LeetCode in Kotlin

3393. Count Paths With the Given XOR Value

Medium

You are given a 2D integer array grid with size m x n. You are also given an integer k.

Your task is to calculate the number of paths you can take from the top-left cell (0, 0) to the bottom-right cell (m - 1, n - 1) satisfying the following constraints:

• You can either move to the right or down. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j) if the target cell exists.
• The XOR of all the numbers on the path must be equal to k.

Return the total number of such paths.

Since the answer can be very large, return the result modulo 109 + 7.

Example 1:

Input: grid = [[2, 1, 5], [7, 10, 0], [12, 6, 4]], k = 11

Output: 3

Explanation:

The 3 paths are:

• (0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2)
• (0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2)
• (0, 0) → (0, 1) → (1, 1) → (2, 1) → (2, 2)

Example 2:

Input: grid = [[1, 3, 3, 3], [0, 3, 3, 2], [3, 0, 1, 1]], k = 2

Output: 5

Explanation:

The 5 paths are:

• (0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (2, 3)
• (0, 0) → (1, 0) → (1, 1) → (2, 1) → (2, 2) → (2, 3)
• (0, 0) → (1, 0) → (1, 1) → (1, 2) → (1, 3) → (2, 3)
• (0, 0) → (0, 1) → (1, 1) → (1, 2) → (2, 2) → (2, 3)
• (0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (2, 3)

Example 3:

Input: grid = [[1, 1, 1, 2], [3, 0, 3, 2], [3, 0, 2, 2]], k = 10

Output: 0

Constraints:

• 1 <= m == grid.length <= 300
• 1 <= n == grid[r].length <= 300
• 0 <= grid[r][c] < 16
• 0 <= k < 16

Solution

class Solution {
    private var m = -1
    private var n = -1
    private lateinit var dp: Array<Array<IntArray>>

    fun countPathsWithXorValue(grid: Array<IntArray>, k: Int): Int {
        m = grid.size
        n = grid[0].size
        dp = Array(m) { Array(n) { IntArray(16) { -1 } } }
        return dfs(grid, 0, k, 0, 0)
    }

    private fun dfs(grid: Array<IntArray>, xorVal: Int, k: Int, i: Int, j: Int): Int {
        var xorVal = xorVal
        if (i < 0 || j < 0 || j >= n || i >= m) {
            return 0
        }
        xorVal = xorVal xor grid[i][j]
        if (dp[i][j][xorVal] != -1) {
            return dp[i][j][xorVal]
        }
        if (i == m - 1 && j == n - 1 && xorVal == k) {
            return 1
        }
        val down = dfs(grid, xorVal, k, i + 1, j)
        val right = dfs(grid, xorVal, k, i, j + 1)
        dp[i][j][xorVal] = (down + right) % MOD
        return dp[i][j][xorVal]
    }

    companion object {
        private val MOD = (1e9 + 7).toInt()
    }
}

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