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USSU Algorithm Analyzer v4.0 - Dynamic Programming Suite
Classic DP problems with table reconstruction and complexity analysis.
"""
import math
from typing import List, Dict, Tuple, Any
from utils.core import profile_algorithm, OperationCounter
class DynamicProgramming(OperationCounter):
"""Dynamic Programming algorithm collection for ADA"""
def __init__(self):
super().__init__()
self.dp_table = []
self.traceback = []
def reset(self):
self.reset_counters()
self.dp_table = []
self.traceback = []
# ==================== 0/1 KNAPSACK ====================
@profile_algorithm
def knapsack_01(self, weights: List[int], values: List[int], capacity: int) -> Dict:
self.reset()
n = len(weights)
dp = [[0] * (capacity + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(capacity + 1):
self.iterations += 1
self.comparisons += 1
if weights[i-1] <= w:
dp[i][w] = max(dp[i-1][w], dp[i-1][w - weights[i-1]] + values[i-1])
else:
dp[i][w] = dp[i-1][w]
# Traceback
w = capacity
selected = []
for i in range(n, 0, -1):
self.accesses += 1
if dp[i][w] != dp[i-1][w]:
selected.append(i-1)
w -= weights[i-1]
self.dp_table = dp
return {
'algorithm': '0/1 Knapsack (DP)',
'max_value': dp[n][capacity],
'selected_items': list(reversed(selected)),
'time_complexity': 'O(n × W)',
'space_complexity': 'O(n × W)',
'dp_table': dp,
'iterations': self.iterations,
'comparisons': self.comparisons,
}
# ==================== UNBOUNDED KNAPSACK ====================
@profile_algorithm
def knapsack_unbounded(self, weights: List[int], values: List[int], capacity: int) -> Dict:
self.reset()
n = len(weights)
dp = [0] * (capacity + 1)
choice = [-1] * (capacity + 1)
for w in range(1, capacity + 1):
for i in range(n):
self.iterations += 1
self.comparisons += 1
if weights[i] <= w and dp[w - weights[i]] + values[i] > dp[w]:
dp[w] = dp[w - weights[i]] + values[i]
choice[w] = i
# Traceback
w = capacity
items_used = []
while w > 0 and choice[w] != -1:
items_used.append(choice[w])
w -= weights[choice[w]]
self.dp_table = [dp]
return {
'algorithm': 'Unbounded Knapsack (DP)',
'max_value': dp[capacity],
'items_used': items_used,
'time_complexity': 'O(n × W)',
'space_complexity': 'O(W)',
'dp_table': [dp],
'iterations': self.iterations,
'comparisons': self.comparisons,
}
# ==================== LONGEST COMMON SUBSEQUENCE ====================
@profile_algorithm
def lcs(self, s1: str, s2: str) -> Dict:
self.reset()
m, n = len(s1), len(s2)
dp = [[0] * (n + 1) for _ in range(m + 1)]
for i in range(1, m + 1):
for j in range(1, n + 1):
self.iterations += 1
self.comparisons += 1
if s1[i-1] == s2[j-1]:
dp[i][j] = dp[i-1][j-1] + 1
else:
dp[i][j] = max(dp[i-1][j], dp[i][j-1])
# Reconstruct LCS
i, j = m, n
lcs_str = []
while i > 0 and j > 0:
self.accesses += 1
if s1[i-1] == s2[j-1]:
lcs_str.append(s1[i-1])
i -= 1
j -= 1
elif dp[i-1][j] > dp[i][j-1]:
i -= 1
else:
j -= 1
self.dp_table = dp
return {
'algorithm': 'Longest Common Subsequence',
'length': dp[m][n],
'subsequence': ''.join(reversed(lcs_str)),
'time_complexity': 'O(m × n)',
'space_complexity': 'O(m × n)',
'dp_table': dp,
'iterations': self.iterations,
'comparisons': self.comparisons,
}
# ==================== COIN CHANGE (Min Coins) ====================
@profile_algorithm
def coin_change_min(self, coins: List[int], amount: int) -> Dict:
self.reset()
dp = [float('inf')] * (amount + 1)
dp[0] = 0
parent = [-1] * (amount + 1)
for i in range(1, amount + 1):
for coin in coins:
self.iterations += 1
self.comparisons += 1
if coin <= i and dp[i - coin] + 1 < dp[i]:
dp[i] = dp[i - coin] + 1
parent[i] = coin
if dp[amount] == float('inf'):
return {
'algorithm': 'Coin Change (Min Coins)',
'min_coins': -1,
'time_complexity': 'O(amount × |coins|)',
'space_complexity': 'O(amount)',
}
# Traceback
coins_used = []
cur = amount
while cur > 0:
coins_used.append(parent[cur])
cur -= parent[cur]
self.dp_table = [dp]
return {
'algorithm': 'Coin Change (Min Coins)',
'min_coins': dp[amount],
'coins_used': coins_used,
'time_complexity': 'O(amount × |coins|)',
'space_complexity': 'O(amount)',
'dp_table': [dp],
'iterations': self.iterations,
'comparisons': self.comparisons,
}
# ==================== COIN CHANGE (Ways) ====================
@profile_algorithm
def coin_change_ways(self, coins: List[int], amount: int) -> Dict:
self.reset()
dp = [0] * (amount + 1)
dp[0] = 1
for coin in coins:
for i in range(coin, amount + 1):
self.iterations += 1
dp[i] += dp[i - coin]
self.dp_table = [dp]
return {
'algorithm': 'Coin Change (Ways)',
'ways': dp[amount],
'time_complexity': 'O(amount × |coins|)',
'space_complexity': 'O(amount)',
'dp_table': [dp],
'iterations': self.iterations,
}
# ==================== MATRIX CHAIN MULTIPLICATION ====================
@profile_algorithm
def matrix_chain_order(self, dims: List[int]) -> Dict:
self.reset()
n = len(dims) - 1
dp = [[0] * n for _ in range(n)]
split = [[0] * n for _ in range(n)]
for chain_len in range(2, n + 1):
for i in range(n - chain_len + 1):
j = i + chain_len - 1
dp[i][j] = float('inf')
for k in range(i, j):
self.iterations += 1
self.comparisons += 1
cost = dp[i][k] + dp[k+1][j] + dims[i] * dims[k+1] * dims[j+1]
if cost < dp[i][j]:
dp[i][j] = cost
split[i][j] = k
def print_optimal(i, j):
if i == j:
return f"A{i+1}"
k = split[i][j]
return f"({print_optimal(i, k)} × {print_optimal(k+1, j)})"
self.dp_table = dp
return {
'algorithm': 'Matrix Chain Multiplication',
'min_multiplications': dp[0][n-1],
'optimal_parenthesization': print_optimal(0, n-1),
'time_complexity': 'O(n³)',
'space_complexity': 'O(n²)',
'dp_table': dp,
'split_table': split,
'iterations': self.iterations,
'comparisons': self.comparisons,
}
# ==================== EDIT DISTANCE ====================
@profile_algorithm
def edit_distance(self, s1: str, s2: str) -> Dict:
self.reset()
m, n = len(s1), len(s2)
dp = [[0] * (n + 1) for _ in range(m + 1)]
for i in range(m + 1):
dp[i][0] = i
for j in range(n + 1):
dp[0][j] = j
for i in range(1, m + 1):
for j in range(1, n + 1):
self.iterations += 1
self.comparisons += 1
if s1[i-1] == s2[j-1]:
dp[i][j] = dp[i-1][j-1]
else:
dp[i][j] = 1 + min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1])
# Traceback operations
i, j = m, n
operations = []
while i > 0 or j > 0:
self.accesses += 1
if i > 0 and j > 0 and s1[i-1] == s2[j-1]:
operations.append(('match', s1[i-1]))
i -= 1
j -= 1
elif j > 0 and (i == 0 or dp[i][j] == dp[i][j-1] + 1):
operations.append(('insert', s2[j-1]))
j -= 1
elif i > 0 and (j == 0 or dp[i][j] == dp[i-1][j] + 1):
operations.append(('delete', s1[i-1]))
i -= 1
else:
operations.append(('replace', s1[i-1], s2[j-1]))
i -= 1
j -= 1
self.dp_table = dp
return {
'algorithm': 'Edit Distance (Levenshtein)',
'distance': dp[m][n],
'operations': list(reversed(operations)),
'time_complexity': 'O(m × n)',
'space_complexity': 'O(m × n)',
'dp_table': dp,
'iterations': self.iterations,
'comparisons': self.comparisons,
}
# ==================== LONGEST INCREASING SUBSEQUENCE ====================
@profile_algorithm
def lis(self, arr: List[int]) -> Dict:
self.reset()
n = len(arr)
if n == 0:
return {'algorithm': 'LIS', 'length': 0, 'subsequence': [], 'time_complexity': 'O(n²)', 'space_complexity': 'O(n)'}
dp = [1] * n
parent = [-1] * n
for i in range(1, n):
for j in range(i):
self.iterations += 1
self.comparisons += 1
if arr[j] < arr[i] and dp[j] + 1 > dp[i]:
dp[i] = dp[j] + 1
parent[i] = j
max_len = max(dp)
idx = dp.index(max_len)
seq = []
while idx != -1:
seq.append(arr[idx])
idx = parent[idx]
self.dp_table = [dp]
return {
'algorithm': 'Longest Increasing Subsequence',
'length': max_len,
'subsequence': list(reversed(seq)),
'time_complexity': 'O(n²)',
'space_complexity': 'O(n)',
'dp_table': [dp],
'iterations': self.iterations,
'comparisons': self.comparisons,
}
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