Recursion & Backtracking
View on GitHubRecursion and Backtracking
Recursion and backtracking are important concepts in competitive programming. They are used to solve problems that can be broken down into smaller subproblems. In this document, we will discuss what recursion and backtracking are, their uses in competitive programming, and provide code snippets to illustrate their implementation.
Recursion
Recursion is a technique where a function calls itself to solve a problem. It is particularly useful when dealing with problems that can be broken down into smaller subproblems. The function continues to call itself until a base case is reached, at which point the function returns the result.
Example
def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n-1)
In this example, the factorial function calls itself with a smaller n until n reaches 0, at which point the function returns 1.
Backtracking
Backtracking is a technique used to find all possible solutions to a problem by incrementally building a solution and checking if it satisfies the problem's constraints. If a constraint is not satisfied, the algorithm backtracks and tries a different solution.
Example
def solve_sudoku(board):
for i in range(9):
for j in range(9):
if board[i][j] == '.':
for k in range(1, 10):
if is_valid(board, i, j, str(k)):
board[i][j] = str(k)
if solve_sudoku(board):
return True
else:
board[i][j] = '.'
return False
return True
In this example, we use backtracking to solve a Sudoku puzzle. The algorithm starts by iterating through the board and finding an empty cell. It then tries each number from 1 to 9 until a valid solution is found. If a solution is not found, the algorithm backtracks and tries a different number.
Recursion and backtracking are important techniques in competitive programming. They allow us to solve complex problems by breaking them down into smaller subproblems and finding all possible solutions. By understanding these concepts and knowing when to use them, we can write efficient and effective code.
And we are here to learn them in practice and get benefit of using them.
Enjoy Recursion and Backtracking!