How to initialize Multi-Dimensional cache in TS

The issue lies in how the 2D cache array is initialized. The original code uses:

const cache = Array(m).fill(Array(n).fill(null));

This creates an array with melements, but ​​each element references the same inner array​​ due to Array(n).fill(null)being evaluated once and shared across all rows. When you update cache[i][j], it affects all rows because they share the same array.

​​Solution:​​ Initialize the cache with distinct arrays for each row:

const cache = Array(m).fill(null).map(() => Array(n).fill(null));

​​Explanation:​​

• Array(m).fill(null)creates an array of melements, each initially null.

• .map(() => Array(n).fill(null))replaces each nullwith a ​​new array​​ of size nfilled with null. This ensures each row is a separate array.

​​Corrected Code:​​

function minDistance(word1: string, word2: string): number {
    const m = word1.length;
    const n = word2.length;
    const cache = Array(m).fill(null).map(() => Array(n).fill(null)); // Fixed initialization

    function dfs(i, j) {
        if (i < 0 || j < 0) { return i < 0 ? j + 1 : i + 1 }
        if (cache[i][j] !== null) { return cache[i][j] }
        let res;
        if (word1[i] === word2[j]) {
            res = dfs(i - 1, j - 1);
        }
        else {
            res = Math.min(
                dfs(i - 1, j - 1),
                dfs(i - 1, j),
                dfs(i, j - 1),
            ) + 1;
        }
        cache[i][j] = res;
        return res;
    }

    return dfs(m - 1, n - 1);
};

​​Why the original fails:​​

• All rows in cachepoint to the same array.

• Updating cache[i][j]overwrites values for the same column jin ​​all rows​​.

• Subsequent accesses to cache[i][j]return incorrect memoized values, leading to wrong results.

The fix ensures each row is independent, preserving correct memoization.