The problem link is here. The problem is basically to count all such sub matrices of a given matrix of size N by M, whose sum of elements is between A and B inclusive. N,M<=250. 10^-9<=A<=B<=10^9.
People have solved it using DP and BIT. I am not clear how.
First, i tried to solve a simpler version, 1-D case of the above problem: Given an array A, of length N, count all subarrays, where sum of elements in the subarray lies between A and B, but still couldn't think of better than O(n^2). Here is what i did :
I thought of making another array for keeping prefix sum of the original array, say prefix[N]. prefix[i] = A1 + A[2] + A[3] + ...A[i]. set prefix[ 1] = A [ 1]. Then for each i from 2 to N, problem is to count all j <= i such that sum Z = A[j] + A[j+1] + ..A[i] lies between A and B. This is equivalent to prefix[i] - prefix[j-1]. But it's still O(n^2), as for each i, j is hitting i places.
can anybody help me step by step to advance me in the given approach to solve the main problem ?.
