> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/dynamic-programming/untitled-9.md).
# Largest 1-Bordered Square
Given a 2D `grid` of `0`s and `1`s, return the number of elements in the largest **square** subgrid that has all `1`s on its **border**, or `0` if such a subgrid doesn't exist in the `grid`.
**Example 1:**
```
Input: grid = [[1,1,1],[1,0,1],[1,1,1]]
Output: 9
```
**Example 2:**
```
Input: grid = [[1,1,0,0]]
Output: 1
```
**Constraints:**
* `1 <= grid.length <= 100`
* `1 <= grid[0].length <= 100`
* `grid[i][j]` is `0` or `1`
***Explaination:***
Create auxillary horizontal and vertical arrays first\
For example :
Then starting from bottom right,for every i,j ; we find small=min (ver\[i]\[j], hor\[i]\[j]) (marked in orange) , then look at all distances in \[1,small] vertically in hor array and horizontally in ver array. If values(shown in blue) are greater than small and if small is greater than curr result, then we update result
```java
class Solution {
public int largest1BorderedSquare(int[][] grid) {
int m = grid.length, n = grid[0].length;
int[][] ver = new int[m][n];
int[][] hor = new int[m][n];
for (int j = 0; j < n; j++) {
for (int i = 0; i < m; i++) {
if (i == 0)
ver[i][j] = grid[i][j];
else
ver[i][j] = grid[i][j] == 1 ? (ver[i - 1][j] + grid[i][j]) : 0;
if (j == 0)
hor[i][j] = grid[i][j];
else
hor[i][j] = grid[i][j] == 1 ? (hor[i][j - 1] + grid[i][j]) : 0;
}
}
int max = 0;
for (int i = m - 1; i >= 0; i--) {
for (int j = n - 1; j >= 0; j--) {
int small = Math.min(hor[i][j], ver[i][j]); // choose smallest of horizontal and vertical value
while (small > max) {
if (ver[i][j - small + 1] >= small && hor[i - small + 1][j] >= small)
// check if square exists with 'small' length
max = small;
small--;
}
}
}
return max * max;
}
}
```
---
# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.
## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.
Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:
```
GET https://mayanktyagi3111.gitbook.io/interview-prep/dynamic-programming/untitled-9.md?ask=&goal=
```
`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.
Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.