LeetCode-in-Java

3459. Length of Longest V-Shaped Diagonal Segment

Hard

You are given a 2D integer matrix grid of size n x m, where each element is either 0, 1, or 2.

A V-shaped diagonal segment is defined as:

• The segment starts with 1.
• The subsequent elements follow this infinite sequence: 2, 0, 2, 0, ....
• The segment:
  • Starts along a diagonal direction (top-left to bottom-right, bottom-right to top-left, top-right to bottom-left, or bottom-left to top-right).
  • Continues the sequence in the same diagonal direction.
  • Makes at most one clockwise 90-degree turn to another diagonal direction while maintaining the sequence.

Return the length of the longest V-shaped diagonal segment. If no valid segment exists, return 0.

Example 1:

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

Output: 5

Explanation:

The longest V-shaped diagonal segment has a length of 5 and follows these coordinates: (0,2) → (1,3) → (2,4), takes a 90-degree clockwise turn at (2,4), and continues as (3,3) → (4,2).

Example 2:

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

Output: 4

Explanation:

The longest V-shaped diagonal segment has a length of 4 and follows these coordinates: (2,3) → (3,2), takes a 90-degree clockwise turn at (3,2), and continues as (2,1) → (1,0).

Example 3:

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

Output: 5

Explanation:

The longest V-shaped diagonal segment has a length of 5 and follows these coordinates: (0,0) → (1,1) → (2,2) → (3,3) → (4,4).

Example 4:

Input: grid = [[1]]

Output: 1

Explanation:

The longest V-shaped diagonal segment has a length of 1 and follows these coordinates: (0,0).

Constraints:

• n == grid.length
• m == grid[i].length
• 1 <= n, m <= 500
• grid[i][j] is either 0, 1 or 2.

Solution

import java.util.Arrays;

public class Solution {
    private final int[][] ds = { {1, 1}, {1, -1}, {-1, -1}, {-1, 1}};
    private final int[] nx = {2, 2, 0};
    private int[][] grid;
    private int n;
    private int m;
    private int[][][][] dp;

    public int lenOfVDiagonal(int[][] g) {
        this.grid = g;
        this.n = g.length;
        this.m = g[0].length;
        this.dp = new int[n][m][4][2];
        for (int[][][] d1 : dp) {
            for (int[][] d2 : d1) {
                for (int[] d3 : d2) {
                    Arrays.fill(d3, -1);
                }
            }
        }
        int res = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (g[i][j] == 1) {
                    for (int d = 0; d < 4; d++) {
                        res = Math.max(res, dp(i, j, 1, d, 1));
                    }
                }
            }
        }
        return res;
    }

    private int dp(int i, int j, int x, int d, int k) {
        if (i < 0 || i >= n || j < 0 || j >= m) {
            return 0;
        }
        if (grid[i][j] != x) {
            return 0;
        }
        if (dp[i][j][d][k] != -1) {
            return dp[i][j][d][k];
        }
        int res = dp(i + ds[d][0], j + ds[d][1], nx[x], d, k) + 1;
        if (k > 0) {
            int d2 = (d + 1) % 4;
            int res2 = dp(i + ds[d2][0], j + ds[d2][1], nx[x], d2, 0) + 1;
            res = Math.max(res, res2);
        }
        dp[i][j][d][k] = res;
        return res;
    }
}

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