Leetcode题解（７）L51/N-Queens

L51: 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..”]

]

解题思路：典型的回溯法，可用递归或非递归解决

class Solution {
public:
bool isAttack(vector<int> queens, int k)
{
if(k == 0)
return false;
for (int i=0; i<k; i++)
{
if(queens[k] == queens[i] || abs(k-i) == abs(queens[k]-queens[i]))
return true;
}
return false;
}

void showQueens(vector<int> queens, vector<vector<string> >& result){
int n = queens.size();
vector<string> vec(n, string(n,'.'));

for(int i = 0; i < n; i++)
vec[i][queens[i]] = 'Q';

result.push_back(vec);
}

vector<vector<string> > solveNQueens(int n) {
vector<vector<string> > result;
vector<int> queens(n,0);

if(n == 1)
{
vector<string> vec(1, string('Q'));
result.push_back(vec);
return result;
}

int i = 0;

while(1)
{
while(i < n)
{
while(queens[i] == n)
{
queens[i--] = 0;
if(i == -1)
return result;
queens[i]++;
}
if(isAttack(queens,i))
queens[i]++;
else
i++;
}
showQueens(queens,result);

queens[n-1] = 0;
i = n-2;
queens[i]++;
}
}
};