AI005. 分类阈值优化器

# 按分数从高到低排序,同分整组一起跨线,增量维护 TP/FP(FN=正样本总数−TP);
# 每档算 F1=2TP/(2TP+FP+FN),严格大于才更新——并列自然保留更大阈值。
import sys


def solve() -> None:
    data = sys.stdin.buffer.read().split()
    if not data:
        return
    n = int(data[0])
    items = []
    at = 1
    for _ in range(n):
        score = float(data[at]); at += 1
        label = int(data[at]); at += 1
        items.append((score, label))
    items.sort(reverse=True)
    total_pos = sum(label for _, label in items)
    tp = fp = 0
    best_f1 = -1.0
    best_threshold = items[0][0]
    i = 0
    while i < n:
        score = items[i][0]
        while i < n and items[i][0] == score:
            if items[i][1] == 1:
                tp += 1
            else:
                fp += 1
            i += 1
        fn = total_pos - tp
        denom = 2 * tp + fp + fn
        f1 = 0.0 if denom == 0 else (2 * tp) / denom
        if f1 > best_f1 + 1e-12 or (abs(f1 - best_f1) <= 1e-12 and score > best_threshold):
            best_f1 = f1
            best_threshold = score
    print(f"{best_threshold:.4f} {best_f1:.6f}")


if __name__ == "__main__":
    solve()