LeetCode #52: N-Queens II (C/C++).

hard

source: https://leetcode.com/problems/n-queens-ii/
C/C++ Solution to LeetCode problem 52. N-Queens II.

Problem

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The n-queens puzzle is the problem of placing n queens on an n x 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.

Examples

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Example 1:

Input: n = 4
Output: 2
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

Example 2:

Input: n = 1
Output: 1

Constraints

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• 1 <= n <= 9

Solution

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Same solution as for problem 51.

The only difference is that, instead of saving the solution, we just increase a counter.

Solution 1:

---

class Solution {
private:
  int result = 0;

  bool isValid(int n, int r, int c, set<pair<int, int>>& tmpSol) {
    for (const auto& pair: tmpSol) {
      if (pair.first == r || pair.second == c)
        return false;
      
      if (abs(pair.first - r) == abs(pair.second - c))
        return false;
    }

    return true;
  }

  void solve(int n, set<pair<int, int>>& tmpSol, int r) {
    if (r == n) {
      result ++;
      return;
    }

    for (int c=0; c<n; c++) {
      if (!isValid(n, r, c, tmpSol))
        continue;

      tmpSol.insert({r, c});
      solve(n, tmpSol, r+1);
      tmpSol.erase({r, c});
    }
  }

public:
  int totalNQueens(int n) {
    set<pair<int,int>> tmpSol;
    solve(n, tmpSol, 0);

    return result;
  }
};

Solution 2:

---

class Solution {
private:
  int result = 0;

  bool isValid(int n, vector<string>& tmpSol, int row, int col){
    for (int i=0; i<n; i++){
      if (tmpSol[i][col] == 'Q')
        return false;
    }
    
    for(int i=row-1, j=col-1; i>=0 && j>=0; i--, j--){
      if(tmpSol[i][j] == 'Q')
        return false;
    }

    for (int i=row-1, j=col+1; i>=0 && j<n; i--, j++) {
      if(tmpSol[i][j] == 'Q')
        return false;
    }
    return true;
  }

  void solve(int n, vector<string>& tmpSol, int r){
    if (r == n) {
      result ++;
      return;
    }

    for (int c=0; c<n; c++) {
      if (isValid(n, tmpSol, r, c)) {
        tmpSol[r][c] = 'Q';
        solve(n, tmpSol, r+1);
        tmpSol[r][c] = '.';
      }
    }
  }

public:
  int totalNQueens(int n) {
    vector<string> tmpSol(n , string(n, '.'));
    solve(n, tmpSol, 0);
    return result;
  }
};