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2482. Difference Between Ones and Zeros in Row and Column

Description

You are given a 0-indexed m x n binary matrix grid.

A 0-indexed m x n difference matrix diff is created with the following procedure:

  • Let the number of ones in the ith row be onesRowi.
  • Let the number of ones in the jth column be onesColj.
  • Let the number of zeros in the ith row be zerosRowi.
  • Let the number of zeros in the jth column be zerosColj.
  • diff[i][j] = onesRowi + onesColj - zerosRowi - zerosColj

Return the difference matrix diff.

 

Example 1:

Input: grid = [[0,1,1],[1,0,1],[0,0,1]]
Output: [[0,0,4],[0,0,4],[-2,-2,2]]
Explanation:
- diff[0][0] = onesRow0 + onesCol0 - zerosRow0 - zerosCol0 = 2 + 1 - 1 - 2 = 0 
- diff[0][1] = onesRow0 + onesCol1 - zerosRow0 - zerosCol1 = 2 + 1 - 1 - 2 = 0 
- diff[0][2] = onesRow0 + onesCol2 - zerosRow0 - zerosCol2 = 2 + 3 - 1 - 0 = 4 
- diff[1][0] = onesRow1 + onesCol0 - zerosRow1 - zerosCol0 = 2 + 1 - 1 - 2 = 0 
- diff[1][1] = onesRow1 + onesCol1 - zerosRow1 - zerosCol1 = 2 + 1 - 1 - 2 = 0 
- diff[1][2] = onesRow1 + onesCol2 - zerosRow1 - zerosCol2 = 2 + 3 - 1 - 0 = 4 
- diff[2][0] = onesRow2 + onesCol0 - zerosRow2 - zerosCol0 = 1 + 1 - 2 - 2 = -2
- diff[2][1] = onesRow2 + onesCol1 - zerosRow2 - zerosCol1 = 1 + 1 - 2 - 2 = -2
- diff[2][2] = onesRow2 + onesCol2 - zerosRow2 - zerosCol2 = 1 + 3 - 2 - 0 = 2

Example 2:

Input: grid = [[1,1,1],[1,1,1]]
Output: [[5,5,5],[5,5,5]]
Explanation:
- diff[0][0] = onesRow0 + onesCol0 - zerosRow0 - zerosCol0 = 3 + 2 - 0 - 0 = 5
- diff[0][1] = onesRow0 + onesCol1 - zerosRow0 - zerosCol1 = 3 + 2 - 0 - 0 = 5
- diff[0][2] = onesRow0 + onesCol2 - zerosRow0 - zerosCol2 = 3 + 2 - 0 - 0 = 5
- diff[1][0] = onesRow1 + onesCol0 - zerosRow1 - zerosCol0 = 3 + 2 - 0 - 0 = 5
- diff[1][1] = onesRow1 + onesCol1 - zerosRow1 - zerosCol1 = 3 + 2 - 0 - 0 = 5
- diff[1][2] = onesRow1 + onesCol2 - zerosRow1 - zerosCol2 = 3 + 2 - 0 - 0 = 5

 

Constraints:

  • m == grid.length
  • n == grid[i].length
  • 1 <= m, n <= 105
  • 1 <= m * n <= 105
  • grid[i][j] is either 0 or 1.

Solutions

Solution 1: Simulation

We can solve this problem by simulating the process as described in the problem statement.

The time complexity is $O(m \times n)$, and if we ignore the space used by the answer, the space complexity is $O(m + n)$. Here, $m$ and $n$ are the number of rows and columns in the matrix, respectively.

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class Solution:
    def onesMinusZeros(self, grid: List[List[int]]) -> List[List[int]]:
        m, n = len(grid), len(grid[0])
        rows = [0] * m
        cols = [0] * n
        for i, row in enumerate(grid):
            for j, v in enumerate(row):
                rows[i] += v
                cols[j] += v
        diff = [[0] * n for _ in range(m)]
        for i, r in enumerate(rows):
            for j, c in enumerate(cols):
                diff[i][j] = r + c - (n - r) - (m - c)
        return diff

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class Solution {
    public int[][] onesMinusZeros(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        int[] rows = new int[m];
        int[] cols = new int[n];
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                int v = grid[i][j];
                rows[i] += v;
                cols[j] += v;
            }
        }
        int[][] diff = new int[m][n];
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                diff[i][j] = rows[i] + cols[j] - (n - rows[i]) - (m - cols[j]);
            }
        }
        return diff;
    }
}

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class Solution {
public:
    vector<vector<int>> onesMinusZeros(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size();
        vector<int> rows(m);
        vector<int> cols(n);
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                int v = grid[i][j];
                rows[i] += v;
                cols[j] += v;
            }
        }
        vector<vector<int>> diff(m, vector<int>(n));
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                diff[i][j] = rows[i] + cols[j] - (n - rows[i]) - (m - cols[j]);
            }
        }
        return diff;
    }
};

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func onesMinusZeros(grid [][]int) [][]int {
    m, n := len(grid), len(grid[0])
    rows := make([]int, m)
    cols := make([]int, n)
    diff := make([][]int, m)
    for i, row := range grid {
        diff[i] = make([]int, n)
        for j, v := range row {
            rows[i] += v
            cols[j] += v
        }
    }
    for i, r := range rows {
        for j, c := range cols {
            diff[i][j] = r + c - (n - r) - (m - c)
        }
    }
    return diff
}

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function onesMinusZeros(grid: number[][]): number[][] {
    const m = grid.length;
    const n = grid[0].length;
    const rows = new Array(m).fill(0);
    const cols = new Array(n).fill(0);
    for (let i = 0; i < m; i++) {
        for (let j = 0; j < n; j++) {
            if (grid[i][j]) {
                rows[i]++;
                cols[j]++;
            }
        }
    }
    const ans = Array.from({ length: m }, () => new Array(n).fill(0));
    for (let i = 0; i < m; i++) {
        for (let j = 0; j < n; j++) {
            ans[i][j] = rows[i] + cols[j] - (m - rows[i]) - (n - cols[j]);
        }
    }
    return ans;
}

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impl Solution {
    pub fn ones_minus_zeros(grid: Vec<Vec<i32>>) -> Vec<Vec<i32>> {
        let m = grid.len();
        let n = grid[0].len();
        let mut rows = vec![0; m];
        let mut cols = vec![0; n];
        for i in 0..m {
            for j in 0..n {
                if grid[i][j] == 1 {
                    rows[i] += 1;
                    cols[j] += 1;
                }
            }
        }
        let mut ans = vec![vec![0; n]; m];
        for i in 0..m {
            for j in 0..n {
                ans[i][j] = (rows[i] + cols[j] - (m - rows[i]) - (n - cols[j])) as i32;
            }
        }
        ans
    }
}

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/**
 * Return an array of arrays of size *returnSize.
 * The sizes of the arrays are returned as *returnColumnSizes array.
 * Note: Both returned array and *columnSizes array must be malloced, assume caller calls free().
 */
int** onesMinusZeros(int** grid, int gridSize, int* gridColSize, int* returnSize, int** returnColumnSizes) {
    int* rows = malloc(sizeof(int) * gridSize);
    int* cols = malloc(sizeof(int) * gridColSize[0]);
    memset(rows, 0, sizeof(int) * gridSize);
    memset(cols, 0, sizeof(int) * gridColSize[0]);
    for (int i = 0; i < gridSize; i++) {
        for (int j = 0; j < gridColSize[0]; j++) {
            if (grid[i][j]) {
                rows[i]++;
                cols[j]++;
            }
        }
    }
    int** ans = malloc(sizeof(int*) * gridSize);
    for (int i = 0; i < gridSize; i++) {
        ans[i] = malloc(sizeof(int) * gridColSize[0]);
        for (int j = 0; j < gridColSize[0]; j++) {
            ans[i][j] = rows[i] + cols[j] - (gridSize - rows[i]) - (gridColSize[0] - cols[j]);
        }
    }
    *returnSize = gridSize;
    *returnColumnSizes = gridColSize;
    return ans;
}

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