# Posts tagged as “square”

Given a m * n matrix of ones and zeros, return how many square submatrices have all ones.

Example 1:

Input: matrix =
[
[0,1,1,1],
[1,1,1,1],
[0,1,1,1]
]
Output: 15
Explanation:
There are 10 squares of side 1.
There are 4 squares of side 2.
There is  1 square of side 3.
Total number of squares = 10 + 4 + 1 = 15.


Example 2:

Input: matrix =
[
[1,0,1],
[1,1,0],
[1,1,0]
]
Output: 7
Explanation:
There are 6 squares of side 1.
There is 1 square of side 2.
Total number of squares = 6 + 1 = 7.


Constraints:

• 1 <= arr.length <= 300
• 1 <= arr[0].length <= 300
• 0 <= arr[i][j] <= 1

## Solution: DP

dp[i][j] := edge of largest square with bottom right corner at (i, j)
dp[i][j] = min(dp[i – 1][j], dp[i – 1][j – 1], dp[i][j – 1]) if m[i][j] == 1 else 0
ans = sum(dp)

Time complexity: O(n*m)
Space complexity: O(n*m)

# Problem

https://leetcode.com/problems/valid-square/description/

Given the coordinates of four points in 2D space, return whether the four points could construct a square.

The coordinate (x,y) of a point is represented by an integer array with two integers.

Example:

Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
Output: True


Note:

1. All the input integers are in the range [-10000, 10000].
2. A valid square has four equal sides with positive length and four equal angles (90-degree angles).
3. Input points have no order.

# Solution

Time complexity: O(1)

Space complexity: O(1)

C++

Mission News Theme by Compete Themes.