromstring(sys.stdin.read(), dtype=np.int64, sep=' ')
ans = solve(inp)
print(ans)

Submission status: Accepted

Solution code:
import os
import sys

import numpy as np


def solve(inp):
    r, c, k = inp[:3]
    items = np.zeros((r + 1, c + 1), dtype=np.int64)
    rrr = inp[3::3]
    ccc = inp[4::3]
    vvv = inp[5::3]
    for r_, c_, v in zip(rrr, ccc, vvv):
        items[r_][c_] = v

    dp = np.zeros((c + 1, 4), dtype=np.int64)

    for i in range(1, r + 1):
        for j in range(1, c + 1):
            v = items[i][j]
            dp[j] = np.maximum(dp[j - 1], dp[j])
            if v > 0:
                dp[j, 1:] = np.maximum(dp[j, 1:], dp[j, :-1] + v)
        dp[:, 0] = dp[:, 1] = dp[:, 2] = dp[:, 3]

    return dp[-1][3]


if sys.argv[-1] == 'ONLINE_JUDGE':
    from numba.pycc import CC

    cc = CC('my_module')
    cc.export('solve', '(i8[:],)')(solve)
    cc.compile()
    exit()

if os.name == 'posix':
    # noinspection PyUnresolvedReferences
    from my_module import solve
else:
    from numba import njit

    solve = njit('(i8[:],)', cache=True)(solve)
    print('compiled', file=sys.stderr)

inp = np.fromstring(sys.stdin.read(), dtype=np.int64, sep=' ')
ans = solve(inp)
print(ans)