Contents
How do you find the sum of submatrix in a matrix?
So total occurance of Arr(x,y) will be (X + 1) * (Y + 1) * (N – X) * (N – Y). Let’s call this total number of occurance be S(x,y). So, total sum of produced by this element will be Arr(x,y) * S(x,y). Now, we can figure out total sum of submatrices by adding total sum of all the elements of matrix.
How do I find submatrix?
Find sub-matrix with the given sum
- Create an array dp[N + 1][N + 1] where dp[i][j] stores the sum of all the elements with row between 1 to i and column between 1 to j.
- Once the 2-D matrix is generated, now suppose we wish to find sum of square starting with (i, j) to (i + x, j + x).
How do you create an auxiliary sum of a matrix?
The idea is to first create an auxiliary matrix aux[M][N] such that aux[i][j] stores sum of elements in submatrix from (0,0) to (i,j). Once aux[][] is constructed, we can compute sum of submatrix between (tli, tlj) and (rbi, rbj) in O(1) time. We need to consider aux[rbi][rbj] and subtract all unncessary elements.
How to find the maximum sum in a matrix?
Find maximum sum submatrix present in a matrix Given an N × Nmatrix, find the maximum sum submatrix present in it. For example, the maximum sum submatrix is highlighted in green in the following matrices: The idea is to preprocess the matrix.
How to find the size of a sub-matrix?
Given a Matrix arr [] [] of size M x N having positive integers and a number K, the task is to find the size of the largest square sub-matrix whose sum of elements is less than or equals to K .
How to find the maximum sum of a rectangle?
Finding the maximum-sum sub=rectangle within a matrix [duplicate] Given a 2-dimensional array of positive and negative integers, find the sub-rectangle with the largest sum. The sum of a rectangle is the sum of all the elements in that rectangle. In this problem the sub-rectangle with the largest sum is referred to as the maximal sub-rectangle.
How to find the maximum sum in constant time?
We can easily calculate the value of sum [i] [j] in constant time using the following relation: Now to find the maximum sum k × k submatrix, consider every submatrix of size k × k and calculate their sum in constant time by directly using the following relation: Here, (i, j) represents the bottom-right corner coordinates of the k × k submatrix.