Dream11 & MakeMyTrip: Data Scientist

• Entropy H(X) = −Σ p(x) log₂ p(x) measures uncertainty.
• A fair coin has H = 1 bit; a biased (0.9/0.1) coin has H ≈ 0.47; a certain outcome has H = 0.
• Uses:
• Decision-tree splits (information gain = parent entropy − weighted child entropy).
• Cross-entropy loss for classification.
• KL divergence (distillation, VAEs, RLHF penalties).
• Uncertainty sampling in active learning.
• Perplexity = 2^H for language models.

• Target: the expected sale price (or price range) for a listing. The heavy-tailed distribution calls for log-price regression or quantiles.
• Features:
• Artist: past sales, followers, volume.
• Collection: floor price, rarity traits, trend.
• Item: image embeddings (CLIP), trait rarity scores.
• Market: overall volume, crypto price, time.
• Model: gradient boosting on tabular features plus image embeddings; quantile regression (P10/P50/P90) to show the uncertainty.
• Pitfalls: wash trading (filter suspicious sales), very little data for new artists (use hierarchical priors by collection), market regime shifts (time-based validation, frequent retraining).
• Evaluation: MAPE on log price, interval coverage; product impact on listing success and time to sale.

• Unit: the user, split 50/50. The primary metric is booking conversion (sessions → bookings) or revenue per user; guardrails are cancellations, latency and complaints.
• Duration: at least 2 full weeks to cover weekday and weekend patterns (travel intent varies); compute the sample size from the baseline conversion and the minimum detectable effect.
• Pitfalls:
• Novelty effects.
• Seasonality (holidays).
• Long consideration windows (users browse for days), so attribute bookings within N days.
• Analysis: conversion lift with confidence intervals; segment by new vs returning users and by domestic vs international.

• Build an additive model F(x) = Σ ηₘ hₘ(x) of shallow trees. Each new tree fits the negative gradient of the loss (the residuals for MSE) of the current model, so every step corrects the remaining error.
• The learning rate η shrinks each step: a smaller η with more trees generalises better.
• Regularisation: tree depth, subsampling (stochastic GB), column sampling, L1/L2 on leaf weights (XGBoost), early stopping.

• Precision@k / Recall@k: binary relevance with a fixed list length.
• MRR: where the first relevant item appears (search with one right answer).
• NDCG@k: graded relevance with position discounting (hotel lists, feeds).
• MAP: averages precision over all relevant items.
• Online: CTR, conversion, revenue per search, and time to first click.

from collections import deque
class Stack:
    def __init__(self): self.q = deque()
    def push(self, x):
        self.q.append(x)
        for _ in range(len(self.q) - 1): self.q.append(self.q.popleft())   # rotate so x is at the front
    def pop(self): return self.q.popleft()
    def top(self): return self.q[0]
    def empty(self): return not self.q

• Push is O(n) and pop is O(1). The alternative makes push O(1) and pop O(n).