Repository navigation
Expand file tree
/
Copy pathnQueuens.cpp
More file actions
121 lines (100 loc) · 3.35 KB
/
Copy pathnQueuens.cpp
File metadata and controls
121 lines (100 loc) · 3.35 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
// Source : https://oj.leetcode.com/problems/n-queens/
// Author : Hao Chen
// Date : 2014-08-22
/**********************************************************************************
*
* 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.."]
* ]
*
*
**********************************************************************************/
#include <stdlib.h>
#include <iostream>
#include <vector>
#include <string>
using namespace std;
vector< vector<string> > solveNQueens(int n);
void solveNQueensRecursive(int n, int currentRow, vector<int>& solution, vector< vector<string> >& result);
bool isValid(int attemptedColumn, int attemptedRow, vector<int> &queenInColumn);
vector< vector<string> > solveNQueens(int n) {
vector< vector<string> > result;
vector<int> solution(n);
solveNQueensRecursive(n, 0, solution, result);
return result;
}
//The following recursion is easy to understand. Nothing's tricky.
// 1) recursively find all of possible columns row by row.
// 2) solution[] array only stores the columns index. `solution[row] = col;`
void solveNQueensRecursive(int n, int currentRow, vector<int>& solution, vector< vector<string> >& result) {
//if no more row need to do, shape the result
if (currentRow == n){
vector<string> s;
vector<string> s(n, string(n, '.'));
for (int row = 0; row < n; row++) {
s[row][solution[row]] = 'Q';
}
result.push_back(s);
return;
}
//for each column
for (int col = 0; col < n; col++) {
//if the current column is valid
if (isValid(col, currentRow, solution) ) {
//place the Queue
solution[currentRow] = col;
//recursively put the Queen in next row
solveNQueensRecursive(n, currentRow+1, solution, result);
}
}
}
//Attempting to put the Queen into [row, col], check it is valid or not
//Notes:
// 1) we just checking the Column not Row, because the row cannot be conflicted
// 2) to check the diagonal, we just check |x'-x| == |y'-y|, (x',y') is a Queen will be placed
bool isValid(int attemptedColumn, int attemptedRow, vector<int> &queenInColumn) {
for(int i=0; i<attemptedRow; i++) {
if (attemptedColumn == queenInColumn[i] ||
abs(attemptedColumn - queenInColumn[i]) == abs(attemptedRow - i)) {
return false;
}
}
return true;
}
void printMatrix(vector< vector<string> >& matrix ){
for (int i = 0; i < matrix.size(); i++) {
cout << "-----------" << endl;
for (int j = 0; j < matrix[i].size(); j++) {
cout << matrix[i][j] << endl;
}
}
}
int main(int argc, char** argv)
{
int n = 8;
if (argc>1){
n = atoi(argv[1]);
}
vector< vector<string> > result = solveNQueens(n);
printMatrix(result);
return 0;
}