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

Solution (Python):
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from collections import defaultdict, deque, Counter
from sys import exit
from decimal import *
import heapq
from math import sqrt
from fractions import gcd
import random
import string
import copy
from itertools import combinations, permutations, product
from operator import mul, itemgetter
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7





R, C, K = getNM()
point = [[0] * C for i in range(R)]
for i in range(K):
    r, c, v = getNM()
    point[r - 1][c - 1] = v



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

for i in range(R):
    next = [[0] * 4 for _ in range(C + 1)]
    for j in range(C):
        
        
        
        for n in range(2, -1, -1):
            prev[j][n + 1] = max(prev[j][n + 1], prev[j][n] + point[i][j])

        
        for n in range(4):
            prev[j + 1][n] = max(prev[j + 1][n], prev[j][n])

        
        next[j][0] = max(prev[j])

    prev = next

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

Solution (Python):

R, C, K = map(int, input().split())
X = [list(map(int, input().split())) for _ in range(K)]

items = [[0] * (C + 1) for _ in range(R + 1)]
for r, c, v in X:
    items[r][c] = v

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

    
    for j in range(1, C + 1):
        for k in reversed(range(4)):
            dp[j][k] = max(dp[j][k], dp[j - 1][k])
            if items[i][j] and k < 3:
                dp[j][k + 1] = max(dp[j][k + 1], dp[j][k] + items[i][j])

print(max(dp[-1]))

Solution (Python):
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from collections import defaultdict, deque, Counter
from sys import exit
from decimal import *
import heapq
from math import sqrt
from fractions import gcd
import random
import string
import copy
from itertools import combinations, permutations, product
from operator import mul, itemgetter
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7





R, C, K = getNM()
point = [[0] * C for i in range(R)]
for i in range(K):
    r, c, v = getNM()
    point[r - 1][c - 1] = v


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

for i in range(R):
    next = [[0] * 4 for _ in range(C + 1)]
    for j in range(C):
        
        for n in range(2, -1, -1):
            prev[j][n + 1] = max(prev[j][n + 1], prev[j][n] + point[i][j])

        
        next[j][0] = max(prev[j])

        
        for n in range(4):
            prev[j + 1][n] = max(prev[j + 1][n], prev[j][n])
    prev = next

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

Solution (Python):
import sys,queue,math,copy,itertools,bisect,collections,heapq

def main():
    LI = lambda : [int(x) for x in sys.stdin.readline().split()]

    R,C,K = LI()

    m = [[0] * (C+1) for _ in range(R+1)]
    dp = [[0] * 4 for _ in range(C+1)]
    for _ in range(K):
        r,c,v = LI()
        m[r][c] = v

    for i in range(1,R+1):
        for j in range(1,C+1):
            b_max = max(dp[j])
            dp[j][0] = max(dp[j-1][0],b_max)
            if m[i][j] > 0:
                for k in range(1,4):
                    dp[j][k] = max(dp[j-1][k],dp[j-1][k-1]+m[i][j])
                dp[j][1] = max(dp[j][1],b_max+m[i][j])
            else:
                for k in range(1,4):
                    dp[j][k] = dp[j-1][k]
    print(max(dp[-1]))

if __name__ == '__main__':
    main()

Solution (Python):
import sys
input = sys.stdin.readline

R,C,K=list(map(int,input().split()))
itemMap = [[0]*(C+1) for _ in range(R+1)]
dp =[[[0]*(C+1) for _ in range(R+1)] for _ in range(4)]

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

for ir in range(R):
    for ic in range(C):
        for k in range(2,-1,-1):
            
            dp[k+1][ir][ic] = max(dp[k+1][ir][ic],dp[k][ir][ic]+itemMap[ir][ic])
        
        for k in range(4):
            dp[0][ir+1][ic] = max(dp[0][ir+1][ic],dp[k][ir][ic])
            dp[k][ir][ic+1] = max(dp[k][ir][ic+1],dp[k][ir][ic])

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

Solution (Python):
R, C, K = map(int, input().split())

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

grid = [[0] * C for _ in range(R)]
for _ in range(K):
    r, c, v = map(int, input().split())
    grid[r - 1][c - 1] = v
for i in range(R):
    for j in range(C):
        for k in range(2, -1, -1):
            
            
            dp2[k + 1][i][j] = max(dp2[k + 1][i][j], dp2[k][i][j] + grid[i][j])
        for k in range(4):
            
            dp2[0][i + 1][j] = max(dp2[0][i + 1][j], dp2[k][i][j])
            
            dp2[k][i][j + 1] = max(dp2[k][i][j + 1], dp2[k][i][j])
ans = 0
for k in range(4):
    
    ans = max(ans, dp2[k][R - 1][C - 1])
print(ans)

Solution (Python):
def main():
    import sys
    input = sys.stdin.readline

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

    G = [[0] * W for _ in range(H)]
    for _ in range(K):
        r, c, v = map(int, input().split())
        G[r - 1][c - 1] = v

    pdp = [[0] * 4 for _ in range(W)]
    for r in range(H):
        dp = [[0] * 4 for _ in range(W)]
        left = [0] * 4
        for c in range(W):
            cell = dp[c]

            for k in range(4):
                cell[k] = left[k]

            up = max(pdp[c])
            if cell[0] < up:
                cell[0] = up

            for k in range(2, -1, -1):
                cell[k + 1] = max(
                    cell[k + 1],
                    cell[k] + G[r][c])
            left = cell
        pdp = dp

    
    
    
    
    
    

    

    ans = max(dp[-1])
    print(ans)


if __name__ == '__main__':
    main()

Solution (Python):
R=3002
f=range(1,R)
G,*F=eval("eval('[0]*R,'*R),"*5)
for t in[*open(0)][1:]:r,c,v=map(int,t.split());G[r][c]=v
for r in f:
 for x in 1,2,3:
  for c in f:F[x][r][c]=max(F[x-1][r][c],max(F[x-1][r][c-1],(x<2)*F[3][r-1][c])+G[r][c],F[x][r][c-1])
print(F[3][-1][-1])

Solution (Python):
R,C,K=map(int,input().split())
m=[[0]*(C+1) for _ in range(R+1)]
for _ in range(K):
  r,c,v=map(int,input().split())
  m[r][c]=v
d=[[0]*4 for _ in range(R+1)]
for j in range(1,C+1):
  for i in range(1,R+1):
    t=m[i][j]
    if t>0:
      d[i][3]=max(d[i][3],d[i][2]+t)
      d[i][2]=max(d[i][2],d[i][1]+t)
      d[i][1]=max(d[i][1],d[i][0]+t,max(d[i-1])+t)
      d[i][0]=max(d[i][0],max(d[i-1]))
    else:
      d[i][0]=max(d[i][0],max(d[i-1]))
print(max(d[R]))

Solution (Python):
(R,C,K),*t=[map(int,t.split())for t in open(0)]
G,*F=eval("eval('[0]*-~C,'*R),"*5)
for r,c,v in t:G[r-1][c]=v
for r in range(R):
 for x in 1,2,3:
  for c in range(C):F[x][r][c]=max(F[x-1][r][c],max(F[x-1][r][c-1],(x<2)*F[3][r-1][c])+G[r][c+1],F[x][r][c-1])
print(F[3][-1][-2])

Solution (Python):
f,h=range,input
R,C,K=map(int,h().split())
l=lambda:[-~C*[0]for i in f(R+1)]
G=l()
for i in'_'*K:r,c,v=map(int,h().split());G[r][c]=v
F=[l()for i in f(4)]
for r in f(1,R+1):
	for x in f(3):
		for c in f(1,C+1):F[x+1][r][c]=max(F[x][r][c],max(F[x][r][c-1],(x<1)*F[3][r-1][c])+G[r][c],F[x+1][r][c-1])
print(F[3][R][C])

Solution (Python):
f,h=range,input
R,C,K=map(int,h().split())
l=lambda:[-~C*[0]for i in f(R+1)]
G=l()
for i in'_'*K:r,c,v=map(int,h().split());G[r][c]=v
F=[l()for i in f(4)]
for r in f(1,R+1):
	for x in f(1,4):
		for c in f(1,C+1):F[x][r][c]=max(F[x-1][r][c],max(F[x-1][r][c-1],(x<2)*F[3][r-1][c])+G[r][c],F[x][r][c-1])
print(F[3][R][C])

Solution (Python):
f,h=range,input
R,C,K=map(int,h().split())
G=[-~C*[0]for i in f(R+1)]
for i in'_'*K:r,c,v=map(int,h().split());G[r][c]=v
F=[[-~C*[0]for i in f(R+1)]for i in f(4)]
for r in f(1,R+1):
	for x in f(1,4):
		for c in f(1,C+1):F[x][r][c]=max(F[x-1][r][c],max(F[x-1][r][c-1],(x<2)*F[3][r-1][c])+G[r][c],F[x][r][c-1])
print(F[3][R][C])

Solution (Python):
f,h=range,input
R,C,K=map(int,h().split())
G=[[0]*-~C for i in f(R+1)]
for i in'_'*K:r,c,v=map(int,h().split());G[r][c]=v
F=[[[0]*-~C for i in f(R+1)]for i in f(4)]
for r in f(1,R+1):
	for x in f(1,4):
		for c in f(1,C+1):F[x][r][c]=max(F[x-1][r][c],max(F[x-1][r][c-1],(x<2)*F[3][r-1][c])+G[r][c],F[x][r][c-1])
print(F[3][R][C])

Solution (Python):
f,g,h=range,max,input
R,C,K=map(int,h().split())
G=[[0]*-~C for i in f(R+1)]
for i in'_'*K:r,c,v=map(int,h().split());G[r][c]=v
F=[[[0]*-~C for i in f(R+1)]for i in f(4)]
for r in f(1,R+1):
	for x in f(1,4):
		for c in f(1,C+1):F[x][r][c]=g(F[x-1][r][c],F[x-1][r][c-1]+G[r][c],F[x][r][c-1],(x<2)*(G[r][c]+F[3][r-1][c]))
print(F[3][R][C])

Solution (Python):
f,g,h=range,max,input
R,C,K=map(int,h().split())
G=[[0]*-~C for i in f(R+1)]
for i in'_'*K:r,c,v=map(int,h().split());G[r][c]=v
F=[[[0]*-~C for i in f(R+1)]for i in f(4)]
for r in f(1,R+1):
	for x in f(1,4):
		for c in f(1,C+1):F[x][r][c]=g(F[x-1][r][c],F[x-1][r][c-1]+G[r][c],F[x][r][c-1],(x<2)*(G[r][c]+g(F[1][r-1][c],F[2][r-1][c],F[3][r-1][c])))
print(F[3][R][C])

Solution (Python):
R,C,K=map(int,input().split())
f,g=range,max
G=[[0]*(C+1)for i in f(R+1)]
for i in'_'*K:r,c,v=map(int,input().split());G[r][c]=v
F=[[[0]*(C+1)for i in f(R+1)]for i in f(4)]
for r in f(1,R+1):
	for x in f(1,4):
		for c in f(1,C+1):F[x][r][c]=g(F[x-1][r][c-1]+G[r][c],F[x][r][c-1],(x<2)*(G[r][c]+g(F[1][r-1][c],F[2][r-1][c],F[3][r-1][c])))
print(g(F[1][R][C],F[2][R][C],F[3][R][C]))

Solution (Python):
import sys
import math
import collections
import bisect
import itertools



sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7


ni = lambda: int(sys.stdin.readline().rstrip())
ns = lambda: map(int, sys.stdin.readline().rstrip().split())
na = lambda: list(map(int, sys.stdin.readline().rstrip().split()))
na1 = lambda: list(map(lambda x: int(x) - 1, sys.stdin.readline().rstrip().split()))




def main():
    r, c, k = ns()

    mat = [[0 for _ in range(c + 1)] for __ in range(r + 1)]
    for _ in range(k):
        x, y, v = ns()
        x, y = x - 1, y - 1
        mat[x][y] = v

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

    for i in range(r):
        ndp = [[0] * 4 for _ in range(c + 1)]
        for j in range(c):
            for n in range(2, -1, -1):
                dp[j][n + 1] = max(dp[j][n + 1], dp[j][n] + mat[i][j])

            ndp[j][0] = max(dp[j])
            for n in range(4):
                dp[j + 1][n] = max(dp[j + 1][n], dp[j][n])
        dp = ndp

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


if __name__ == '__main__':
    main()

Solution (Python):
import sys
import math
import collections
import bisect
import itertools



sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7


ni = lambda: int(sys.stdin.readline().rstrip())
ns = lambda: map(int, sys.stdin.readline().rstrip().split())
na = lambda: list(map(int, sys.stdin.readline().rstrip().split()))
na1 = lambda: list(map(lambda x: int(x) - 1, sys.stdin.readline().rstrip().split()))




def main():
    r, c, k = ns()

    mat = [[0]*(c + 1) for __ in range(r + 1)]
    for _ in range(k):
        x, y, v = ns()
        x, y = x - 1, y - 1
        mat[x][y] = v

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

    for i in range(r):
        ndp = [[0]*4 for _ in range(c + 1)]
        for j in range(c):
            for n in range(2, -1, -1):
                dp[j][n + 1] = max(dp[j][n + 1], dp[j][n] + mat[i][j])

            ndp[j][0] = max(dp[j])
            for n in range(4):
                dp[j + 1][n] = max(dp[j + 1][n], dp[j][n])
        dp = ndp

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


if __name__ == '__main__':
    main()

Solution (Python):
import sys
import math
import collections
import bisect
import itertools



sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7


ni = lambda: int(sys.stdin.readline().rstrip())
ns = lambda: map(int, sys.stdin.readline().rstrip().split())
na = lambda: list(map(int, sys.stdin.readline().rstrip().split()))
na1 = lambda: list(map(lambda x: int(x) - 1, sys.stdin.readline().rstrip().split()))




def main():
    r, c, k = ns()

    mat = [[0 for _ in range(c + 1)] for __ in range(r + 1)]
    for _ in range(k):
        x, y, v = ns()
        x, y = x - 1, y - 1
        mat[x][y] = v

    dp = [[0 for __ in range(4)] for _ in range(c + 1)]

    for i in range(r):
        ndp = [[0 for __ in range(4)] for _ in range(c + 1)]
        for j in range(c):
            for n in range(2, -1, -1):
                dp[j][n + 1] = max(dp[j][n + 1], dp[j][n] + mat[i][j])

            ndp[j][0] = max(dp[j])
            for n in range(4):
                dp[j + 1][n] = max(dp[j + 1][n], dp[j][n])
        dp = ndp

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


if __name__ == '__main__':
    main()

Solution (Python):
import sys
import math
import collections
import bisect
import itertools



sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7


ni = lambda: int(sys.stdin.readline().rstrip())
ns = lambda: map(int, sys.stdin.readline().rstrip().split())
na = lambda: list(map(int, sys.stdin.readline().rstrip().split()))
na1 = lambda: list(map(lambda x: int(x) - 1, sys.stdin.readline().rstrip().split()))




def main():
    r, c, k = ns()

    mat = [[0 for _ in range(c + 1)] for __ in range(r + 1)]
    for _ in range(k):
        x, y, v = ns()
        x, y = x - 1, y - 1
        mat[x][y] = v

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

    for i in range(r):
        ndp = [[0] * 4 for _ in range(c + 1)]
        for j in range(c):
            for n in range(2, -1, -1):
                dp[j][n + 1] = max(dp[j][n + 1], dp[j][n] + mat[i][j])

            ndp[j][0] = max(dp[j])
            for n in range(4):
                dp[j + 1][n] = max(dp[j + 1][n], dp[j][n])
        dp = ndp

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


if __name__ == '__main__':
    main()

Solution (Python):
R,C,K=map(int,input().split())
m=[[0]*(C+1) for _ in range(R+1)]
for _ in range(K):
  r,c,v=map(int,input().split())
  m[r][c]=v
d=[[0]*4 for _ in range(R+1)]
for j in range(1,C+1):
  for i in range(1,R+1):
    t=m[i][j]
    if t>0:
      d[i][3]=max(d[i][3],d[i][2]+t)
      d[i][2]=max(d[i][2],d[i][1]+t)
      d[i][1]=max(d[i][1],d[i][0]+t,max(d[i-1])+t)
      d[i][0]=max(d[i][0],max(d[i-1]))
    else:
      d[i][0]=max(d[i][0],max(d[i-1]))
print(max(d[R]))

Solution (Python):
import sys
input = sys.stdin.buffer.readline
R,C,K = map(int,input().split())
goods = [[0]*(C+1) for _ in range(R+1)]
INF = 10**18
for i in range(K):
    ri,ci,vi = map(int,input().split())
    goods[ri][ci] = vi
DP = [[[-INF]*(C+1) for _ in range(R+1)] for _ in range(4)]
DP[0][1][1] = 0
if goods[1][1]:
    DP[1][1][1] = goods[1][1]
for j in range(1,C):
    DP[0][1][j+1] = 0
    if goods[1][j+1]:
        DP[1][1][j+1] = max(DP[1][1][j],DP[0][1][j]+goods[1][j+1])
        DP[2][1][j+1] = max(DP[2][1][j],DP[1][1][j]+goods[1][j+1])
        DP[3][1][j+1] = max(DP[3][1][j],DP[2][1][j]+goods[1][j+1])
    else:
        DP[1][1][j+1] = DP[1][1][j]
        DP[2][1][j+1] = DP[2][1][j]
        DP[3][1][j+1] = DP[3][1][j]
for i in range(1,R):
    DP[0][i+1][1] = max(DP[0][i][1],DP[1][i][1],DP[2][i][1],DP[3][i][1])
    if goods[i+1][1]:
        DP[1][i+1][1] = DP[0][i+1][1] + goods[i+1][1]
for i in range(2,R+1):
    for j in range(2,C+1):
        DP[0][i][j] = max(DP[0][i-1][j],DP[1][i-1][j],DP[2][i-1][j],DP[3][i-1][j],DP[0][i][j-1])
        if goods[i][j]:
            DP[1][i][j] = max(DP[0][i][j]+goods[i][j],DP[1][i][j-1])
            DP[2][i][j] = max(DP[2][i][j-1],DP[1][i][j-1]+goods[i][j])
            DP[3][i][j] = max(DP[3][i][j-1],DP[2][i][j-1]+goods[i][j])
        else:
            DP[1][i][j] = DP[1][i][j-1]
            DP[2][i][j] = DP[2][i][j-1]
            DP[3][i][j] = DP[3][i][j-1]
print(max(DP[0][R][C],DP[1][R][C],DP[2][R][C],DP[3][R][C]))

Solution (Python):
R, C, K = map(int, input().split())

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

memo = [[0]*4 for _ in range(R+1)]

for j in range(1,C+1):
  for i in range(1,R+1):
    if mp[i][j] > 0:
      memo[i][3] = max(memo[i][3], memo[i][2] + mp[i][j])
      memo[i][2] = max(memo[i][2], memo[i][1] + mp[i][j])
      memo[i][1] = max(memo[i][1], memo[i][0] + mp[i][j], max(memo[i-1])+mp[i][j])
      memo[i][0] = max(memo[i][0], max(memo[i-1]))
    else:
      memo[i][0] = max(memo[i][0], max(memo[i-1]))
      
print(max(memo[R]))

Solution (Python):
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(R + 1)]

for x in range(1, C+1):
    for y in range(1, R+1):
        v = Items[y][x]
        if v:
            DP[y][3] = max(DP[y][3], DP[y][2] + v)
            DP[y][2] = max(DP[y][2], DP[y][1] + v)
            DP[y][1] = max(max(DP[y][1], DP[y][0] + v), max(DP[y-1]) + v)
            DP[y][0] = max(DP[y][0], max(DP[y-1]))
        else:
            DP[y][0] = max(DP[y][0], max(DP[y-1]))

print(max(DP[R]))

Solution (Python):
r, c, k = map(int, input().split())
dp = [[[0] * (c+1) for _ in range(r+1)] for _ in range(4)]

v_dict = dict()
for _ in range(k):
    y, x, v = map(int, input().split())
    v_dict[(y, x)] = v

for y in range(1, r+1):
    for x in range(1, c+1):
        prev_y_max = 0
        for i in range(4):
            prev_y_max = max(dp[i][y-1][x], prev_y_max)
        dp[0][y][x] = max(prev_y_max, dp[0][y][x-1])
        if (y, x) in v_dict:
            v = v_dict[(y, x)]
            dp[1][y][x] = max(prev_y_max + v, dp[0][y][x-1] + v, dp[1][y][x-1])
            dp[2][y][x] = max(dp[1][y][x-1] + v, dp[2][y][x-1])
            dp[3][y][x] = max(dp[2][y][x-1] + v, dp[3][y][x-1])
        else:
            for i in range(1, 4):
                dp[i][y][x] = dp[i][y][x-1]
ans = 0
for i in range(4):
    ans = max(dp[i][r][c], ans)
print(ans)

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

Solution (Python):
from copy import copy

C,R,K=map(int,input().split())
dp=[[0]*(R+1) for i1 in range(4)]
M=[[0]*R for i in range(C)]
for i in range(K):
    r,c,v=map(int,input().split())
    M[r-1][c-1]=v
for i,l in enumerate(M):
    for num in range(1,4):
        for j in range(R):
            if num==1:
                dp[num][j]= max(dp[num][j-1],dp[num-1][j-1]+M[i][j])
            else:
                dp[num][j]= max(dp[num][j-1],dp[num-1][j],dp[num-1][j-1]+M[i][j])
    dp[0]=dp[-1][1:-1]+[0,dp[-1][0]]

print(dp[-1][-2])

Solution (Python):
import io
import os
from collections import defaultdict

DEBUG = False
if not DEBUG:

    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    R, C, K = [int(x) for x in input().split()]
    grid = [[0 for c in range(C)] for r in range(R)]
    for r, c, v in ((int(x) for x in input().split()) for i in range(K)):
        grid[r - 1][c - 1] = v
else:
    import random

    random.seed(0)
    R, C = 3000, 3000
    
    grid = [
        [int(random.randint(1, 90) <= 2) * random.randint(0, 10 ** 9) for c in range(C)]
        for r in range(R)
    ]
    print(sum(bool(grid[r][c]) for r in range(R) for c in range(C)))
    print("done gen")

    from timeit import default_timer as timer

    startTime = timer()


currRow = [[0 for i in range(3 + 1)] for c in range(C + 1)]
prevRow = [0 for c in range(C + 1)]
nextPrevRow = [0 for c in range(C + 1)]

inf = float("inf")
for r in range(R):
    for c in range(C):
        for numTakenThisRow in range(3 + 1):
            best = max(
                currRow[c - 1][numTakenThisRow],  
                prevRow[c],  
                currRow[c - 1][numTakenThisRow - 1] + grid[r][c]
                if numTakenThisRow
                else 0,  
                prevRow[c] + grid[r][c]
                if numTakenThisRow == 1
                else 0,  
            )
            currRow[c][numTakenThisRow] = best
        nextPrevRow[c] = max(currRow[c][i] for i in range(3 + 1))
    prevRow, nextPrevRow = nextPrevRow, prevRow
print(prevRow[C - 1])

if DEBUG:
    print(timer() - startTime)

Solution (Python):
import sys
from pprint import pprint

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

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

for i in range(1,R+1):
    cell=[0]*4
    for j in range(C):
        cell[0]=max(cell[0],grid[i-1][j])
        for k in range(2,-1,-1):
            cell[k+1]=max(cell[k+1],cell[k]+grid[i][j])
        grid[i][j]=max(cell)

print(grid[-1][-1])

Solution (Python):


r,c,k=list(map(int,input().split()))

rck=[[0 for i in range(c+1)] for j in range(r+1)]
for i in range(k):
     r_num,c_num,k_num=list(map(int,input().split()))
     rck[r_num][c_num]=k_num


dp_0=[[0 for j in range(c+1)] for k in range(r+1)]
dp_1=[[0 for j in range(c+1)] for k in range(r+1)]
dp_2=[[0 for j in range(c+1)] for k in range(r+1)]
dp_3=[[0 for j in range(c+1)] for k in range(r+1)]

for i in range(1,r+1):
  for j in range(1,c+1):
    dp_1[i][j]=max(dp_3[i-1][j]+rck[i][j],dp_0[i][j-1]+rck[i][j],dp_0[i][j],dp_1[i][j-1])
    dp_2[i][j]=max(dp_3[i-1][j]+rck[i][j],dp_1[i][j-1]+rck[i][j],dp_1[i][j],dp_2[i][j-1])
    dp_3[i][j]=max(dp_3[i-1][j]+rck[i][j],dp_2[i][j-1]+rck[i][j],dp_2[i][j],dp_3[i][j-1])
    
    
    
    
    
    
print(dp_3[r][c])

Solution (Python):
import os,io
input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
r,c,k=map(int,input().split())
dp = [0]*(r*c*4)
m=[0]*(r*c)
for i in range(k):
  ri,ci,v=map(int,input().split())
  m[(ri-1)*c+ci-1]=v
dp[0*r*c+0*c+0]=0
dp[1*r*c+0*c+0]=m[0]
dp[2*r*c+0*c+0]=m[0]
dp[3*r*c+0*c+0]=m[0]
for i in range(r):
  for j in range(c):
    if j+1<c:
      dp[0*r*c+i*c+j+1]=max(dp[0*r*c+i*c+j+1],dp[0*r*c+i*c+j])
      dp[1*r*c+i*c+j+1]=max(dp[1*r*c+i*c+j],max(dp[1*r*c+i*c+j+1],dp[0*r*c+i*c+j]+m[i*c+j+1]))
      dp[2*r*c+i*c+j+1]=max(dp[2*r*c+i*c+j],max(dp[2*r*c+i*c+j+1],dp[1*r*c+i*c+j]+m[i*c+j+1]))
      dp[3*r*c+i*c+j+1]=max(dp[3*r*c+i*c+j],max(dp[3*r*c+i*c+j+1],dp[2*r*c+i*c+j]+m[i*c+j+1]))
    if i+1<r:
      a=dp[3*r*c+i*c+j]
      b=a+m[(i+1)*c+j]
      dp[0*r*c+(i+1)*c+j]=a
      dp[1*r*c+(i+1)*c+j]=b
      dp[2*r*c+(i+1)*c+j]=b
      dp[3*r*c+(i+1)*c+j]=b
print(dp[3*r*c+(r-1)*c+c-1])

Solution (Python):
def main(R,C,K,V):
    dp = [0]*(4*R*C)
    dp[1+4*0+4*C*0] = V[0][0]
    for k in range(4*R*C):
        n = k%4
        j = k//4%C
        i = k//(4*C)
        if n!=0:
            if i != 0 and n==1:
                dp[k] = max(dp[k-4*C-n:k-4*C-n+4])+V[i][j]
            if j != 0:
                dp[k] = max(dp[k],dp[k-4],dp[k-5]+V[i][j])
        if n==0:
            if i != 0:
                dp[k] = max(dp[k-4*C-n:k-4*C-n+4])

    print(max(dp[-5:-1]))

if __name__ == '__main__':
    R,C,K = map(int,input().split())
    C += 1
    rcv = [list(map(int,input().split())) for _ in range(K)]
    V = [[0]*C for _ in range(R)]
    for i in range(K):
        r,c,v = rcv[i]
        r -= 1
        c -= 1
        V[r][c] = v
    main(R,C,K,V)

Solution (Python):
R, C, K = map(int, input().split())
V = [[0 for _ in range(C)] for _ in range(R)]
for _ in range(K):
  r, c, v = map(int, input().split())
  V[r-1][c-1] = v
M = [0] * R * C * 4 




for r in range(R):
  for c in range(C):
    for n_pick in [0, 1] if V[r][c] else [0]:
      M[r*C*4 + c*4 +n_pick] = max(M[r*C*4 + c*4 +n_pick], n_pick*V[r][c])
      if r > 0:
        for n_prev in range(4):
          
          if M[(r-1)*C*4 + c*4 +n_prev] > 0 or n_prev == 0:
            M[r*C*4 + c*4 +n_pick]=max(M[r*C*4 + c*4 +n_pick],
              M[(r-1)*C*4 + c*4 +n_prev] + n_pick*V[r][c])
      if c > 0:
        for n_prev in range(4 - n_pick):
          
          if  M[r*C*4 + (c-1)*4 +n_prev]  > 0 or n_prev == 0:
            M[r*C*4 + c*4 +n_prev+n_pick]=max(M[r*C*4 + c*4 + n_prev+n_pick],
              M[r*C*4 + (c-1)*4 +n_prev] + n_pick*V[r][c])
    
    
    
    
    

print(max(M[((R-1)*C*4 + (C-1) *4):((R-1)*C*4 + (C-1) *4+4)]))

Solution (Python):


import sys
input=sys.stdin.readline

r,c,k=map(int,input().split())
items=[0]*(r*c)
for _ in range(k):
    tr,tc,tv=map(int,input().split())
    items[c*(tr-1)+tc-1]=tv
dp=[0]*(4*r*c)
for i in range(1,r+1):
    for j in range(1,c+1):
        tv=items[c*(i-1)+j-1]
        change_pos=4*(c*(i-1)+j-1)
        left_pos=4*(c*(i-2)+j-1)
        up_pos=4*(c*(i-1)+j-2)
        if i!=1:
          left_max=max(dp[left_pos],dp[left_pos+1],dp[left_pos+2],dp[left_pos+3])
        else:
          left_max=0
        if j!=1:
          dp[change_pos]=max(dp[up_pos],left_max)
          dp[change_pos+1]=max(dp[up_pos+1],dp[up_pos]+tv,left_max+tv)        
          dp[change_pos+2]=max(dp[up_pos+2],dp[up_pos+1]+tv)
          dp[change_pos+3]=max(dp[up_pos+3],dp[up_pos+2]+tv)
        else:
          dp[change_pos]=left_max
          dp[change_pos+1]=left_max+tv
print(max(dp[-1],dp[-2],dp[-3],dp[-4]))

Solution (Python):

(R, C, K), *D = [[*map(int,o.split())] for o in open(0)]
V = [[0] * C for _ in [None] * R]
for r, c, v in D:
    V[r - 1][c - 1] = v

dp = [[[-1] * C for _ in [None] * R] for _ in [None] * 4]

dp[0][0][0] = 0
for r in range(R):
    for c in range(C):
        v = V[r][c]
        for i in range(4):
            if dp[i][r][c] > -1:
                if r < R - 1:
                    dp[0][r + 1][c] = max(dp[0][r + 1][c], dp[i][r][c])
                if c < C - 1:
                    dp[i][r][c + 1] = max(dp[i][r][c + 1], dp[i][r][c])
                if i < 3 and v:
                    if r < R - 1:
                        dp[0][r + 1][c] = max(dp[0][r + 1][c], dp[i][r][c] + v)
                    if c < C - 1:
                        dp[i + 1][r][c + 1] = max(dp[i + 1][r][c + 1], dp[i][r][c] + v)

v = V[R - 1][C - 1]
ans = dp[3][R - 1][C - 1]
for i in range(3):
    ans = max(ans, dp[i][R - 1][C - 1] + v)
print(ans)

Solution (Python):

import sys
input = sys.stdin.readline

R, C, K = map(int, input().split())
V = [[0] * C for _ in [None] * R]
for _ in [None] * K:
    r, c, v = map(int, input().split())
    V[r - 1][c - 1] = v

dp = [[[-1] * C for _ in [None] * R] for _ in [None] * 4]

dp[0][0][0] = 0
for r in range(R):
    for c in range(C):
        v = V[r][c]
        for i in range(4):
            if dp[i][r][c] > -1:
                if r < R - 1:
                    dp[0][r + 1][c] = max(dp[0][r + 1][c], dp[i][r][c])
                if c < C - 1:
                    dp[i][r][c + 1] = max(dp[i][r][c + 1], dp[i][r][c])
                if i < 3 and v:
                    if r < R - 1:
                        dp[0][r + 1][c] = max(dp[0][r + 1][c], dp[i][r][c] + v)
                    if c < C - 1:
                        dp[i + 1][r][c + 1] = max(dp[i + 1][r][c + 1], dp[i][r][c] + v)

v = V[R - 1][C - 1]
ans = dp[3][R - 1][C - 1]
for i in range(3):
    ans = max(ans, dp[i][R - 1][C - 1] + v)
print(ans)