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/**
 * Find the maximum number of cherries collection using both robots.
 * Dynamic Programming (3D) approach.
 *
 * @param {number[][]} grid - Matrix representing a field of cherries
 * @return {number} - Maximum number of cherries
 */
function cherryPickup(grid) {
  const rows = grid.length;
  const cols = grid[0].length;
 
  // Initialize 3D DP array
  const dp = Array(rows).fill().map(() =>
    Array(cols).fill().map(() =>
      Array(cols).fill(-1)
    )
  );
 
  // Define recursive function
  function dfs(row, col1, col2) {
    // Base case: reached the bottom row
    if (row === rows) {
      return 0;
    }
 
    // Check if already computed
    if (dp[row][col1][col2] !== -1) {
      return dp[row][col1][col2];
    }
 
    // Calculate cherries collected at current state
    let cherries = grid[row][col1];
    if (col1 !== col2) {
      cherries += grid[row][col2];
    }
 
    // Initialize maximum cherries
    let maxCherries = 0;
 
    // Try all possible moves for both robots
    for (let d1 = -1; d1 <= 1; d1++) {
      for (let d2 = -1; d2 <= 1; d2++) {
        const newCol1 = col1 + d1;
        const newCol2 = col2 + d2;
 
        // Check if new positions are valid
        if (newCol1 >= 0 && newCol1 < cols && newCol2 >= 0 && newCol2 < cols) {
          maxCherries = Math.max(maxCherries, dfs(row + 1, newCol1, newCol2));
        }
      }
    }
 
    // Update DP array
    dp[row][col1][col2] = cherries + maxCherries;
    return dp[row][col1][col2];
  }
 
  return dfs(0, 0, cols - 1);
}
 
/**
 * Find the maximum number of cherries collection using both robots.
 * Dynamic Programming (2D) approach.
 *
 * @param {number[][]} grid - Matrix representing a field of cherries
 * @return {number} - Maximum number of cherries
 */
function cherryPickupOptimized(grid) {
  const rows = grid.length;
  const cols = grid[0].length;
 
  // Initialize DP arrays
  let curr = Array(cols).fill().map(() => Array(cols).fill(0));
  let next = Array(cols).fill().map(() => Array(cols).fill(0));
 
  // Fill DP arrays from bottom to top
  for (let row = rows - 1; row >= 0; row--) {
    // Reset current row
    for (let col1 = 0; col1 < cols; col1++) {
      for (let col2 = 0; col2 < cols; col2++) {
        curr[col1][col2] = 0;
      }
    }
 
    // Calculate maximum cherries for current row
    for (let col1 = 0; col1 < cols; col1++) {
      for (let col2 = 0; col2 < cols; col2++) {
        // Calculate cherries collected at current state
        let cherries = grid[row][col1];
        if (col1 !== col2) {
          cherries += grid[row][col2];
        }
 
        // Initialize maximum cherries
        let maxCherries = 0;
 
        // Try all possible moves for both robots
        for (let d1 = -1; d1 <= 1; d1++) {
          for (let d2 = -1; d2 <= 1; d2++) {
            const newCol1 = col1 + d1;
            const newCol2 = col2 + d2;
 
            // Check if new positions are valid
            if (newCol1 >= 0 && newCol1 < cols && newCol2 >= 0 && newCol2 < cols) {
              maxCherries = Math.max(maxCherries, next[newCol1][newCol2]);
            }
          }
        }
 
        // Update current row
        curr[col1][col2] = cherries + maxCherries;
      }
    }
 
    // Swap arrays for next iteration
    [curr, next] = [next, curr];
  }
 
  return next[0][cols - 1];
}
 
/**
 * Find the maximum number of cherries collection using both robots.
 * Dynamic Programming with Memoization approach.
 *
 * @param {number[][]} grid - Matrix representing a field of cherries
 * @return {number} - Maximum number of cherries
 */
function cherryPickupMemoization(grid) {
  const rows = grid.length;
  const cols = grid[0].length;
 
  // Initialize memoization map
  const memo = new Map();
 
  // Define recursive function
  function dp(row, col1, col2) {
    // Base case: reached the bottom row
    if (row === rows) {
      return 0;
    }
 
    // Create a unique key for the memo map
    const key = `${row},${col1},${col2}`;
 
    // Check if already computed
    if (memo.has(key)) {
      return memo.get(key);
    }
 
    // Calculate cherries collected at current state
    let cherries = grid[row][col1];
    if (col1 !== col2) {
      cherries += grid[row][col2];
    }
 
    // Initialize maximum cherries
    let maxCherries = 0;
 
    // Try all possible moves for both robots
    for (let d1 = -1; d1 <= 1; d1++) {
      for (let d2 = -1; d2 <= 1; d2++) {
        const newCol1 = col1 + d1;
        const newCol2 = col2 + d2;
 
        // Check if new positions are valid
        if (newCol1 >= 0 && newCol1 < cols && newCol2 >= 0 && newCol2 < cols) {
          maxCherries = Math.max(maxCherries, dp(row + 1, newCol1, newCol2));
        }
      }
    }
 
    // Update memoization map
    const result = cherries + maxCherries;
    memo.set(key, result);
    return result;
  }
 
  return dp(0, 0, cols - 1);
}
 
// Test cases
const grid1 = [
  [3, 1, 1],
  [2, 5, 1],
  [1, 5, 5],
  [2, 1, 1]
];
console.log(cherryPickup(grid1));  // 24
console.log(cherryPickupOptimized(grid1));  // 24
console.log(cherryPickupMemoization(grid1));  // 24
 
const grid2 = [
  [1, 0, 0, 0, 0, 0, 1],
  [2, 0, 0, 0, 0, 3, 0],
  [2, 0, 9, 0, 0, 0, 0],
  [0, 3, 0, 5, 4, 0, 0],
  [1, 0, 2, 3, 0, 0, 6]
];
console.log(cherryPickup(grid2));  // 28
console.log(cherryPickupOptimized(grid2));  // 28
console.log(cherryPickupMemoization(grid2));  // 28