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+ ---
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+ license: llama2
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+ language:
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+ - en
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+ tags:
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+ - Python
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+ - Leetcode
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+ - Problem Solving
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+ - CP
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+ ---
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+
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+ ```
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+ Below is an instruction that describes a task, paired with an input that provides further context. Write a response that appropriately completes the request.
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+
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+ ### Instruction:
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+ Solve the problem using Python.
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+
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+ ### Input:
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+ Consider a matrix M with dimensions width * height, such that every cell has value 0 or 1, and any square sub-matrix of M of size sideLength * sideLength has at most maxOnes ones.
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+
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+ Return the maximum possible number of ones that the matrix M can have.
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+
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+
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+
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+ Example 1:
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+
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+ Input: width = 3, height = 3, sideLength = 2, maxOnes = 1
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+ Output: 4
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+ Explanation:
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+ In a 3*3 matrix, no 2*2 sub-matrix can have more than 1 one.
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+ The best solution that has 4 ones is:
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+ [1,0,1]
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+ [0,0,0]
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+ [1,0,1]
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+
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+ Example 2:
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+
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+ Input: width = 3, height = 3, sideLength = 2, maxOnes = 2
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+ Output: 6
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+ Explanation:
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+ [1,0,1]
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+ [1,0,1]
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+ [1,0,1]
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+
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+
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+
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+ Constraints:
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+
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+ 1 <= width, height <= 100
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+ 1 <= sideLength <= width, height
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+ 0 <= maxOnes <= sideLength * sideLength
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+
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+
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+
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+ ### Response:
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+ Sure, here you have a possible implementation to solve the problem.
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+
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+ '''python
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+ class Solution:
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+ def maximumNumberOfOnes(self, C, R, K, maxOnes):
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+ # every K*K square has at most maxOnes ones
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+ count = [0] * (K*K)
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+ for r in range(R):
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+ for c in range(C):
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+ code = (r%K) * K + c%K
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+ count[code] += 1
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+ count.sort()
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+ ans = 0
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+ for _ in range(maxOnes):
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+ ans += count.pop()
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+ return ans
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+ '''
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+ ```