Leetcode: N-Queens II

N-Queens II

Follow up for N-Queens problem.

Now, instead outputting board configurations, return the total number of distinct solutions.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

## Blog link: https://code.dennyzhang.com/n-queens-ii
## Basic Ideas: backtracking
##              Place queen row by row
##              For the position we have tried, examine conflict for rows and triangles
## Complexity: Time ? Space ?
class Solution(object):
    def totalNQueens(self, n):
        :type n: int
        :rtype: int
        if n <= 0:
            return 0
        self.board = [] * n
        for i in xrange(n):
        self.res = 0
        self.myTotalNQueens(n, 0)
        return self.res

    def myTotalNQueens(self, n, row):
        :type n: int
        :rtype: int
        if row == n:
            self.res += 1

        for col in xrange(n):
            self.board[row][col] = 'Q'
            if self.validQueeens(n, row, col):
                self.myTotalNQueens(n, row+1)
            self.board[row][col] = '.'

    def validQueeens(self, n, row, col):
        # check column
        for index in xrange(n):
            if index == row: continue
            if self.board[index][col] == 'Q':
                return False

        # Check triangle
        for i in xrange(n):
            for j in xrange(n):
                if i == row and j == col: continue
                if abs(i-row) == abs(j-col) and self.board[i][j] == 'Q':
                    return False
        return True

# s = Solution()
# print s.totalNQueens(1) # 1
# print s.totalNQueens(4) # 2

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