Detailed explanation of C++ function recursion: Recursion in backtracking method

C Detailed explanation of function recursion: Recursion is a technique for calling the function itself, which is very useful in algorithms such as backtracking. Backtracking solves problems by systematically trying all solutions and backtracking to dead ends. Sudoku solving is an example of a recursive function in action using the backtracking method.

Detailed explanation of C function recursion: Recursion in the backtracking method

Introduction

Recursion is a programming technique in which a function calls itself. Recursion is very useful when understanding algorithms such as backtracking. This article will explore recursive functions in C in detail, focusing on practical applications of recursion in backtracking.

Recursive functions

The definition of a recursive function contains a call to the function itself. This self-invocation allows the function to repeat its operation until a specific condition is met.

Recursion in Backtracking

Backtracking is a problem-solving method in which we systematically try all possible solutions and backtrack to dead ends. It usually involves using a recursive function that calls itself and changes the input or state to explore different branches.

Practical Case: Sudoku Solving

Sudoku is a popular puzzle in which the goal is to fill a 9x9 grid with the numbers 1 to 9 so that each row and each Each number appears only once in the column and in each 3x3 subblock. We can use recursive functions to solve Sudoku puzzles.

The code is as follows:

#include <vector>

using namespace std;

bool solveSudoku(vector<vector<int>>& board) {
  for (int i = 0; i < 9; i++) {
    for (int j = 0; j < 9; j++) {
      if (board[i][j] == 0) {
        for (int k = 1; k <= 9; k++) {
          if (isValid(board, i, j, k)) {
            board[i][j] = k;
            if (solveSudoku(board)) {
              return true;
            }
            else {
              board[i][j] = 0;
            }
          }
        }
        return false;
      }
    }
  }
  return true;
}

In this example, the solveSudoku function uses recursion to iterate through all possible numbers, trying to place them in the current cell ( i, j). If the placement is valid and results in a solution, the function continues recursively with the remaining cells. If the placement is invalid or results in a contradiction, the function will backtrack and try the next number.

Conclusion

Recursive functions are powerful tools for solving problems, especially when backtracking is involved. By systematically exploring the solution space and backtracking to dead ends, we can use recursion to find solutions to complex problems such as Sudoku.

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