DSA interview question

Number of Enclaves

Medium · Data structures · Topics: graph, dfs, bfs, matrix

The problem

A map grid marks land with 1 and sea with 0. An enclave cell is a land cell from which you can't walk off the edge of the map, moving 4-directionally over land. Count the enclave cells. Like surrounded regions, reverse the question. Flood-fill from every land cell on the border; everything reached can walk off. The land cells left unreached are enclaves.

Example: [[0,0,0,0], [1,0,1,0], [0,1,1,0], [0,0,0,0]] → 3.

Function signature

int numEnclaves(vector<vector<int>> grid);

Test cases

Input	Output	Explanation
`[[0,0,0,0],[1,0,1,0],[0,1,1,0],[0,0,0,0]]`	`3`	The left 1 is on the border
`[[0,1,1,0],[0,0,1,0],[0,0,1,0],[0,0,0,0]]`	`0`	All connected to the top edge
`[[0,0,0],[0,1,0],[0,0,0]]`	`1`
`[[1,1,1],[1,0,1],[1,1,1]]`	`0`	A ring on the border
`[[1]]`	`0`

(Confirm: 4-directional moves; the answer counts cells, not regions.)

How interviewers phrase it

"Return the number of land cells from which we cannot walk off the boundary of the grid in any number of moves" (LeetCode 1020).

Clarifying questions to ask

Count cells or regions? (Cells.)
4-directional? (Yes.)
May I modify the grid? (Yes; otherwise copy it.)

Follow-ups to expect

"Why flood from the border?"
"How is this related to surrounded regions?"
"Could you count per region?"
"Memory?"
"Complexity?"

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