#931. Minimum Falling Path Sum

https://leetcode.com/problems/minimum-falling-path-sum/description/?envType=daily-question&envId=2024-01-19

var minFallingPathSum = function(matrix) {
    if (!matrix || matrix.length === 0) {
        return 0;
    }

    const rows = matrix.length;
    const cols = matrix[0].length;

    // Memoization cache
    const memo = {};

    function findMinPath(row, col) {
        // Base case: if we reach the first row, return the value at that position
        if (row === 0) {
            return matrix[row][col];
        }

        // Check if the result is already memoized
        if (memo.hasOwnProperty(`${row}-${col}`)) {
            return memo[`${row}-${col}`];
        }

        // Calculate the minimum falling path sum recursively
        let left = findMinPath(row - 1, Math.max(col - 1, 0));
        let up = findMinPath(row - 1, col);
        let right = findMinPath(row - 1, Math.min(col + 1, cols - 1));

        // Memoize the result
        memo[`${row}-${col}`] = matrix[row][col] + Math.min(left, up, right);

        // Return the memoized result
        return memo[`${row}-${col}`];
    }

    // Initialize the result with Infinity
    let result = Infinity;

    // Call the recursive function for each element in the first row
    for (let i = 0; i < cols; i++) {
        result = Math.min(result, findMinPath(rows - 1, i));
    }

    return result;
};

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