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描述
Given a rows x cols matrix mat, where mat[i][j] is either 0 or 1, return the number of special positions in mat.
A position (i,j) is called special if mat[i][j] == 1 and all other elements in row i and column j are 0 (rows and columns are 0-indexed).
Example 1:
Input: mat = [[1,0,0],
[0,0,1],
[1,0,0]]
Output: 1
Explanation: (1,2) is a special position because mat[1][2] == 1 and all other elements in row 1 and column 2 are 0.
Example 2:
Input: mat = [[1,0,0],
[0,1,0],
[0,0,1]]
Output: 3
Explanation: (0,0), (1,1) and (2,2) are special positions.
Example 3:
Input: mat = [[0,0,0,1],
[1,0,0,0],
[0,1,1,0],
[0,0,0,0]]
Output: 2
Example 4:
Input: mat = [[0,0,0,0,0],
[1,0,0,0,0],
[0,1,0,0,0],
[0,0,1,0,0],
[0,0,0,1,1]]
Output: 3
Note:
rows == mat.length
cols == mat[i].length
1 <= rows, cols <= 100
mat[i][j] is 0 or 1.
解析
根据题意，就是要找出 mat 中的特殊数字有几个。特殊数字就是必须为 1 且所在的行和列其他位置都为 0 。直接使用内置函数，计算出来水平和垂直两个方向的和 h 和 v ，然后遍历 mat 中的元素，只要该元素为 1 且所在行和列的元素和为 1 ，那就将结果 result 加一，遍历结束即可得到结果。当然按照我的习惯，这种使用内置函数的做法我不推荐。
解答
class Solution(object):
def numSpecial(self, mat):
"""
:type mat: List[List[int]]
:rtype: int
"""
import numpy as np
mat = np.array(mat)
v = np.sum(mat,0)
h = np.sum(mat,1)
result = 0
for i in range(len(mat)):
if h[i]!=1:
continue
for j in range(len(mat[0])):
if mat[i][j]==1 and v[j]==1 and h[i]==1:
result += 1
break
return result
运行结果
Runtime: 184 ms, faster than 20.65% of Python online submissions for Special Positions in a Binary Matrix.
Memory Usage: 26 MB, less than 5.43% of Python online submissions for Special Positions in a Binary Matrix.
解析
直接遍历矩阵 mat 中的每一行，然后计算每一行中 1 的个数只有一个的情况下，找到这个 1 的索引，然后计算这个索引所在的列的中的 1 的个数是否也是只有一个，如果是则计数器 result 加一，遍历结束得到的 result 为最终的结果。结果证明这种方法的速度更快，所占内存更小。
解答
class Solution(object):
def numSpecial(self, mat):
"""
:type mat: List[List[int]]
:rtype: int
"""
result = 0
for i in range(len(mat)):
if mat[i].count(1) == 1:
i = mat[i].index(1)
col = [row[i] for row in mat]
if col.count(1) == 1:
result += 1
return result
运行结果
Runtime: 128 ms, faster than 97.14% of Python online submissions for Special Positions in a Binary Matrix.
Memory Usage: 13.5 MB, less than 87.14% of Python online submissions for Special Positions in a Binary Matrix.
原题链接：leetcode.com/problems/sp…
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