G-52. Making a Large Island - DSU

TL;DR

Given an N x N binary grid, find the largest group of connected ones after changing at most one cell from zero to one.

Transcript

hey everyone welcome back to the channel I hope you guys are doing extremely well so today we will be solving this hard problem where it states that you're given an N cross n binary grid so n cross and Matrix given to you consisting of ones and zeros now the task is you can change at most one cell in the grid from zero to one okay you need to find ... Read More

Key Insights

• 🤑 The problem involves finding the largest group of connected ones in a binary grid.
• 😫 The solution involves dynamically changing the graph using a disjoint set data structure.
• ❓ Cells are considered adjacent if they share a common side, not diagonally.
• 🌥️ The maximum size of the connected components is considered as the largest connected component.
• 🦔 An edge case needs to be considered where a component may be connected in multiple directions.
• ⌛ The time complexity of the solution is approximately O(N^2).

Questions & Answers

Q: What is the problem statement?

The problem asks to find the largest group of connected ones in a binary grid by changing at most one cell from zero to one.

Q: How are cells defined as adjacent?

Cells are considered adjacent if they share a common side, such as top, right, bottom, or left.

Q: What data structure is used to solve the problem?

A disjoint set data structure is used to dynamically change the graph and connect the components.

Q: How are cells represented in the disjoint set data structure?

Cells are represented by their corresponding node numbers, which are computed using a formula based on the row and column numbers.

Q: What is the logic behind finding the largest connected component?

The solution involves trying to convert every zero to one and using the disjoint set data structure to connect the adjacent cells. The size of each connected component is calculated, and the maximum size is considered as the largest connected component.

Key Insights:

• The problem involves finding the largest group of connected ones in a binary grid.
• The solution involves dynamically changing the graph using a disjoint set data structure.
• Cells are considered adjacent if they share a common side, not diagonally.
• The maximum size of the connected components is considered as the largest connected component.
• An edge case needs to be considered where a component may be connected in multiple directions.
• The time complexity of the solution is approximately O(N^2).
• The space complexity is negligible as it depends on the maximum component size.

Summary & Key Takeaways

• The problem involves finding the largest group of connected ones in a binary grid by changing at most one cell from zero to one.

• Cells are considered adjacent if they share a common side but not diagonally.

• The solution involves using a disjoint set data structure to dynamically change the graph and find the largest connected component.