Formatted question description: https://leetcode.ca/all/1351.html

# 1351. Count Negative Numbers in a Sorted Matrix (Easy)

Given a m * n matrix grid which is sorted in non-increasing order both row-wise and column-wise.

Return the number of negative numbers in grid.

Example 1:

Input: grid = [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]]
Output: 8
Explanation: There are 8 negatives number in the matrix.


Example 2:

Input: grid = [[3,2],[1,0]]
Output: 0


Example 3:

Input: grid = [[1,-1],[-1,-1]]
Output: 3


Example 4:

Input: grid = [[-1]]
Output: 1


Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 100
• -100 <= grid[i][j] <= 100

Related Topics:
Array, Binary Search

## Solution 1. Brute Force

// OJ: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix/
// Time: O(MN)
// Space: O(1)
class Solution {
public:
int countNegatives(vector<vector<int>>& grid) {
int ans = 0;
for (auto &row : grid) {
for (int c : row) {
if (c < 0) ++ans;
}
}
return ans;
}
};

// OJ: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix/
// Time: O(MlogN)
// Space: O(1)
class Solution {
public:
int countNegatives(vector<vector<int>>& grid) {
int ans = 0;
for (auto &row : grid) {
ans += upper_bound(row.rbegin(), row.rend(), -1) - row.rbegin();
}
return ans;
}
};


## Solution 3. Search Break Points

Traverse from upper right to lower left.

// OJ: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix/
// Time: O(M+N)
// Space: O(1)
class Solution {
public:
int countNegatives(vector<vector<int>>& grid) {
int M = grid.size(), N = grid.size(), x = 0, y = N - 1, ans = 0;
while (x < M) {
while (y >= 0 && grid[x][y] < 0) --y;
ans += N - 1 - y;
++x;
}
return ans;
}
};


Java

• class Solution {
public int countNegatives(int[][] grid) {
int count = 0;
int rows = grid.length, columns = grid.length;
for (int i = rows - 1; i >= 0; i--) {
if (grid[i][columns - 1] >= 0)
break;
for (int j = columns - 1; j >= 0; j--) {
if (grid[i][j] < 0)
count++;
else
break;
}
}
return count;
}
}

• // OJ: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix/
// Time: O(MN)
// Space: O(1)
class Solution {
public:
int countNegatives(vector<vector<int>>& grid) {
int ans = 0;
for (auto &row : grid) {
for (int c : row) {
if (c < 0) ++ans;
}
}
return ans;
}
};

• print("Todo!")