lab5.py

import math

# ============================================================
# ITEM-BASED рекомендательная система
# ============================================================

products = ['P1', 'P2', 'P3', 'P4', 'P5']
users    = ['U1', 'U2', 'U3', 'U4', 'U5']

ratings = [
#    U1  U2  U3  U4  U5
    [5,  5,  4,  5,  4],   # P1
    [5,  5,  3,  0,  3],   # P2
    [5,  5,  5,  5,  0],   # P3
    [5,  0,  5,  5,  5],   # P4
    [0,  5,  1,  0,  2],   # P5
]

# Матрица косинусного подобия товаров
item_sim_raw = {
    ('P1', 'P2'): 0.80,
    ('P1', 'P3'): 0.85,
    ('P1', 'P4'): 0.82,
    ('P1', 'P5'): 0.70,
    ('P2', 'P3'): 0.78,
    ('P2', 'P4'): 0.75,
    ('P2', 'P5'): 0.90,
    ('P3', 'P4'): 0.95,
    ('P3', 'P5'): 0.72,
    ('P4', 'P5'): 0.68,
}

# ============================================================
# Вспомогательные функции
# ============================================================

def get_item_sim(p1, p2):
    if p1 == p2:
        return 1.0
    key = (p1, p2) if (p1, p2) in item_sim_raw else (p2, p1)
    return item_sim_raw.get(key, 0.0)

def max_user_rating(user_idx):
    rated = [ratings[i][user_idx] for i in range(len(products)) if ratings[i][user_idx] > 0]
    return max(rated) if rated else 0

def avg_user_rating(user_idx):
    rated = [ratings[i][user_idx] for i in range(len(products)) if ratings[i][user_idx] > 0]
    return sum(rated) / len(rated) if rated else 0.0

def is_new_user(user_idx):
    return all(ratings[i][user_idx] == 0 for i in range(len(products)))

def best_avg_product():
    best_p, best_avg = None, -1
    for i, p in enumerate(products):
        rated = [ratings[i][j] for j in range(len(users)) if ratings[i][j] > 0]
        avg = sum(rated) / len(rated) if rated else 0.0
        if avg > best_avg:
            best_avg = avg
            best_p = p
    return best_p, best_avg

# ============================================================
# Формула предсказания (ITEM-BASED):
#
#   Pr(a, i) = sum_{j in K} r(a,j) x cos(i,j)
#              ─────────────────────────────────
#                   sum_{j in K} |cos(i,j)|
#
# K       - товары похожие на i, которые пользователь a оценил (> 0)
# r(a,j)  - оценка пользователя a для товара j из K
# cos(i,j)- косинусное подобие товаров i и j
#
# Критерий рекомендации: Pr(a,i) >= max(оценок пользователя a)
# ============================================================

def predict(user_a_idx, item_i_idx, demo=True):
    a_name = users[user_a_idx]
    i_name = products[item_i_idx]

    K = []
    for j_idx, j_name in enumerate(products):
        if j_idx == item_i_idx:
            continue
        if ratings[j_idx][user_a_idx] > 0:
            sim = get_item_sim(i_name, j_name)
            if sim > 0:
                K.append(j_idx)

    if not K:
        if demo:
            print(f"    K пуст - нет похожих оценённых товаров")
        return None

    if demo:
        print(f"    K = {{ {', '.join(products[j] for j in K)} }}")
        print()

    numerator   = 0.0
    denominator = 0.0

    for j_idx in K:
        j_name = products[j_idx]
        r_aj   = ratings[j_idx][user_a_idx]
        cos_ij = get_item_sim(i_name, j_name)
        term   = r_aj * cos_ij
        numerator   += term
        denominator += abs(cos_ij)
        if demo:
            print(f"      j={j_name}: r({a_name},{j_name})={r_aj},  "
                  f"cos({i_name},{j_name})={cos_ij:.2f}  "
                  f"->  {r_aj} x {cos_ij:.2f} = {term:.4f}")

    if denominator == 0:
        return None

    pr = numerator / denominator
    if demo:
        print(f"\n    Pr({a_name},{i_name}) = {numerator:.4f} / {denominator:.4f} = {pr:.4f}")
    return pr

# ============================================================
# Рекомендация для одного пользователя
# ============================================================

def recommend_for_user(user_idx, demo=True):
    a_name = users[user_idx]

    print(f"\n{'='*60}")
    print(f"  Пользователь: {a_name}")
    print(f"{'='*60}")

    if is_new_user(user_idx):
        best_p, best_avg = best_avg_product()
        print(f"  Новый пользователь (все оценки = 0).")
        print(f"  Рекомендуем товар с наибольшим средним: {best_p} (avg={best_avg:.4f})")
        return {best_p: best_avg}

    unrated = [i for i in range(len(products)) if ratings[i][user_idx] == 0]

    if not unrated:
        print(f"  {a_name} оценил все товары - нечего рекомендовать.")
        return {}

    rated_str = {products[i]: ratings[i][user_idx]
                 for i in range(len(products)) if ratings[i][user_idx] > 0}
    max_a = max_user_rating(user_idx)
    avg_a = avg_user_rating(user_idx)

    print(f"  Оценённые товары : {rated_str}")
    print(f"  Неоценённые      : {[products[i] for i in unrated]}")
    print(f"  r_avg({a_name}) = {avg_a:.4f},   r_max({a_name}) = {max_a}")
    print(f"  Критерий рекомендации: Pr >= r_max({a_name}) = {max_a}")
    print()

    predictions = {}
    for i_idx in unrated:
        i_name = products[i_idx]
        print(f"  -> Pr({a_name}, {i_name}):")
        pr = predict(user_idx, i_idx, demo=demo)
        if pr is not None:
            predictions[i_name] = pr
        else:
            print(f"    Нет данных для предсказания.")
        print()

    if not predictions:
        print(f"  Не удалось предсказать оценки.")
        return {}

    print(f"  Все предсказания: { {k: round(v, 4) for k, v in predictions.items()} }")
    print()

    results = {}
    for item, pr in sorted(predictions.items(), key=lambda x: -x[1]):
        if round(pr, 10) >= max_a:
            print(f"  + Рекомендуем    {a_name} -> {item}  (Pr={pr:.4f} >= max={max_a})")
            results[item] = pr
        else:
            print(f"  - Не рекомендуем {a_name} -> {item}  (Pr={pr:.4f} < max={max_a})")

    return results

# ============================================================
# Вывод исходных данных
# ============================================================

print("=" * 60)
print("  ITEM-BASED РЕКОМЕНДАТЕЛЬНАЯ СИСТЕМА")
print("=" * 60)

col_w = 6
print("\n  Матрица предпочтений:")
print("  " + " " * 4 + "".join(f"{u:>{col_w}}" for u in users))
print("  " + "-" * (4 + col_w * len(users)))
for i, p in enumerate(products):
    row = f"  {p:<4}" + "".join(f"{ratings[i][j]:>{col_w}}" for j in range(len(users)))
    print(row)

print("\n  Матрица косинусного подобия товаров:")
print("  " + " " * 4 + "".join(f"{p:>{col_w}}" for p in products))
print("  " + "-" * (4 + col_w * len(products)))
for i, p1 in enumerate(products):
    row = f"  {p1:<4}"
    for j, p2 in enumerate(products):
        if i == j:
            row += f"{'0':>{col_w}}"
        elif i > j:
            row += f"{'—':>{col_w}}"
        else:
            row += f"{get_item_sim(p1, p2):>{col_w}.2f}"
    print(row)

print("\n\n" + "=" * 60)
print("  РАСЧЁТ РЕКОМЕНДАЦИЙ")
print("=" * 60)

all_results = {}
for j in range(len(users)):
    rec = recommend_for_user(j, demo=True)
    all_results[users[j]] = rec

print("\n" + "=" * 60)
print("  ИТОГОВЫЕ РЕКОМЕНДАЦИИ")
print("=" * 60)
for u, rec in all_results.items():
    if rec:
        for item, pr in rec.items():
            print(f"  + {u} -> рекомендовать {item}  (Pr={pr:.4f})")
    else:
        print(f"  - {u} -> нечего рекомендовать")