- Platform: YouTube
- Channel/Creator: NeetCode
- Duration: 00:13:17
- Release Date: Jun 2, 2022
- Video Link: https://www.youtube.com/watch?v=KE8MQuwE2yA
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Rust handles memory safety by using ownership and borrowing rules, but here we're focusing on a 2D matrix sum query. You get a 2D matrix and need to compute the sum of any submatrix defined by its top-left (row1, col1) and bottom-right (row2, col2) coordinates. Multiple queries make efficiency key.
Key takeaway: The goal is constant-time queries after preprocessing, building on prefix sum ideas to avoid repeated nested loops for each query.
To compute a submatrix sum, loop through rows from row1 to row2, and for each row, loop through columns from col1 to col2, adding up values. This works but gets slow with many queries, as each could take O(rows * cols) time in the worst case.
Key example: For a submatrix from (1,2) to (2,4), nest loops to sum elements row by row.
In 1D, precompute a prefix array where prefix[i] is the sum from index 0 to i-1. Then, sum from left to right is prefix[right+1] - prefix[left]. This takes O(n) preprocessing and O(1) per query, efficient for many subarray sums.
Key example: For array [3,3,1,4,2], prefix becomes [0,3,6,7,11,13]. Sum from index 1 to 3: 6 +1 +4 =11, or prefix[4] - prefix[1] =11-3=8? Wait, adjust indices properly.
In 2D, create a prefix matrix where prefix[r][c] holds the sum from (0,0) to (r-1,c-1). To get a submatrix sum, use inclusion-exclusion: prefix[row2+1][col2+1] - prefix[row1][col2+1] - prefix[row2+1][col1] + prefix[row1][col1]. This subtracts overlapping regions correctly.
Key takeaway: Precomputing the 2D prefix takes O(m*n) time, enabling O(1) queries by treating each bottom-right as a potential submatrix end.
To avoid out-of-bounds checks for queries at the matrix edges, make the prefix matrix (rows+1) x (cols+1) initialized to zeros. This way, subtracting from row-1 or col-1 hits zeros naturally, simplifying code without if-statements.
Key example: For a 3x4 matrix, prefix is 4x5 with top row and left column as zeros.
In the constructor, get matrix dimensions m (rows) and n (cols). Create sum_mat as [[0] * (n+1) for _ in range(m+1)]. Then, for r in range(m), for c in range(n): sum_mat[r+1][c+1] = matrix[r][c] + sum_mat[r+1][c] + sum_mat[r][c+1] - sum_mat[r][c]. This accumulates row-wise and column-wise sums.
self.sum_mat = [[0] * (cols + 1) for _ in range(rows + 1)]
for r in range(rows):
for c in range(cols):
self.sum_mat[r + 1][c + 1] = (
matrix[r][c] +
self.sum_mat[r + 1][c] +
self.sum_mat[r][c + 1] -
self.sum_mat[r][c]
)Ask AI: Building 2D Prefix Matrix
In sumRegion, add 1 to all inputs for offset: r1 +=1, c1 +=1, r2 +=1, c2 +=1. Then return sum_mat[r2][c2] - sum_mat[r1-1][c2] - sum_mat[r2][c1-1] + sum_mat[r1-1][c1-1]. This gives the exact submatrix sum in O(1) time.
def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
r1, c1, r2, c2 = row1 + 1, col1 + 1, row2 + 1, col2 + 1
return (
self.sum_mat[r2][c2] -
self.sum_mat[r1 - 1][c2] -
self.sum_mat[r2][c1 - 1] +
self.sum_mat[r1 - 1][c1 - 1]
)Ask AI: 2D Sum Query Implementation
About the summarizer
I'm Ali Sol, a Backend Developer. Learn more:
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