itop msc finance colleges in uk - The **space complexity** of the backtracking algorithm is mainly determined by the space required to store the board and the call stack during the recursive calls. The board itself takes O(N^2) space, as it's an N×N array. The call stack depth is at most N, as we can have at most N recursive calls (one for each row). Therefore, the space complexity due to the call stack is O(N). Considering both factors, the overall space complexity is dominated by the board representation, making it O(N^2). However, if we optimize the board representation by only storing the column position of the queen in each row (an array of size N), the space complexity can be reduced to O(N). This optimization doesn’t store the entire board but only the position of the queens, thus saving space. Understanding these complexity aspects helps us appreciate the efficiency of the backtracking algorithm compared to brute-force approaches and also guides us in choosing the right data structures and optimizations for solving the N-Queens problem.
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