Given an integer N and an infinite table where ith row and jth column contains the value i *j. The task is to find the minimum number of moves to reach the cell containing N starting from the cell (1, 1).
Note: From (i, j) only valid moves are (i + 1, j) and (i, j + 1)
Input: N = 10
(1, 1) -> (2, 1) -> (2, 2) -> (2, 3) -> (2, 4) -> (2, 5)
Input: N = 7
Approach: Note that any cell (i, j) can be reached in i + j – 2 steps. Thus, only the pair (i, j) is required with i * j = N that minimizes i + j. It can be found out by finding all the possible pairs (i, j) and check them in O(√N). To do this, without loss of generality, it can be assumed that i ≤ j and i ≤ √N since N = i * j ≥ i2. So √N ≥ i2 i.e. √N ≥ i.
Thus, iterate over all the possible values of i from 1 to √N and, among all the possible pairs (i, j), pick the lowest value of i + j – 2 and that is the required answer.
Below is the implementation of the above approach:
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