Introduction to Backtracking

Backtracking is a general problem-solving algorithm that involves iteratively searching for a solution to a problem by exploring all possible candidates. It is especially useful when the problem has multiple valid solutions, and the goal is to find one or more of these solutions.

The idea behind backtracking is to build a solution incrementally by selecting candidates one by one and then evaluating if the current candidate leads to a valid solution. If the current candidate does not satisfy the problem constraints, the algorithm backtracks to the previous step and tries a different candidate.

Backtracking can be visualized as exploring a tree-like search space, where each level of the tree represents a step closer to the final solution. The algorithm explores all possible paths in the search space until it finds a valid solution or exhausts all possible candidates.

Backtracking can be a powerful technique for solving a variety of problems, such as finding combinations, permutations, or solving puzzles like Sudoku or the N-Queens problem.

Let's take a look at an example of an N-Queens problem solved using backtracking in C++:

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}

#include <iostream>

using namespace std;

​

int main() {

  // Backtracking example

  int N = 4;

  int board[N][N];

  // Initialize the board

  for(int i = 0; i < N; i++) {

    for(int j = 0; j < N; j++) {

      board[i][j] = 0;

    }

  }

​

  // Function to check if a queen can be placed at a given position

  bool isSafe(int row, int col) {

    // Check if there is a queen in the same column

    for(int i = 0; i < row; i++) {

      if(board[i][col] == 1) {

        return false;

      }

    }

​

    // Check if there is a queen in the upper diagonal

    for(int i = row, j = col; i >= 0 && j >= 0; i--, j--) {

      if(board[i][j] == 1) {

        return false;

      }

    }