Maximum Number of Moves in a Grid - DP [JS]

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Description 

Solution: DP - Recursion w/ Memoization

Memoize each dp(row, col), where dp(row, col) = the maximum number of moves we can perform starting from (row, col).
For each dp(row, col), traverse in three directions and record the maximum number of moves.

m = number of rows, n = number of columns
Time Complexity: O(mn)
Space Complexity: O(mn)

var maxMoves = function(grid) {
  let m = grid.length, n = grid[0].length;
  let memo = Array(m).fill(0).map(() => Array(n).fill(-1));
  const directions = [[-1, 1], [0, 1], [1, 1]];
  let maxMoves = 0;
  for (let i = 0; i < m; i++) {
    maxMoves = Math.max(maxMoves, dp(i, 0));
  }
  return maxMoves;
  
  function dp(row, col) {
    if (col === n - 1) return 0;
    if (memo[row][col] !== -1) return memo[row][col];
    
    let ans = 0;
    for (let [x, y] of directions) {
      let newRow = row + x, newCol = col + y;
      if (newRow < 0 || newRow >= m || newCol < 0 || newCol >= n || grid[newRow][newCol] <= grid[row][col]) continue; // out of bounds or value is not bigger
      ans = Math.max(ans, 1 + dp(newRow, newCol));
    }
    return memo[row][col] = ans;
  }
};
Location: Auckland, New Zealand

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