1252. Cells with Odd Values in a Matrix

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Created At : 2023-10-28 15:14

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There is an m x n matrix that is initialized to all 0‘s. There is also a 2D array indices where each indices[i] = [ri, ci] represents a 0-indexed location to perform some increment operations on the matrix.

For each location indices[i], do both of the following:

Increment all the cells on row ri.
Increment all the cells on column ci.

Given m, n, and indices, return *the number of odd-valued cells in the matrix after applying the increment to all locations in *indices.

Example 1:

Input: m = 2, n = 3, indices = [[0,1],[1,1]]
Output: 6
Explanation: Initial matrix = [[0,0,0],[0,0,0]].
After applying first increment it becomes [[1,2,1],[0,1,0]].
The final matrix is [[1,3,1],[1,3,1]], which contains 6 odd numbers.

Example 2:

Input: m = 2, n = 2, indices = [[1,1],[0,0]]
Output: 0
Explanation: Final matrix = [[2,2],[2,2]]. There are no odd numbers in the final matrix.

Constraints:

1 <= m, n <= 50
1 <= indices.length <= 100
0 <= ri < m
0 <= ci < n

Follow up: Could you solve this in O(n + m + indices.length) time with only O(n + m) extra space?

这道题给了一个大小为 m by n 的矩阵，初始化均为0，又给了一个坐标数组 indices，说是对于其中的每个坐标 (r, c)，将对应的行和列上的数字分别自增1，最后问数组中有多少个数字是奇数。当然最简单暴力的解法就是就是遍历每个坐标，分别将对应的行列上的数字自增1，然后最后再判断奇偶，虽然这是一道 Easy 的题目，但博主还是怀疑这种方法可能会超时，所以根本就没有尝试。对于每个坐标都遍历一次行和列，实在是不太高效，因为该行和该列可能后面还会多次出现，有没有办法能够一次性统计出某行某列到底需要更新多少次呢？答案是肯定的，这里可以建立两个数组 rowCnt 和 colCnt，分别来统计某行和某列需要更新的次数。之后遍历整个初始数组，对于任意位置 (i, j)，去 rowCnt 和 colCnt 中取出行i和列j需要的更新次数，二者之和就是当前位置需要增加的数字，直接判断奇偶，奇数的话加到结果 res 中即可，参见代码如下：

class Solution {
public:
    int oddCells(int m, int n, vector<vector<int>>& indices) {
        int res = 0;
        vector<int> rowCnt(m), colCnt(n);
        for (auto idx : indices) {
            ++rowCnt[idx[0]];
            ++colCnt[idx[1]];
        }
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                res += (rowCnt[i] + colCnt[j]) % 2;
            }
        }
        return res;
    }
};

Github 同步地址:

https://github.com/grandyang/leetcode/issues/1252

参考资料：

https://leetcode.com/problems/cells-with-odd-values-in-a-matrix/

https://leetcode.com/problems/cells-with-odd-values-in-a-matrix/discuss/425100/JavaPython-3-2-methods%3A-time-O(m-*-n-%2B-L)-and-O(L)-codes-w-comment-and-analysis.

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