[LeetCode] 1252. Cells with Odd Values in a Matrix 奇數值單元格的數目

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:

1. Increment all the cells on row ri.
2. 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?

這道題給了一個大小為 m by n 的矩陣，初始化均為0，又給了一個坐標數組 indices，說是對於其中的每個坐標 (r, c)，將對應的行和列上的數字分別自增1，最后問數組中有多少個數字是奇數。當然最簡單暴力的解法就是就是遍歷每個坐標，分別將對應的行列上的數字自增1，然后最后再判斷奇偶，雖然這是一道 Easy 的題目，但博主還是懷疑這種方法可能會超時，所以根本就沒有嘗試。對於每個坐標都遍歷一次行和列，實在是不太高效，因為該行和該列可能后面還會多次出現，有沒有辦法能夠一次性統計出某行某列到底需要更新多少次呢？答案是肯定的，這里可以建立兩個數組 rowCnt 和 colCnt，分別來統計某行和某列需要更新的次數。之后遍歷整個初始數組，對於任意位置 (i, j)，去 rowCnt 和 colCnt 中取出行i和列j需要的更新次數，二者之和就是當前位置需要增加的數字，直接判斷奇偶，奇數的話加到結果 res 中即可，參見代碼如下：

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

參考資料：

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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