sum query in 2d immutable array dynamic programming скачать в хорошем качестве

sum query in 2d immutable array dynamic programming

Download 1M+ code from https://codegive.com/4b4f4dd sure! the sum query in a 2d immutable array can be efficiently solved using a technique often referred to as the "2d prefix sum" or "2d cumulative sum." this technique allows us to preprocess the array so that we can answer sum queries in constant time after an initial preprocessing step. tutorial on 2d sum queries 1. understanding the problem given a 2d array (or matrix) `matrix` of size `m x n`, you want to answer multiple queries of the form: *sum of elements in a sub-matrix* defined by the top-left corner `(x1, y1)` and bottom-right corner `(x2, y2)`. 2. prefix sum concept the prefix sum array helps in calculating the sum of any sub-matrix efficiently. the idea is to create a new 2d array `prefix` where each element `prefix[i][j]` contains the sum of all elements in the rectangle defined by the top-left corner `(0, 0)` and the bottom-right corner `(i, j)`. the relationship for filling the `prefix` array is: this formula accounts for: the current cell `matrix[i][j]` the sum of the previous row `prefix[i-1][j]` the sum of the previous column `prefix[i][j-1]` subtracting the overlapping area `prefix[i-1][j-1]` 3. preprocessing the prefix sum array we will first build the `prefix` sum array from the original matrix. this preprocessing step takes `o(m * n)` time. 4. answering the queries once we have the `prefix` array, we can answer the sum query for any sub-matrix in constant time `o(1)` using the following formula: 5. implementation here is a python implementation of the above concept: explanation of the code **initialization (`__init__`)**: we create a prefix sum array based on the input matrix. the prefix sums are computed using the relationships described above. **sum query (`sumregion`)**: for any query, we calculate the sum using the prefix array and the boundaries provided by the input. conclusion the 2d prefix sum technique is a powerful way to handle sum queries in static or immutable 2d arrays. by preprocess ... #DynamicProgramming #2DArray #javacollections 2D array immutable array dynamic programming sum query range sum prefix sum cumulative sum 2D prefix array query optimization space complexity time complexity array manipulation interval sum data structure algorithm efficiency