# 562.Longest-Line-of-Consecutive-One-in-Matrix

## 562. Longest Line of Consecutive One in Matrix

## 题目地址

<https://leetcode.com/problems/longest-line-of-consecutive-one-in-matrix/>

## 题目描述

```
Given a 01 matrix M, find the longest line of consecutive one in the matrix. The line could be horizontal, vertical, diagonal or anti-diagonal.
Example:
Input:
[[0,1,1,0],
 [0,1,1,0],
 [0,0,0,1]]
Output: 3
Hint: The number of elements in the given matrix will not exceed 10,000.
```

## 代码

### Approach #1 Brute Force

Time: O(N^2) && Space: O(1)

```java
class Solution {
  public int longestLine(int[][] M) {
        if (M.length == 0)        return 0;
    int ones = 0;
    // horizontal
    for (int i = 0; i < M.length; i++) {
      int count = 0;
      for (int j = 0; j < M[0].length; j++) {
        if (M[i][j] == 1) {
          count++;
          ones = Math.max(ones, count);
        } else {
          count = 0;
        }
      }
    }

    // vertical
    for (int i = 0; i < M[0].length; i++) {
      int count = 0;
      for (int j = 0; j < M.length; j++) {
        if (M[j][i] == 1) {
          count++;
          ones = Math.max(ones, count);
        } else {
          count = 0;
        }
      }
    }

    // upper diagonal
    for (int i = 0; i < M[0].length || i < M.length; i++) {
      int count = 0;
      for (int x = 0; y = i; x < M.length && y < M[0].length; x++, y++) {
        if (M[x][y] == 1) {
          count++;
          ones = Math.max(ones, count);
        } else {
          count = 0;
        }
      }
    }

    // lower diagonal
    for (int i = 0; i < M[0].length || i < M.length; i++) {
      int count = 0;
      for (int x = i, y = 0; x < M.length && y < M[0].length; x++, y++) {
        if (M[x][y] == 1) {
          count++;
          ones = Math.max(ones, count);
        } else {
          count = 0;
        }
      }
    }

    // upper anti-diagonal
    for (int i = 0; i < M[0].length || i < M.length; i++) {
      int count = 0;
      for (int x = 0, y = M[0].length - i - 1; x < M.length && y >= 0; x++, y--) {
        if (M[x][y] == 1) {
          count++;
          ones = Math.max(ones, count);
        } else {
          count = 0;
        }
      }
    }

    // lower anti-diagonal
    for (int i = 0; i < M[0].length || i < M.length; i++) {
      int count = 0;
      for (int x = i, y = M[0].length - 1; x < M.length && y >= 0; x++, y--) {
        if (M[x][y] == 1) {
          count++;
          ones = Math.max(ones, count);
        } else {
          count = 0;
        }
      }
    }
    return ones;
  }
}
```

### Approach #3 3D Dynamic Programming

Time complexity && Space complexity : O(mn)

```java
class Solution {
  public int longestLine(int[][] M) {
        if (M.length == 0)        return 0;
    int ones = 0;
    int[][][] dp = new int[M.length][M[0].length][4];
    for (int i = 0; i < M.length; i++) {
      for (int j = 0; j < M[0].length; j++) {
        if (M[i][j] == 1) {
          dp[i][j][0] = j > 0 ? dp[i][j - 1][0] + 1 : 1;
          dp[i][j][1] = i > 0 ? dp[i - 1][j][1] + 1: 1;
          dp[i][j][2] = (i > 0 && j > 0) ? dp[i - 1][j - 1][2] + 1 : 1;
          dp[i][j][3] = (i > 0 && j < M[0].length - 1) ? dp[i - 1][j + 1][3] + 1 : 1;
          ones = Math.max(ones, Math.max(
          Math.max(dp[i][j][0], dp[i][j][1]),
          Math.max(dp[i][j][2], dp[i][j][3])
          ));
        }
      }
    }

    return ones;
  }
}
```

### Approach #3 2D Dynamic Programming

```java
class Solution {
  public int longestLine(int[][] M) {
    if (M.length == 0)        return 0;
    int ones = 0;
    int[][] dp = new int[M[0].length][4];
    for (int i = 0; i < M.length; i++) {
      int old = 0;
      for (int j = 0; j < M[0].length; j++) {
        if (M[i][j] == 1) {
          dp[j][0] = j > 0 ? dp[j - 1][0] + 1 : 1; // horizontal
          dp[j][1] = i > 0 ? dp[j][1] + 1 : 1;    // vertial
          int prev = dp[j][2];
          dp[j][2] = (i > 0 && j > 0) ? old + 1 : 1;
          old = prev;
          dp[j][3] = (i > 0 && j < M[0].length - 1) ? dp[j + 1][3] + 1 : 1;
          ones = Math.max(ones, 
                          Math.max(Math.max(dp[j][0], dp[j][1]),
                                  Math.max(dp[j][2], dp[j][3])));
        } else {
          old = dp[j][2];
          dp[j][0] = dp[j][1] = dp[j][2] = dp[j][3] = 0;
        }
      } 
    }

      return ones;
  }
}
```


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