Question:
Follow up for N-Queens problem.
Now, instead outputting board configurations, return the total number of distinct solutions.
Anwser 1: O(n^3) based-on Row
class Solution {
public:
bool check(int row, int* colArray) {
for (int i = 0; i < row; ++i)
{
int diff = abs(colArray[i] - colArray[row]); // in a col
if (diff == 0 || diff == row - i) { // int a row or line
return false;
}
}
return true;
}
void placeQueens(int row, int n, int &count, int* colArray) {
if (row == n) {
++count;
return;
}
for (int col = 0; col < n; ++col) { // in 0 row, test n col
colArray[row] = col;
if (check(row, colArray)){
placeQueens(row+1, n, count, colArray); // test other rows
}
}
}
int totalNQueens(int n) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
int *colArray = new int[n];
int count = 0;
placeQueens(0, n, count, colArray);
return count;
}
};
Anwser 2: O(n^3) based-on Col
class Solution {
public:
bool check(int col, int *rowArray){
for(int i = 0; i < col; i++){
if(rowArray[i] == rowArray[col] || abs(rowArray[i] - rowArray[col]) == col - i)
return false;
}
return true;
}
void placeQueens(int col, int n, int &count, int *rowArray){
if(col == n){
count++;
return;
}
for(int row = 0; row < n; row++){
rowArray[col] = row;
if(check(col, rowArray)){
placeQueens(col+1, n, count, rowArray);
}
}
}
int totalNQueens(int n) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
int *rowArray = new int[n];
int count = 0;
placeQueens(0, n, count, rowArray);
return count;
}
};
Anwser 3: O(n^3) while
bool check(int row, int* colArray) {
for (int i = 0; i < row; ++i)
{
int diff = abs(colArray[i] - colArray[row]); // in a col
if (diff == 0 || diff == row - i) { // int a row or line
return false;
}
}
return true;
}
int totalNQueens(int n) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
if(n == 1) return 1;
int *colArray = new int[n+1];
int count = 0;
colArray[1] = 0;
int k = 1;
while(k > 0){
colArray[k] += 1;
while( (colArray[k] <= n) && !check(k, colArray) ){
colArray[k]++;
}
if(colArray[k] <= n){
if(k == n){
count++;
} else {
colArray[++k] = 0;
}
} else {
k--;
}
}
return count;
}
More Code: g++
n-queue.c
#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <math.h>
bool check(int row, int* colArray) {
for (int i = 0; i < row; ++i)
{
int diff = abs(colArray[i] - colArray[row]);
if (diff == 0 || diff == row - i) {
return false;
}
}
return true;
}
int totalNQueens(int n) {
if(n == 1) return 1;
int *colArray = new int[n+1];
int count = 0;
colArray[1] = 0;
int k = 1;
while(k > 0){
colArray[k] += 1;
while( (colArray[k] <= n) && !check(k, colArray) ){
colArray[k]++;
}
if(colArray[k] <= n){
if(k == n){
count++;
} else {
colArray[++k] = 0;
}
} else {
k--;
}
}
printf("%d\t%d\n", n, count);
return count;
}
int main(){
int num = 16;
for(int i = 0; i < num; i++){
totalNQueens(i);
}
return 0;
}
cmd: g++ -g n-queue.c -o n-queue && ./n-queue
Result:
0 1 1 1 2 0 3 0 4 2 5 10 6 4 7 40 8 92 9 352 10 724 11 2680 12 14200 13 73712 14 365596 15 2279184
参考推荐: