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You are given an array of positive integers arr. Perform some operations (possibly none) on arr so that it satisfies these conditions: The value of the first element in arr must be 1. The absolute difference between any 2 adjacent elements must be less than or equal to 1. In other words, abs(arr[i] - arr[i - 1]) <= 1 for each i where 1 <= i < arr.length (0-indexed). abs(x) is the absolute value of x. There are 2 types of operations that you can perform any number of times: Decrease the value of any element of arr to a smaller positive integer. Rearrange the elements of arr to be in any order. Return the maximum possible value of an element in arr after performing the operations to satisfy the conditions.

You are given an array of positive integers nums. You need to select a subset of nums which satisfies the following condition: You can place the selected elements in a 0-indexed array such that it follows the pattern: [x, x2, x4, ..., xk/2, xk, xk/2, ..., x4, x2, x] (Note that k can be be any non-negative power of 2). For example, [2, 4, 16, 4, 2] and [3, 9, 3] follow the pattern while [2, 4, 8, 4, 2] does not. Return the maximum number of elements in a subset that satisfies these conditions.

You are given an integer array nums and an integer target. Return the number of subarrays of nums in which target is the majority element. The majority element of a subarray is the element that appears strictly more than half of the times in that subarray.

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# Metabolic Causal Planner A compact and interpretable deep learning framework for predicting cancer immunotherapy response from pre-treatment bulk RNA-seq profiles by integrating computational immunology, metabolic representation learning, and uncertainty-aware prediction. ## Overview **Metabolic Causal Planner** is designed for supervised patient-level cancer immunotherapy response prediction. Given a pre-treatment tumor bulk RNA-seq expression profile, the model predicts whether a patient is likely to respond to immune checkpoint blockade therapy. The framework integrates three coordinated modules: 1. **Counterfactual Metabolic Adjuster** Learns a latent biological state from transcriptomic profiles and estimates response-relevant metabolic perturbations in the latent space. 2. **Agent-driven Immune Response Mapper** Maps the adjusted molecular representation into an immune-response embedding to capture immune–metabolic interactions. 3. **Uncertainty-guided Response Predictor** Performs stochastic response prediction and estimates patient-level predictive uncertainty for robust decision making. An additional **Uncertainty-aware Refinement** strategy is used to regularize the final decision representation and reduce unstable or over-confident predictions. ## Key Features - Prediction from pre-treatment tumor bulk RNA-seq profiles - Immune–metabolic representation learning - Counterfactual latent metabolic adjustment - Stochastic uncertainty-aware response prediction - Entropy-guided refinement for robust classification - Internal evaluation on IMvigor210 - External validation on Hugo/GSE78220 - Comparison with classical machine learning, gradient boosting, neural, and immunotherapy-specific baselines ## Task The task is formulated as binary classification: - **Responder**: complete response or partial response - **Non-responder**: stable disease or progressive disease Given a normalized gene-expression vector, the model outputs a responder probability between 0 and 1. ## Datasets This project uses two public immune checkpoint blockade cohorts: | Dataset | Cancer Type | Treatment | Role | |---|---|---|---| | IMvigor210 | Metastatic urothelial carcinoma | Atezolizumab / anti-PD-L1 | Development cohort | | Hugo / GSE78220 | Metastatic melanoma | Anti-PD-1 | External test cohort | The IMvigor210 cohort is used for training, validation, and internal testing. Hugo/GSE78220 is used only for independent external validation. ## Model Architecture The overall framework follows the pipeline below: ```text Pre-treatment bulk RNA-seq | v Counterfactual Metabolic Adjuster | v Adjusted latent biological state | v Agent-driven Immune Response Mapper | v Immune-response embedding | v Uncertainty-guided Response Predictor | v Responder probability + predictive uncertainty Method Counterfactual Metabolic Adjuster The input RNA-seq vector is encoded into a compact latent biological state. A perturbation network estimates a counterfactual adjustment vector, which is added to the latent state to obtain an adjusted immune–metabolic representation. Agent-driven Immune Response Mapper The adjusted representation is transformed into an immune-response embedding using a neural mapping module with nonlinear activation, layer normalization, and dropout. Uncertainty-guided Response Predictor The predictor performs multiple stochastic forward passes using Monte Carlo dropout. The final responder probability is computed as the average prediction, while predictive uncertainty is estimated from the variance across stochastic predictions. Uncertainty-aware Refinement The model applies entropy-guided regularization and gradient-based feedback updates to refine the response decision representation before final classification. Evaluation Metrics The model is evaluated using: AUROC AUPRC Balanced Accuracy Macro-F1 Number of trainable parameters FLOPs per patient-level inference Confidence intervals, calibration analysis, Brier score, expected calibration error, and decision curve analysis may also be used for clinical AI reliability evaluation. Baselines The proposed method is compared with: Logistic Regression Random Forest XGBoost Multi-Layer Perceptron TIDE LightGBM All baselines use the same preprocessed RNA-seq input, label definition, data split protocol, and evaluation metrics. Installation git clone https://github.com/your-username/Metabolic-Causal-Planner.git cd Metabolic-Causal-Planner conda create -n mcp python=3.10 conda activate mcp pip install -r requirements.txt Requirements Recommended environment: Python 3.10 PyTorch 2.1.0 CUDA 11.8 NumPy 1.24.4 pandas 2.0.3 scikit-learn 1.3.2 SciPy 1.10.1 LightGBM 4.1.0 XGBoost Repository Structure Metabolic-Causal-Planner/ ├── configs/ │ └── default.yaml ├── data/ │ ├── raw/ │ └── processed/ ├── src/ │ ├── preprocessing.py │ ├── model.py │ ├── train.py │ ├── evaluate.py │ └── utils.py ├── scripts/ │ ├── run_train.sh │ ├── run_eval.sh │ └── run_ablation.sh ├── results/ ├── checkpoints/ ├── requirements.txt └── README.md Usage Data Preprocessing python src/preprocessing.py \ --config configs/default.yaml Training python src/train.py \ --config configs/default.yaml \ --seed 13 Evaluation python src/evaluate.py \ --config configs/default.yaml \ --checkpoint checkpoints/best_model_seed13.pt Repeated Runs for seed in 13 21 34 55 89 do python src/train.py --config configs/default.yaml --seed $seed python src/evaluate.py --config configs/default.yaml --seed $seed done Reproducibility The experimental protocol uses five random seeds: 13, 21, 34, 55, 89 For each run, IMvigor210 is split at the patient level into training, validation, and internal test subsets using an 8:1:1 stratified ratio. Hugo/GSE78220 is reserved as an independent external test cohort and is not used for training, validation, normalization fitting, hyperparameter tuning, or early stopping. Data Availability The raw datasets are obtained from public immunotherapy cohort resources. Due to data-access requirements, raw patient-level data are not redistributed in this repository. Scripts are provided to reproduce the processed matrices from the original public sources, subject to the corresponding data-access terms. Model Availability Trained model checkpoints, prediction files, split identifiers, and evaluation outputs can be deposited in an archival repository such as Zenodo after release. Citation If you use this repository or find this work useful, please cite: @article{fang2025metaboliccausalplanner, title={Integrating Computational Immunology and Metabolic Profiling for Cancer Immunotherapy Response Prediction from Pre-treatment Bulk RNA-seq Profiles}, author={Fang, Xuan}, journal={}, year={2025} } License This project is released for academic and research use. Please check the repository license file for details.

You are given an integer array nums and an integer target. Return the number of subarrays of nums in which target is the majority element. The majority element of a subarray is the element that appears strictly more than half of the times in that subarray.

You are given three integers n, l, and r. A ZigZag array of length n is defined as follows: Each element lies in the range [l, r]. No two adjacent elements are equal. No three consecutive elements form a strictly increasing or strictly decreasing sequence. Return the total number of valid ZigZag arrays. Since the answer may be large, return it modulo 109 + 7. A sequence is said to be strictly increasing if each element is strictly greater than its previous one (if exists). A sequence is said to be strictly decreasing if each element is strictly smaller than its previous one (if exists).

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