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Formatted question description: https://leetcode.ca/all/2201.html

# 2201. Count Artifacts That Can Be Extracted (Medium)

There is an `n x n`

**0-indexed** grid with some artifacts buried in it. You are given the integer `n`

and a **0-indexed **2D integer array `artifacts`

describing the positions of the rectangular artifacts where `artifacts[i] = [r1`

denotes that the _{i}, c1_{i}, r2_{i}, c2_{i}]`i`

artifact is buried in the subgrid where:^{th}

`(r1`

is the coordinate of the_{i}, c1_{i})**top-left**cell of the`i`

artifact and^{th}`(r2`

is the coordinate of the_{i}, c2_{i})**bottom-right**cell of the`i`

artifact.^{th}

You will excavate some cells of the grid and remove all the mud from them. If the cell has a part of an artifact buried underneath, it will be uncovered. If all the parts of an artifact are uncovered, you can extract it.

Given a **0-indexed** 2D integer array `dig`

where `dig[i] = [r`

indicates that you will excavate the cell _{i}, c_{i}]`(r`

, return _{i}, c_{i})*the number of artifacts that you can extract*.

The test cases are generated such that:

- No two artifacts overlap.
- Each artifact only covers at most
`4`

cells. - The entries of
`dig`

are unique.

**Example 1:**

Input:n = 2, artifacts = [[0,0,0,0],[0,1,1,1]], dig = [[0,0],[0,1]]Output:1Explanation:The different colors represent different artifacts. Excavated cells are labeled with a 'D' in the grid. There is 1 artifact that can be extracted, namely the red artifact. The blue artifact has one part in cell (1,1) which remains uncovered, so we cannot extract it. Thus, we return 1.

**Example 2:**

Input:n = 2, artifacts = [[0,0,0,0],[0,1,1,1]], dig = [[0,0],[0,1],[1,1]]Output:2Explanation:Both the red and blue artifacts have all parts uncovered (labeled with a 'D') and can be extracted, so we return 2.

**Constraints:**

`1 <= n <= 1000`

`1 <= artifacts.length, dig.length <= min(n`

^{2}, 10^{5})`artifacts[i].length == 4`

`dig[i].length == 2`

`0 <= r1`

_{i}, c1_{i}, r2_{i}, c2_{i}, r_{i}, c_{i}<= n - 1`r1`

_{i}<= r2_{i}`c1`

_{i}<= c2_{i}- No two artifacts will overlap.
- The number of cells covered by an artifact is
**at most**`4`

. - The entries of
`dig`

are unique.

**Companies**:

IMC

**Related Topics**:

Array, Hash Table

**Similar Questions**:

## Solution 1.

Create an `NxN`

array `M`

. `M[i][j] = true`

if the cell `(i, j)`

is digged.

For each artifact, traverse all its cells. If all the cells are digged, increment the answer.

```
// OJ: https://leetcode.com/problems/count-artifacts-that-can-be-extracted/
// Time: O(DIG + N^2)
// Space: O(N^2)
class Solution {
public:
int digArtifacts(int n, vector<vector<int>>& A, vector<vector<int>>& dig) {
vector<vector<bool>> M(n, vector<bool>(n)); // M[i][j] = true if it's digged.
for (auto &d : dig) M[d[0]][d[1]] = true;
int ans = 0;
for (auto &v : A) {
bool good = true;
for (int x = v[0]; x <= v[2] && good; ++x) {
for (int y = v[1]; y <= v[3] && good; ++y) {
if (!M[x][y]) good = false;
}
}
if (good) ++ans;
}
return ans;
}
};
```

## Discussion

https://leetcode.com/problems/count-artifacts-that-can-be-extracted/discuss/1844106