Given a 2D array of size M x N. Calculate count of positions in 2D array where address as per row major order equals to address as per column major order.
Input : 3 5
Output : 3
Row major address is same as column major for following i, j
pairs (1, 1), (2, 3) & (3, 5)
Input : 4 4
Output : 4
Lets consider element with index i, j
Row major address = B + w * (N * (i-1) + j-1) Column major address = B + w * (M * (j-1) + i-1)
B : Base address of the array
w : Size of each element of the array
Equating both addresses, we get B + w * (N * (i-1) + j-1) = B + w * (M * (j-1) + i-1) N * (i-1) + j = M * (j-1) + i N*i - N + j = M*j - M + i M*j - j = N*i - N + M - i (M-1) * j = N*i - N + M - i j = (N*i - N + M - i)/(M-1) - (Eq. 1) Similarly i = (M*j - M + N - j)/(N-1) - (Eq. 2)
Now we have established a relation between i and j
Iterate for all possible i and find corresponding j If j comes out to be an integer in the range 1 to N, increment the counter.
Below is the implementation of above approach.
Time Complexity: O(M)
Complexity can be reduced to O(min(M, N)) by establishing relation of i in terms of j(Eq. 2) and iterating for all possible j in case N<M and by establishing relation j in terms of i(Eq. 1) and iterating for all possible i otherwise.
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Improved By : vt_m