Tuesday, May 27, 2014

Leetcode (Python): N-Queens

The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle.
Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.
For example,
There exist two distinct solutions to the 4-queens puzzle:

[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

Solution:

class Solution:
    # @return a list of lists of string
    def solveNQueens(self, n):
        solution = []
        
        oneSolution = []
        for i in range(0, n):
            row =[]
            for j in range(0, n):
                row.append('.')
            oneSolution.append(row)
        self.solveNQueensRec(0, n, oneSolution, solution)
        return solution
    
    def solveNQueensRec(self, row, n, oneSolution, solution):
        if row==n:
            tempSolution = []
            for i in range(0,n):
                tempSolution.append(''.join(oneSolution[i]))
            solution.append(tempSolution)
            
        for col in range(0,n):
            if self.canAdd(oneSolution, row, col):
                oneSolution[row][col]='Q'
                self.solveNQueensRec(row+1, n, oneSolution, solution)
                oneSolution[row][col]='.'
                
    def canAdd(self, oneSolution, row, col):
        for i in range(0,row):
            if oneSolution[i][col]=='Q':
                return False
            if col-row+i>=0 and oneSolution[i][col-row+i]=='Q':
                return False
            if col+row-i<len(oneSolution) and oneSolution[i][col+row-i]=='Q':
                return False
        return True

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