Given a m x n matrix, if an element is 0, set its entire row and column to 0. Do it in-place.

Example 1:

Input:
[
[1,1,1],
[1,0,1],
[1,1,1]
]
Output:
[
[1,0,1],
[0,0,0],
[1,0,1]
]


Example 2:

Input:
[
[0,1,2,0],
[3,4,5,2],
[1,3,1,5]
]
Output:
[
[0,0,0,0],
[0,4,5,0],
[0,3,1,0]
]


• A straight forward solution using O(mn) space is probably a bad idea.
• A simple improvement uses O(m + n) space, but still not the best solution.
• Could you devise a constant space solution?

## Solutions

### 1. Space O(m+n)

注意理解位操作，以及最后是要成行或成列都要变成 0.

# Time Complexity: O(mn)
# Space Complexity: O(m+n)
class Solution:
def setZeroes(self, matrix: List[List[int]]) -> None:
"""
Do not return anything, modify matrix in-place instead.
"""
if not matrix:
return matrix
lr, ll = len(matrix), len(matrix)
row = [0 for i in range(lr)]
col = [0 for i in range(ll)]
for i in range(lr):
for j in range(ll):
row[i] = row[i] | (matrix[i][j] == 0)
col[j] = col[j] | (matrix[i][j] == 0)

for i in range(lr):
for j in range(ll):
if row[i] or col[j]:
matrix[i][j] = 0

return matrix
# Runtime: 160 ms, faster than 35.48% of Python3 online submissions for Set Matrix Zeroes.
# Memory Usage: 14.5 MB, less than 5.13% of Python3 online submissions for Set Matrix Zeroes.


### 2. Space O(1)

# Time Complexity: O(mn)
# Space Complexity: O(1)
class Solution:
def setZeroes(self, matrix: List[List[int]]) -> None:
"""
Do not return anything, modify matrix in-place instead.
"""
if not matrix:
return matrix
lr, ll = len(matrix), len(matrix)
r0 = False
c0 = False
# if there is 0 in edge
for i in range(lr):
r0 = r0 | (matrix[i] == 0)
for j in range(ll):
c0 = c0 | (matrix[j] == 0)

for i in range(1, lr):
for j in range(1, ll):
if matrix[i][j] == 0:
matrix[i] = 0
matrix[j] = 0

for i in range(1, lr):
for j in range(1, ll):
if matrix[i] == 0 or matrix[j] == 0:
matrix[i][j] = 0

if r0:
for i in range(lr):
matrix[i] = 0
if c0:
for j in range(ll):
matrix[j] = 0

return matrix
# Runtime: 148 ms, faster than 93.53% of Python3 online submissions for Set Matrix Zeroes.
# Memory Usage: 14.4 MB, less than 5.13% of Python3 online submissions for Set Matrix Zeroes.