A* algorithm

def calculate_optimal_form_score(df_team, window=5):
    """
    Implements the A* logic: calculates the rolling cumulative cost (g(n))
    over the window for a single team.
    """

    # 1. Determine the outcome cost (g(n)) for the team being analyzed
    def get_team_cost(row):
        result = row['FullTimeResult']
        role = row['Role']

        # Win (Cost 0)
        if (role == 'H' and result == 'H') or (role == 'A' and result == 'A'):
            return 0
        # Draw (Cost 1)
        elif result == 'D':
            return 1
        # Loss (Cost 3)
        else:
            return 3

    # Apply the cost function to create the g(n) column
    df_team['Cost'] = df_team.apply(get_team_cost, axis=1)

    # 2. Calculate the rolling sum (cumulative cost) and shift by 1 (PREVENTS DATA LEAKAGE)
    df_team['Optimal_Form_Score'] = df_team['Cost'].rolling(
        window=window, min_periods=1
    ).sum().shift(1).fillna(0) # Fill initial NaNs with 0 (assuming perfect form before history)

    return df_team[['MatchDate', 'Team', 'Optimal_Form_Score']]

# --- Prepare Data for Sequential Group-wise Application ---

# 1. Prepare Home Matches: Rename and add 'Role'
home_matches = DH[['MatchDate', 'HomeTeam', 'FullTimeResult']].copy()
home_matches.rename(columns={'HomeTeam': 'Team'}, inplace=True)
home_matches['Role'] = 'H'

# 2. Prepare Away Matches: Rename and add 'Role'
away_matches = DH[['MatchDate', 'AwayTeam', 'FullTimeResult']].copy()
away_matches.rename(columns={'AwayTeam': 'Team'}, inplace=True)
away_matches['Role'] = 'A'

# 3. Combine and sort
all_matches = pd.concat([home_matches, away_matches]).sort_values(by='MatchDate').reset_index(drop=True)

# 4. Apply the A* logic to each team group
form_scores = all_matches.groupby('Team', group_keys=False).apply(
    calculate_optimal_form_score, window=5
)

# Prepare the scores for merging in the next step
form_scores.rename(columns={'Team': 'TeamName'}, inplace=True)
form_scores['Form_Check'] = form_scores['MatchDate'].astype(str) + form_scores['TeamName']

print("Optimal Form Scores calculated. Sample (First 10 rows):")
print(form_scores.head(10))