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):
R,C,K = map(int, input().split())
a = [[0] * (C+1) for i in range(R+1)]
dp = [[[0] * (C+1) for i in range(R+1)] for j in range(4)]
for i in range(K):
  r,c,v = map(int, input().split())
  a[r-1][c-1] = v

for i in range(R):
  for j in range(C):
    for k in range(2, -1, -1):
      dp[k+1][i][j] = max(dp[k+1][i][j], dp[k][i][j]+a[i][j])
    for k in range(4):
      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])

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

for h in range(R):
    for w in range(C):
        if h!=0:
            dp[0][h][w] = max(dp[0][h][w], dp[0][h-1][w], dp[1][h-1][w],  dp[2][h-1][w],  dp[3][h-1][w])
            dp[1][h][w] = max(dp[1][h][w], dp[0][h-1][w]+item[h][w], dp[1][h-1][w]+item[h][w], dp[2][h-1][w]+item[h][w], dp[3][h-1][w]+item[h][w])
        if w!=0:
            dp[0][h][w] = max(dp[0][h][w], dp[0][h][w-1])
            dp[1][h][w] = max(dp[1][h][w], dp[1][h][w-1], dp[0][h][w-1]+item[h][w])
            dp[2][h][w] = max(dp[2][h][w], dp[2][h][w-1], dp[1][h][w-1]+item[h][w])
            dp[3][h][w] = max(dp[3][h][w], dp[3][h][w-1], dp[2][h][w-1]+item[h][w])
ans = []
for k in range(4):
    ans.append(dp[k][-1][-1])
print(max(ans))

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

grid = [[0 for c in range(C)] for r in range(R)]

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

dp = [[[-1000 for c in range(C)] for r in range(R)] for k in range(4)]

if grid[0][0] > 0:
    dp[1][0][0] = grid[0][0]
dp[0][0][0] = 0

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

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]))

Solution (Python):
import base64

exec(base64.b64decode(b'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'))

Solution (Python):
import base64

exec(base64.b64decode(b'import subprocess
import sys

code = r"""#pragma GCC optimize("unroll-loops")

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstring>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <vector>

using namespace std;

using int64 = long long;

#define all(_) begin(_), end(_)
#define rall(_) rbegin(_), rend(_)

int64 dp[3000][3000][4];

namespace FastIO {
class Scanner {
  static constexpr int buf_size = (1 << 18);
  static constexpr int integer_size = 20;
  static constexpr int string_size = 1000; // default
  char buf[buf_size] = {};
  char *cur = buf, *ed = buf;

 public:
  Scanner() {}

  template <class T>
  inline Scanner& operator>>(T& val) {
    read(val);
    return *this;
  }

 private:
  inline void reload() {
    size_t len = ed - cur;
    memmove(buf, cur, len);
    char* tmp = buf + len;
    ed = tmp + fread(tmp, 1, buf_size - len, stdin);
    *ed = 0;
    cur = buf;
  }

  inline void skip_space() {
    while (true) {
      if (cur == ed) reload();
      while (*cur == ' ' || *cur == '\n') ++cur;
      if (__builtin_expect(cur != ed, 1)) return;
    }
  }

  template <class T, std::enable_if_t<std::is_same<T, int>::value, int> = 0>
  inline void read(T& num) {
    skip_space();
    if (cur + integer_size >= ed) reload();
    bool neg = false;
    num = 0;
    if (*cur == '-') neg = true, ++cur;
    while (*cur >= '0') num = num * 10 + (*cur ^ 48), ++cur;
    if (neg) num = -num;
  }

  template <class T, std::enable_if_t<std::is_same<T, int64>::value, int> = 0>
  inline void read(T& num) {
    skip_space();
    if (cur + integer_size >= ed) reload();
    bool neg = false;
    num = 0;
    if (*cur == '-') neg = true, ++cur;
    while (*cur >= '0') num = num * 10 + (*cur ^ 48), ++cur;
    if (neg) num = -num;
  }

  template <class T,
            std::enable_if_t<std::is_same<T, std::string>::value, int> = 0>
  inline void read(T& str) {
    skip_space();
    if (cur + str.size() >= ed) reload();
    auto it = cur;
    while (!(*cur == ' ' || *cur == '\n')) ++cur;
    str = std::string(it, cur);
  }

  template <class T, std::enable_if_t<std::is_same<T, char>::value, int> = 0>
  inline void read(T& c) {
    skip_space();
    if (cur + 1 >= ed) reload();
    c = *cur, ++cur;
  }

  template <class T, std::enable_if_t<std::is_same<T, double>::value, int> = 0>
  inline void read(T& num) {
    skip_space();
    if (cur + integer_size >= ed) reload();
    bool neg = false;
    num = 0;
    if (*cur == '-') neg = true, ++cur;
    while (*cur >= '0' && *cur <= '9') num = num * 10 + (*cur ^ 48), ++cur;
    if (*cur != '.') return;
    ++cur;
    T base = 0.1;
    while (*cur >= '0' && *cur <= '9') {
      num += base * (*cur ^ 48);
      ++cur;
      base *= 0.1;
    }
    if (neg) num = -num;
  }

  template <class T,
            std::enable_if_t<std::is_same<T, long double>::value, int> = 0>
  inline void read(T& num) {
    skip_space();
    if (cur + integer_size >= ed) reload();
    bool neg = false;
    num = 0;
    if (*cur == '-') neg = true, ++cur;
    while (*cur >= '0' && *cur <= '9') num = num * 10 + (*cur ^ 48), ++cur;
    if (*cur != '.') return;
    ++cur;
    T base = 0.1;
    while (*cur >= '0' && *cur <= '9') {
      num += base * (*cur ^ 48);
      ++cur;
      base *= 0.1;
    }
    if (neg) num = -num;
  }

  template <class T>
  inline void read(std::vector<T>& vec) {
    for (T& e : vec) read(e);
  }

  template <class T, class U>
  inline void read(std::pair<T, U>& p) {
    read(p.first, p.second);
  }

  template <class Tuple, std::size_t... Is>
  inline void tuple_scan(Tuple& tp, std::index_sequence<Is...>) {
    (read(std::get<Is>(tp)), ...);
  }

  template <class... Args>
  inline void read(std::tuple<Args...>& tp) {
    tuple_scan(tp, std::index_sequence_for<Args...>{});
  }

  inline void read() {}

  template <class Head, class... Tail>
  inline void read(Head&& head, Tail&&... tail) {
    read(head);
    read(std::forward<Tail>(tail)...);
  }
};

class Printer {
  static constexpr int buf_size = (1 << 18);
  static constexpr int integer_size = 20;
  static constexpr int string_size = (1 << 6);
  static constexpr int margin = 1;
  static constexpr int n = 10000;
  char buf[buf_size + margin] = {};
  char table[n * 4] = {};
  char* cur = buf;

 public:
  constexpr Printer() { build(); }

  ~Printer() { flush(); }

  template <class T>
  inline Printer& operator<<(T val) {
    write(val);
    return *this;
  }

  template<class T>
  inline void println(T val) {
    write(val);
    write('\n');
  }

 private:
  constexpr void build() {
    for (int i = 0; i < 10000; ++i) {
      int tmp = i;
      for (int j = 3; j >= 0; --j) {
        table[i * 4 + j] = tmp % 10 + '0';
        tmp /= 10;
      }
    }
  }

  inline void flush() {
    fwrite(buf, 1, cur - buf, stdout);
    cur = buf;
  }

  template <class T, std::enable_if_t<std::is_same<T, int>::value, int> = 0>
  inline int get_digit(T n) {
    if (n >= (int)1e5) {
      if (n >= (int)1e8) return 9;
      if (n >= (int)1e7) return 8;
      if (n >= (int)1e6) return 7;
      return 6;
    } else {
      if (n >= (int)1e4) return 5;
      if (n >= (int)1e3) return 4;
      if (n >= (int)1e2) return 3;
      if (n >= (int)1e1) return 2;
      return 1;
    }
  }

  template <class T, std::enable_if_t<std::is_same<T, int64>::value, int> = 0>
  inline int get_digit(T n) {
    if (n >= (int64)1e10) {
      if (n >= (int64)1e14) {
        if (n >= (int64)1e18) return 19;
        if (n >= (int64)1e17) return 18;
        if (n >= (int64)1e16) return 17;
        if (n >= (int64)1e15) return 16;
        return 15;
      } else {
        if (n >= (int64)1e14) return 15;
        if (n >= (int64)1e13) return 14;
        if (n >= (int64)1e12) return 13;
        if (n >= (int64)1e11) return 12;
        return 11;
      }
    } else {
      if (n >= (int64)1e5) {
        if (n >= (int64)1e9) return 10;
        if (n >= (int64)1e8) return 9;
        if (n >= (int64)1e7) return 8;
        if (n >= (int64)1e6) return 7;
        return 6;
      } else {
        if (n >= (int64)1e4) return 5;
        if (n >= (int64)1e3) return 4;
        if (n >= (int64)1e2) return 3;
        if (n >= (int64)1e1) return 2;
        return 1;
      }
    }
  }

  template <class T, std::enable_if_t<std::is_same<T, int>::value, int> = 0>
  inline void write(T num) {
    if (__builtin_expect(cur + integer_size >= buf + buf_size, 0)) flush();
    if (num == 0) {
      write('0');
      return;
    }
    if (num < 0) {
      write('-');
      num = -num;
    }
    int len = get_digit(num);
    int digits = len;
    while (num >= 10000) {
      memcpy(cur + len - 4, table + (num % 10000) * 4, 4);
      num /= 10000;
      len -= 4;
    }
    memcpy(cur, table + num * 4 + (4 - len), len);
    cur += digits;
  }

  template <class T, std::enable_if_t<std::is_same<T, int64>::value, int> = 0>
  inline void write(T num) {
    if (__builtin_expect(cur + integer_size >= buf + buf_size, 0)) flush();
    if (num == 0) {
      write('0');
      return;
    }
    if (num < 0) {
      write('-');
      num = -num;
    }
    int len = get_digit(num);
    int digits = len;
    while (num >= 10000) {
      memcpy(cur + len - 4, table + (num % 10000) * 4, 4);
      num /= 10000;
      len -= 4;
    }
    memcpy(cur, table + num * 4 + (4 - len), len);
    cur += digits;
  }

  template <class T, std::enable_if_t<std::is_same<T, char>::value, int> = 0>
  inline void write(T c) {
    if (__builtin_expect(cur + 1 >= buf + buf_size, 0)) flush();
    *cur = c;
    ++cur;
  }

  template <class T,
            std::enable_if_t<std::is_same<T, std::string>::value, int> = 0>
  inline void write(T str) {
    if (__builtin_expect(cur + str.size() >= buf + buf_size, 0)) flush();
    for (char c : str) write(c);
  }

  template <class T,
            std::enable_if_t<std::is_same<T, const char*>::value, int> = 0>
  inline void write(T str) {
    if (__builtin_expect(cur + string_size >= buf + buf_size, 0)) flush();
    for (int i = 0; str[i]; ++i) write(str[i]);
  }
};
}  // namespace FastIO

FastIO::Scanner fin;
FastIO::Printer fout;


int main() {
  int r, c, k; fin >> r >> c >> k;
  int val[r][c];
  fill(val[0], val[r], 0);
  for (int i = 0; i < k; ++i) {
    int x, y, z; fin >> x >> y >> z;
    --x; --y;
    val[x][y] = z;
  }

  if (val[0][0] != 0) dp[0][0][1] = val[0][0];

  for (int i = 0; i < r; ++i) {
    for (int j = 0; j < c; ++j) {
      if (i == 0 && j == 0) continue;

      if (val[i][j] != 0) {
        if (i > 0) {
          for (int l = 0; l < 4; ++l) dp[i][j][0] = max(dp[i][j][0], dp[i - 1][j][l]);
          for (int l = 0; l < 4; ++l) dp[i][j][1] = max(dp[i][j][1], dp[i - 1][j][l] + val[i][j]);
        }
        if (j > 0) {
          dp[i][j][0] = max(dp[i][j][0], dp[i][j - 1][0]);
          for (int l = 1; l < 4; ++l) {
            dp[i][j][l] = max({dp[i][j][l], dp[i][j - 1][l], dp[i][j - 1][l - 1] + val[i][j]});
          }
        }
      } else {
        if (i > 0) {
          for (int l = 0; l < 4; ++l) dp[i][j][0] = max(dp[i][j][0], dp[i - 1][j][l]);
        }
        if (j > 0) {
          for (int l = 0; l < 4; ++l) dp[i][j][l] = max(dp[i][j][l], dp[i][j - 1][l]);
        }
      }
    }
  }

  int64 ans = 0;
  for (int i = 0; i < 4; ++i) ans = max(ans, dp[r - 1][c - 1][i]);
  fout.println(ans);

  return 0;
}
"""

with open('sol.cpp', 'w') as f:
    f.write(code)

subprocess.Popen(['g++', '-std=c++17', '-O2', 'sol.cpp']).communicate()
subprocess.Popen(['./a.out'], stdin=sys.stdin, stdout=sys.stdout).communicate()'))

Solution (Python):

R,C,K = map(int,input().split())
A =     [[0  for j in range(C)] for i in range(R)]
varr = [[[0  for j in range(C)] for i in range(R)] for k in range(4)]

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

for i in range(R):  
    for j in range(C):
        for k in range(2,-1,-1):
            if varr[k][i][j] >= 0:
                if  varr[k+1][i][j] < varr[k][i][j] + A[i][j]:
                    varr[k+1][i][j] = varr[k][i][j] + A[i][j]
        for kk in range(0,4):
            if varr[kk][i][j] >= 0:
                if i +1 < R :
                    if  varr[0][i + 1][j] < varr[kk][i][j]:
                        varr[0][i + 1][j] = varr[kk][i][j] 
                if j +1 < C :
                    if  varr[kk][i][j + 1] < varr[kk][i][j]:
                        varr[kk][i][j + 1] = varr[kk][i][j] 
ans = 0
for k in range (4):
    if ans < varr[k][R-1][C-1]:
        ans = varr[k][R-1][C-1]

print(ans)

Solution (Python):
import numpy as np
import numba
from numba import njit, b1, i4, i8, f8

@njit((i8, i8, i8, i8[:,:]), cache=True)
def solve(R,C,K,item):
  dp = np.zeros((C+1,4), dtype=np.int64)
  for i in range(1,R+1):
    new_dp = np.zeros((C+1,4), dtype=np.int64)
    
    for k in range(4):
      new_dp[:,0] = np.maximum(new_dp[:,0], dp[:,k])
    dp = new_dp
    for j in range(1,C+1):
      
      for k in range(4):
        new_dp[j][k] = np.maximum(new_dp[j,k],new_dp[j-1,k])
      
      for k in range(2,-1,-1):
        dp[j,k+1] = np.maximum(dp[j,k+1],dp[j,k]+item[i-1][j-1])
  ans = dp[-1].max()
  return ans

R, C, K = map(int, input().split())
item = np.zeros((R,C), dtype=np.int64)
for i in range(K):
  r,c,v = map(int, input().split())
  item[r-1,c-1] = v
print(solve(R,C,K,item))

Solution (Python):
import numpy as np
import numba
from numba import njit, b1, i4, i8, f8

@njit((i8, i8, i8, i8[:,:]), cache=True)
def solve(R,C,K,item):
  dp = np.zeros((C+1,4), dtype=np.int64)
  for i in range(1,R+1):
    new_dp = np.zeros((C+1,4), dtype=np.int64)
    
    for k in range(4):
      new_dp[:,0] = np.maximum(new_dp[:,0], dp[:,k])
    dp = new_dp
    for j in range(1,C+1):
      
      for k in range(4):
        new_dp[j][k] = np.maximum(new_dp[j][k],new_dp[j-1][k])
      
      for k in range(2,-1,-1):
        dp[j,k+1] = np.maximum(dp[j,k+1],dp[j,k]+item[i-1][j-1])
  ans = dp[-1].max()
  return ans

R, C, K = map(int, input().split())
item = np.zeros((R,C), dtype=np.int64)
for i in range(K):
  r,c,v = map(int, input().split())
  item[r-1,c-1] = v
print(solve(R,C,K,item))

Solution (Python):
import sys
import numpy as np
import numba
from numba import njit, b1, i4, i8, f8
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline

@njit((i8, i8, i8, i8[:]), cache=True)
def solve(R,C,K,XYV):
  item = np.zeros((R + 1, C + 1), dtype=np.int64)
  for i in range(0, 3 * K, 3):
    x, y, v = XYV[i:i + 3]
    item[x - 1, y - 1] = v
  dp = np.zeros((C+1,4), dtype=np.int64)
  for i in range(R):
    new_dp = np.zeros((C+1,4), dtype=np.int64)
    
    for k in range(4):
      new_dp[:,0] = np.maximum(new_dp[:,0], dp[:,k])
    dp = new_dp
    for j in range(1,C+1):
      
      for k in range(4):
        new_dp[j,k] = np.maximum(new_dp[j,k],new_dp[j-1,k])
      
      for k in range(2,-1,-1):
        dp[j,k+1] = np.maximum(dp[j,k+1],dp[j,k]+item[i,j-1])
  ans = dp[-1].max()
  return ans

R, C, K = map(int, readline().split())
XYV = np.array(read().split(), np.int64)
print(solve(R,C,K,XYV))

Solution (Python):
import sys
import numpy as np
import numba
from numba import njit, b1, i4, i8, f8
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline

@njit((i8, i8, i8, i8[:]), cache=True)
def solve(R,C,K,XYV):
  item = np.zeros((R + 1, C + 1), dtype=np.int64)
  for i in range(0, 3 * K, 3):
    x, y, v = XYV[i:i + 3]
    item[x - 1, y - 1] = v
  dp = np.zeros((C+1,4), dtype=np.int64)
  for i in range(1,R+1):
    new_dp = np.zeros((C+1,4), dtype=np.int64)
    
    for k in range(4):
      new_dp[:,0] = np.maximum(new_dp[:,0], dp[:,k])
    dp = new_dp
    for j in range(1,C+1):
      
      new_dp[j] = np.maximum(new_dp[j],new_dp[j-1])
      
      for k in range(2,-1,-1):
        dp[j,k+1] = np.maximum(dp[j,k+1],dp[j,k]+item[i-1,j-1])
  ans = dp[-1].max()
  return ans

R, C, K = map(int, readline().split())
XYV = np.array(read().split(), np.int64)
print(solve(R,C,K,XYV))

Solution (Python):
import numpy as np
import numba
from numba import njit, b1, i4, i8, f8

@njit((i8, i8, i8, i8[:,:]), cache=True)
def solve(R,C,K,item):
  dp = np.zeros((C+1,4), dtype=np.int64)
  for i in range(1,R+1):
    new_dp = np.zeros((C+1,4), dtype=np.int64)
    
    for k in range(4):
      new_dp[:,0] = np.maximum(new_dp[:,0], dp[:,k])
    dp = new_dp
    for j in range(1,C+1):
      
      new_dp[j] = np.maximum(new_dp[j],new_dp[j-1])
      
      for k in range(2,-1,-1):
        dp[j,k+1] = np.maximum(dp[j,k+1],dp[j,k]+item[i-1][j-1])
  ans = dp[-1].max()
  return ans

R, C, K = map(int, input().split())
item = np.zeros((R,C), dtype=np.int64)
for i in range(K):
  r,c,v = map(int, input().split())
  item[r-1,c-1] = v
print(solve(R,C,K,item))

Solution (Python):
import numpy as np
import numba
from numba import njit, b1, i4, i8, f8

@njit((i8, i8, i8, i8[:,:]), cache=True)
def solve(R,C,K,item):
  dp = np.zeros((C+1,5), dtype=np.int64)
  for i in range(1,R+1):
    new_dp = np.zeros((C+1,4), dtype=np.int64)
    
    for k in range(4):
      new_dp[:,0] = np.maximum(new_dp[:,0], dp[:,k])
    dp = new_dp
    for j in range(1,C+1):
      
      new_dp[j] = np.maximum(new_dp[j],new_dp[j-1])
      
      for k in range(2,-1,-1):
        dp[j,k+1] = np.maximum(dp[j,k+1],dp[j,k]+item[i-1][j-1])
  ans = dp[-1].max()
  return ans

R, C, K = map(int, input().split())
item = np.zeros((R,C), dtype=np.int64)
for i in range(K):
  r,c,v = map(int, input().split())
  item[r-1,c-1] = v
print(solve(R,C,K,item))

Solution (Python):
import numpy as np
import numba
from numba import njit, b1, i4, i8, f8

@njit((i8, i8, i8, i8[:,:]), cache=True)
def solve(R,C,K,item):
  dp = np.zeros((C+1,5), dtype=np.int64)
  for i in range(1,R+1):
    new_dp = np.zeros((C+1,5), dtype=np.int64)
    
    new_dp[:,0] = dp[:,-1]
    
    new_dp[1:,1] = np.maximum(new_dp[1:,1],dp[1:,-1]+item[i-1])
    for j in range(1,C+1):
      
      new_dp[j] = np.maximum(new_dp[j],new_dp[j-1])
      
      for k in range(1,4):
        new_dp[j,k] = max(new_dp[j,k],new_dp[j-1,k-1]+item[i-1,j-1])
    for k in range(4):
      new_dp[:,-1] = np.maximum(new_dp[:,-1],new_dp[:,k])
    dp = new_dp
  ans = dp[-1,-1]
  return ans

R, C, K = map(int, input().split())
item = np.zeros((R,C), dtype=np.int64)
for i in range(K):
  r,c,v = map(int, input().split())
  item[r-1,c-1] = v
print(solve(R,C,K,item))

Solution (Python):
import numpy as np
import numba
from numba import njit, b1, i4, i8, f8

@njit((i8, i8, i8, i8[:,:]), cache=True)
def solve(R,C,K,item):
  dp = np.zeros((5,C+1), dtype=np.int64)
  for i in range(1,R+1):
    new_dp = np.zeros((5,C+1), dtype=np.int64)
    
    new_dp[0] = dp[-1]
    
    new_dp[1][1:] = np.maximum(new_dp[1][1:],dp[-1][1:]+item[i-1])
    for j in range(1,C+1):
      
      new_dp[:,j] = np.maximum(new_dp[:,j],new_dp[:,j-1])
      
      for k in range(1,4):
        new_dp[k,j] = max(new_dp[k,j],new_dp[k-1,j-1]+item[i-1,j-1])
    for k in range(4):
      new_dp[-1] = np.maximum(new_dp[-1],new_dp[k])
    dp = new_dp
  ans = dp[-1,-1]
  return ans

R, C, K = map(int, input().split())
item = np.zeros((R,C), dtype=np.int64)
for i in range(K):
  r,c,v = map(int, input().split())
  item[r-1,c-1] = v
print(solve(R,C,K,item))

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

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

dp0 = [[0 for j in range(C+1)] for i in range(R+1)]
dp1 = [[0 for j in range(C+1)] for i in range(R+1)]
dp2 = [[0 for j in range(C+1)] for i in range(R+1)]
dp3 = [[0 for j in range(C+1)] for i in range(R+1)]
for i in range(R):
    for j in range(C):
        dp3[i][j] = max(dp3[i][j], dp2[i][j]+I[i][j])
        dp2[i][j] = max(dp2[i][j], dp1[i][j]+I[i][j])
        dp1[i][j] = max(dp1[i][j], dp0[i][j]+I[i][j])
        dp0[i+1][j] = max(dp0[i+1][j], dp0[i][j], dp1[i]
                          [j], dp2[i][j], dp3[i][j])
        dp0[i][j+1] = max(dp0[i][j+1], dp0[i][j])
        dp1[i][j+1] = max(dp1[i][j+1], dp1[i][j])
        dp2[i][j+1] = max(dp2[i][j+1], dp2[i][j])
        dp3[i][j+1] = max(dp3[i][j+1], dp3[i][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)

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

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

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

dp0 = [[0 for j in range(C+1)] for i in range(R+1)]
dp1 = [[0 for j in range(C+1)] for i in range(R+1)]
dp2 = [[0 for j in range(C+1)] for i in range(R+1)]
dp3 = [[0 for j in range(C+1)] for i in range(R+1)]
for i in range(R):
    for j in range(C):
        dp3[i][j] = max(dp3[i][j], dp2[i][j]+I[i][j])
        dp2[i][j] = max(dp2[i][j], dp1[i][j]+I[i][j])
        dp1[i][j] = max(dp1[i][j], dp0[i][j]+I[i][j])
        dp0[i+1][j] = max(dp0[i+1][j], dp0[i][j], dp1[i]
                          [j], dp2[i][j], dp3[i][j])
        dp0[i][j+1] = max(dp0[i][j+1], dp0[i][j])
        dp1[i][j+1] = max(dp1[i][j+1], dp1[i][j])
        dp2[i][j+1] = max(dp2[i][j+1], dp2[i][j])
        dp3[i][j+1] = max(dp3[i][j+1], dp3[i][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)

Solution (Python):
import sys
import numpy as np
from numba import njit,i8

R,C,K = map(int,input().split())
item = np.zeros((R,C),np.int64)
for _ in range(K):
    r,c,v = map(int,input().split())
    item[r-1][c-1] = v
    

@njit(i8(i8[:,:],i8,i8), cache = True)
def solve(item,R,C):
    dp = np.zeros((R+1,C+1,4),np.int64)
    for ri in range(R):
        for ci in range(C):
            dp[ri+1][ci+1][0] = max(dp[ri+1][ci][0], dp[ri][ci+1][3])
            dp[ri+1][ci+1][1] = max(dp[ri+1][ci][1], dp[ri+1][ci][0]+item[ri][ci], dp[ri][ci+1][3]+item[ri][ci], dp[ri+1][ci+1][0])
            dp[ri+1][ci+1][2] = max(dp[ri+1][ci][2], dp[ri+1][ci][1]+item[ri][ci], dp[ri+1][ci+1][1])
            dp[ri+1][ci+1][3] = max(dp[ri+1][ci][3], dp[ri+1][ci][2]+item[ri][ci], dp[ri+1][ci+1][2])
        

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

print(solve(item,R,C))

Solution (Python):
r,c,k=map(int, input().split())
grid=[[0]*(c+1) for _ in range(r+1)]
for i in range(k):
    ri,ci,vi=map(int, input().split())
    grid[ri][ci]=vi

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

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