N-Queens II

https://leetcode.com/problems/n-queens-ii/

Follow up for N-Queens problem.

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

解题思路：

这题和N-Queens相比，有啥简单的方法？没看出，无非就是算出所有解后返回结果的size。当然可能也可以维护一个值，有结果就递增，最后返回他就可以了。

public class Solution {
    public int totalNQueens(int n) {
        List<String[]> result = new ArrayList<String[]>();
        if(n < 1) {
            return 0;
        }
        String[] current = new String[n];
        for(int i = 0; i < n; i++) {
            StringBuffer bf = new StringBuffer();
            for(int j = 0; j < n; j++) {
                bf.append(‘.‘);
            }
            current[i] = bf.toString();
        }
        int[] columnInRow = new int[n];
        for(int i = 0; i < n; i++) {
            columnInRow[i] = -1;
        }
        dfs(n, result, current, columnInRow, 0);
        return result.size();
    }

    public void dfs(int n, List<String[]> result, String[] current, int[] columnInRow, int row) {
        if(row == n) {
            String[] temp = Arrays.copyOf(current, current.length);
            result.add(temp);
            return;
        }
        for(int i = 0; i < n; i++) {
            if(checkValid(columnInRow, row, i)) {
                columnInRow[row] = i;
                String temp = current[row];
                current[row] = current[row].substring(0, i) + "Q" + current[row].substring(i + 1);
                dfs(n, result, current, columnInRow, row + 1);
                current[row] = temp;
                columnInRow[row] = -1;
            }
        }
    }

    public boolean checkValid(int[] columnInRow, int row, int column) {
        int temp = row - 1, i = 1;
        while(temp >= 0) {
            if(columnInRow[temp] == column) {
                return false;
            }
            if(column - i >= 0 && columnInRow[temp] == column - i) {
                return false;
            }
            if(column + i < columnInRow.length && columnInRow[temp] == column + i) {
                return false;
            }
            i++;
            temp--;
        }

        temp = row + 1;
        i = 1;
        while(temp < columnInRow.length) {
            if(columnInRow[temp] == column) {
                return false;
            }
            if(column - i >= 0 && columnInRow[temp] == column - i) {
                return false;
            }
            if(column + i < columnInRow.length && columnInRow[temp] == column + i) {
                return false;
            }
            i++;
            temp++;
        }
        return true;
    }
}

又优化了一下省去了构造string的过程，并直接返回这个size。

public class Solution {
    public int totalNQueens(int n) {
        if(n < 1) {
            return 0;
        }
        int[] columnInRow = new int[n];
        for(int i = 0; i < n; i++) {
            columnInRow[i] = -1;
        }
        int result = 0;
        result = dfs(n, columnInRow, 0, result);
        return result;
    }

    public int dfs(int n, int[] columnInRow, int row, int result) {
        if(row == n) {
            result++;
            return result;
        }
        for(int i = 0; i < n; i++) {
            if(checkValid(columnInRow, row, i)) {
                columnInRow[row] = i;
                result = dfs(n, columnInRow, row + 1, result);
                columnInRow[row] = -1;
            }
        }
        return result;
    }

    public boolean checkValid(int[] columnInRow, int row, int column) {
        int temp = row - 1, i = 1;
        while(temp >= 0) {
            if(columnInRow[temp] == column) {
                return false;
            }
            if(column - i >= 0 && columnInRow[temp] == column - i) {
                return false;
            }
            if(column + i < columnInRow.length && columnInRow[temp] == column + i) {
                return false;
            }
            i++;
            temp--;
        }

        temp = row + 1;
        i = 1;
        while(temp < columnInRow.length) {
            if(columnInRow[temp] == column) {
                return false;
            }
            if(column - i >= 0 && columnInRow[temp] == column - i) {
                return false;
            }
            if(column + i < columnInRow.length && columnInRow[temp] == column + i) {
                return false;
            }
            i++;
            temp++;
        }
        return true;
    }
}