51. N-Queens
Hard
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.
Example:
Input: 4
Output: [
[".Q..", // Solution 1
"...Q",
"Q...",
"..Q."],
["..Q.", // Solution 2
"Q...",
"...Q",
".Q.."]
]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.
题目大意：在nxn的棋盘上放置n个国际象棋的皇后，要求皇后之间不能够相互攻击到。
解题思路：利用DFS，从第一行开始，放置皇后在安全的位置。
class Solution {
public:
// check if put a queen at [row, col] is valid
bool isValid(const vector<string> &cur, int row, int col){
// check if queen exists in the same col
for(int i = 0; i < row; i++){
if(cur[i][col] == 'Q'){
return false;
}
}
// check if queen exists in up-left diag
for(int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--){
if(cur[i][j] == 'Q'){
return false;
}
}
// check if queen exists in up-right diag
for(int i = row - 1, j = col + 1; i >= 0 && j < cur.size(); i--, j++){
if(cur[i][j] == 'Q'){
return false;
}
}
return true;
}
void solveNQueensDFS(vector<string> &cur, int row, vector<vector<string>> &ans){
if(row == cur.size()){
//if all queens have been positioned
ans.push_back(cur);
return;
}
// try to place queen at one col of current row
for(int col = 0; col < cur.size(); col++){
if(isValid(cur, row, col)){
cur[row][col] = 'Q';
solveNQueensDFS(cur, row + 1, ans);
cur[row][col] = '.';
}
}
}
vector<vector<string>> solveNQueens(int n) {
vector<vector<string>> ans;
vector<string> cur(n, string(n, '.'));
solveNQueensDFS(cur, 0, ans);
return move(ans);
}
};
测试一下
Success
Details
Runtime: 8 ms, faster than 92.21% of C++ online submissions for N-Queens.
Memory Usage: 10.1 MB, less than 66.69% of C++ online submissions for N-Queens.
52. N-Queens II
Hard
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 the number of distinct solutions to the n-queens puzzle.
Example:
Input: 4 Output: 2 Explanation: There are two distinct solutions to the 4-queens puzzle as shown below. [ [“.Q..”, // Solution 1 “…Q”, “Q…”, “..Q.”],
[”..Q.”, // Solution 2 “Q…”, “…Q”, “.Q..”] ]
题目大意：和上题相比稍加修改，要求求出可能的解法个数。
解题思路：思路与上题相同。
class Solution {
public:
int totalNQueens(int n) {
int cnt = 0;
vector<string> cur(n, string(n, '.'));
solveNQueensDFS(cur, 0, cnt);
return cnt;
}
bool isValid(const vector<string> &cur, int row, int col){
for(int i = 0; i < row; i++){
if(cur[i][col] == 'Q'){
return false;
}
}
for(int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--){
if(cur[i][j] == 'Q'){
return false;
}
}
for(int i = row - 1, j = col + 1; i >= 0 && j < cur.size(); i--, j++){
if(cur[i][j] == 'Q'){
return false;
}
}
return true;
}
void solveNQueensDFS(vector<string> &cur, int row, int &cnt){
if(row == cur.size()){
cnt++;
return;
}
for(int col = 0; col < cur.size(); col++){
if(isValid(cur, row, col)){
cur[row][col] = 'Q';
solveNQueensDFS(cur, row + 1, cnt);
cur[row][col] = '.';
}
}
}
};
测试一下，
Success
Details
Runtime: 0 ms, faster than 100.00% of C++ online submissions for N-Queens II.
Memory Usage: 8.5 MB, less than 39.40% of C++ online submissions for N-Queens II.
##77. Combinations
Medium
Given two integers n and k, return all possible combinations of k numbers out of 1 … n.
Example:
Input: n = 4, k = 2
Output:
[
[2,4],
[3,4],
[2,3],
[1,2],
[1,3],
[1,4],
]
题目大意：从1-n中找k个数形成组合，要求列出所有可能的组合。
解题思路：用DFS穷举所有的组合，保存符合条件的。
class Solution {
public:
void combineDFS(int start, const int k, const int n, vector<int> &path, vector<vector<int>> &ans){
if(path.size() == k){
ans.push_back(path);
return;
}
for(int i = start; i <= n; i++){
path.push_back(i);
combineDFS(i + 1, k, n, path, ans);
path.pop_back();
}
}
vector<vector<int>> combine(int n, int k) {
vector<vector<int>> ans;
vector<int> path;
combineDFS(1, k, n, path, ans);
return move(ans);
}
};
测试一下，
Success
Details
Runtime: 84 ms, faster than 70.48% of C++ online submissions for Combinations.
Memory Usage: 11.8 MB, less than 67.96% of C++ online submissions for Combinations.