Problems

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K-Fold Split (Indices Only)

Data Processing

Hard

Split indices 0..N-1 into k folds for cross-validation. Return a list of (train_idx, val_idx) pairs where each index appears exactly once in validation across all folds.

Mathematical Definition

K-Fold Partitioning:

\{0, 1, \ldots, N-1\} = F_{1} \cup F_{2} \cup \cdots \cup F_{k}

where F_i∩F_j=∅ for i≠j, and ∣Fi∣−∣Fj∣≤1 for all i, j.

For fold i:

\text{val}_{i} = F_{i} \qquad \text{train}_{i} = \bigcup_{j \ne i} F_{j}

Function Arguments

N: int - total number of samples
k: int - number of folds
shuffle: bool - whether to shuffle before splitting
rng: np.random.Generator or None - random generator for reproducibility

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Examples

Input: N=5, k=2, shuffle=False

Output: [(train=[3,4], val=[0,1,2]), (train=[0,1,2], val=[3,4])]

5 items split into 2 folds of sizes [3, 2]. Each fold uses one part as validation, the rest as training.

Input: N=7, k=3, shuffle=False

Output: [(train=[3,4,5,6], val=[0,1,2]), (train=[0,1,2,5,6], val=[3,4]), (train=[0,1,2,3,4], val=[5,6])]

7 items → 3 folds of sizes [3, 2, 2]. Larger folds come first (7 mod 3 = 1 extra item in fold 1).

Hint 1

Create np.arange(), optionally shuffle, then split into k contiguous chunks using np.array_split().

Hint 2

For fold i, validation is fold i, training is np.concatenate() of all other folds.

Requirements

Return list of k tuples: (train_idx, val_idx)
Both arrays are 1D numpy arrays of dtype int
Each index 0..N-1 appears exactly once in validation
Fold sizes differ by at most 1
Use rng.permutation() if rng provided, else np.random.shuffle()

Constraints

2 ≤ k ≤ N ≤ 100,000
NumPy only
Time limit: 300ms

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