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1314. Matrix Block Sum
Description
Given a m x n matrix mat and an integer k, return a matrix answer where each answer[i][j] is the sum of all elements mat[r][c] for:
i - k <= r <= i + k,j - k <= c <= j + k, and(r, c)is a valid position in the matrix.
Example 1:
Input: mat = [[1,2,3],[4,5,6],[7,8,9]], k = 1 Output: [[12,21,16],[27,45,33],[24,39,28]]
Example 2:
Input: mat = [[1,2,3],[4,5,6],[7,8,9]], k = 2 Output: [[45,45,45],[45,45,45],[45,45,45]]
Constraints:
m == mat.lengthn == mat[i].length1 <= m, n, k <= 1001 <= mat[i][j] <= 100
Solutions
Dynamic programming - 2D preSum.
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class Solution { private int[][] pre; private int m; private int n; public int[][] matrixBlockSum(int[][] mat, int k) { int m = mat.length, n = mat[0].length; int[][] pre = new int[m + 1][n + 1]; for (int i = 1; i < m + 1; ++i) { for (int j = 1; j < n + 1; ++j) { pre[i][j] = pre[i - 1][j] + pre[i][j - 1] + -pre[i - 1][j - 1] + mat[i - 1][j - 1]; } } this.pre = pre; this.m = m; this.n = n; int[][] ans = new int[m][n]; for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { ans[i][j] = get(i + k + 1, j + k + 1) - get(i + k + 1, j - k) - get(i - k, j + k + 1) + get(i - k, j - k); } } return ans; } private int get(int i, int j) { i = Math.max(Math.min(m, i), 0); j = Math.max(Math.min(n, j), 0); return pre[i][j]; } } -
class Solution { public: vector<vector<int>> matrixBlockSum(vector<vector<int>>& mat, int k) { int m = mat.size(), n = mat[0].size(); vector<vector<int>> pre(m + 1, vector<int>(n + 1)); for (int i = 1; i < m + 1; ++i) { for (int j = 1; j < n + 1; ++j) { pre[i][j] = pre[i - 1][j] + pre[i][j - 1] + -pre[i - 1][j - 1] + mat[i - 1][j - 1]; } } vector<vector<int>> ans(m, vector<int>(n)); for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { ans[i][j] = get(i + k + 1, j + k + 1, m, n, pre) - get(i + k + 1, j - k, m, n, pre) - get(i - k, j + k + 1, m, n, pre) + get(i - k, j - k, m, n, pre); } } return ans; } int get(int i, int j, int m, int n, vector<vector<int>>& pre) { i = max(min(m, i), 0); j = max(min(n, j), 0); return pre[i][j]; } }; -
class Solution: def matrixBlockSum(self, mat: List[List[int]], k: int) -> List[List[int]]: m, n = len(mat), len(mat[0]) pre = [[0] * (n + 1) for _ in range(m + 1)] for i in range(1, m + 1): for j in range(1, n + 1): pre[i][j] = ( pre[i - 1][j] + pre[i][j - 1] - pre[i - 1][j - 1] + mat[i - 1][j - 1] ) def get(i, j): i = max(min(m, i), 0) j = max(min(n, j), 0) return pre[i][j] ans = [[0] * n for _ in range(m)] for i in range(m): for j in range(n): ans[i][j] = ( get(i + k + 1, j + k + 1) - get(i + k + 1, j - k) - get(i - k, j + k + 1) + get(i - k, j - k) ) return ans -
func matrixBlockSum(mat [][]int, k int) [][]int { m, n := len(mat), len(mat[0]) pre := make([][]int, m+1) for i := 0; i < m+1; i++ { pre[i] = make([]int, n+1) } for i := 1; i < m+1; i++ { for j := 1; j < n+1; j++ { pre[i][j] = pre[i-1][j] + pre[i][j-1] + -pre[i-1][j-1] + mat[i-1][j-1] } } get := func(i, j int) int { i = max(min(m, i), 0) j = max(min(n, j), 0) return pre[i][j] } ans := make([][]int, m) for i := 0; i < m; i++ { ans[i] = make([]int, n) for j := 0; j < n; j++ { ans[i][j] = get(i+k+1, j+k+1) - get(i+k+1, j-k) - get(i-k, j+k+1) + get(i-k, j-k) } } return ans } -
function matrixBlockSum(mat: number[][], k: number): number[][] { const m: number = mat.length; const n: number = mat[0].length; const s: number[][] = Array.from({ length: m + 1 }, () => Array(n + 1).fill(0)); for (let i = 0; i < m; i++) { for (let j = 0; j < n; j++) { s[i + 1][j + 1] = s[i][j + 1] + s[i + 1][j] - s[i][j] + mat[i][j]; } } const ans: number[][] = Array.from({ length: m }, () => Array(n).fill(0)); for (let i = 0; i < m; i++) { for (let j = 0; j < n; j++) { const x1: number = Math.max(i - k, 0); const y1: number = Math.max(j - k, 0); const x2: number = Math.min(m - 1, i + k); const y2: number = Math.min(n - 1, j + k); ans[i][j] = s[x2 + 1][y2 + 1] - s[x1][y2 + 1] - s[x2 + 1][y1] + s[x1][y1]; } } return ans; }