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USSU Algorithm Analyzer v4.0 - Backtracking & Branch-Bound Suite
N-Queens, Sudoku, Subset Sum, Graph Coloring, Hamiltonian Path.
"""
from typing import List, Dict, Tuple, Optional, Set
from utils.core import profile_algorithm, OperationCounter
class BacktrackingAlgorithms(OperationCounter):
"""Backtracking and Branch & Bound algorithm collection"""
def __init__(self):
super().__init__()
self.solutions = []
self.state_tree = []
def reset(self):
self.reset_counters()
self.solutions = []
self.state_tree = []
# ==================== N-QUEENS ====================
@profile_algorithm
def n_queens(self, n: int = 8) -> Dict:
self.reset()
board = [[0] * n for _ in range(n)]
solutions = []
def is_safe(row, col):
self.comparisons += 1
for i in range(col):
if board[row][i] == 1:
return False
for i, j in zip(range(row, -1, -1), range(col, -1, -1)):
if board[i][j] == 1:
return False
for i, j in zip(range(row, n, 1), range(col, -1, -1)):
if board[i][j] == 1:
return False
return True
def solve(col):
self.recursions += 1
if col >= n:
sol = [row[:] for row in board]
solutions.append(sol)
return True
res = False
for i in range(n):
self.iterations += 1
if is_safe(i, col):
board[i][col] = 1
res = solve(col + 1) or res
board[i][col] = 0
return res
solve(0)
return {
'algorithm': 'N-Queens (Backtracking)',
'n': n,
'solutions_found': len(solutions),
'first_solution': solutions[0] if solutions else None,
'time_complexity': 'O(n!)',
'space_complexity': 'O(n²)',
'recursions': self.recursions,
'comparisons': self.comparisons,
}
# ==================== SUDOKU SOLVER ====================
@profile_algorithm
def sudoku_solver(self, grid: List[List[int]]) -> Dict:
self.reset()
n = len(grid)
sqrt_n = int(n ** 0.5)
def is_valid(row, col, num):
self.comparisons += 1
for x in range(n):
if grid[row][x] == num or grid[x][col] == num:
return False
start_row, start_col = row - row % sqrt_n, col - col % sqrt_n
for i in range(sqrt_n):
for j in range(sqrt_n):
if grid[i + start_row][j + start_col] == num:
return False
return True
def solve():
self.recursions += 1
for i in range(n):
for j in range(n):
if grid[i][j] == 0:
for num in range(1, n + 1):
self.iterations += 1
if is_valid(i, j, num):
grid[i][j] = num
if solve():
return True
grid[i][j] = 0
return False
return True
solved = solve()
return {
'algorithm': 'Sudoku Solver (Backtracking)',
'solved': solved,
'grid': grid,
'time_complexity': 'O(9^(n²)) worst',
'space_complexity': 'O(n²)',
'recursions': self.recursions,
'comparisons': self.comparisons,
}
# ==================== SUBSET SUM ====================
@profile_algorithm
def subset_sum(self, arr: List[int], target: int) -> Dict:
self.reset()
n = len(arr)
result = []
def find_subsets(index, current, current_sum):
self.recursions += 1
if current_sum == target:
result.append(current[:])
return
if index >= n or current_sum > target:
return
self.iterations += 1
current.append(arr[index])
find_subsets(index + 1, current, current_sum + arr[index])
current.pop()
find_subsets(index + 1, current, current_sum)
find_subsets(0, [], 0)
return {
'algorithm': 'Subset Sum (Backtracking)',
'target': target,
'subsets': result,
'count': len(result),
'time_complexity': 'O(2ⁿ)',
'space_complexity': 'O(n)',
'recursions': self.recursions,
}
# ==================== GRAPH COLORING ====================
@profile_algorithm
def graph_coloring(self, adj: List[List[int]], m: int) -> Dict:
self.reset()
n = len(adj)
colors = [0] * n
def is_safe(v, c):
self.comparisons += 1
for i in range(n):
if adj[v][i] == 1 and colors[i] == c:
return False
return True
def solve(v):
self.recursions += 1
if v == n:
return True
for c in range(1, m + 1):
self.iterations += 1
if is_safe(v, c):
colors[v] = c
if solve(v + 1):
return True
colors[v] = 0
return False
possible = solve(0)
return {
'algorithm': 'Graph Coloring (Backtracking)',
'colors_needed': max(colors) if possible else 0,
'coloring': colors if possible else [],
'possible': possible,
'time_complexity': 'O(m^V)',
'space_complexity': 'O(V)',
'recursions': self.recursions,
'comparisons': self.comparisons,
}
# ==================== HAMILTONIAN CYCLE ====================
@profile_algorithm
def hamiltonian_cycle(self, adj: List[List[int]], start: int = 0) -> Dict:
self.reset()
n = len(adj)
path = [-1] * n
path[0] = start
def is_safe(v, pos):
self.comparisons += 1
if adj[path[pos - 1]][v] == 0:
return False
for i in range(pos):
if path[i] == v:
return False
return True
def solve(pos):
self.recursions += 1
if pos == n:
return adj[path[pos - 1]][start] == 1
for v in range(n):
self.iterations += 1
if is_safe(v, pos):
path[pos] = v
if solve(pos + 1):
return True
path[pos] = -1
return False
found = solve(1)
return {
'algorithm': 'Hamiltonian Cycle (Backtracking)',
'cycle': path + [start] if found else [],
'found': found,
'time_complexity': 'O((V-1)!)',
'space_complexity': 'O(V)',
'recursions': self.recursions,
'comparisons': self.comparisons,
}
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