Function build_first_valid_path 

pub fn build_first_valid_path<V>(
    target: &Certificate,
    pool: &CertPool,
    anchors: &[TrustAnchor],
    policy: &ValidationPolicy,
    verifier: &V,
) -> Result<Vec<Certificate>>
where
    V: SignatureVerifier,

Build a certification path that both (a) is topologically valid through pool to one of anchors and (b) passes pkix_path::validate_path under policy and verifier.

Iterates build_path_candidates until the first candidate chain validates. Returns the validating chain. If every candidate is rejected by validate_path, returns Error::NoValidPath carrying the count of candidates tried and the Display rendering of the last pkix_path::Error.

When to use this over build_path

build_path is single-shot: it returns the first DFS candidate without any knowledge of which signature algorithms verifier actually dispatches or which intermediates are within their validity window at policy’s validation time. In adversarial pools — for example, cross-signed graphs that include an alternative intermediate signed under ecdsa-with-SHA1 (RFC 5758 §3.2 legacy OID, not dispatched by pkix_path::DefaultVerifier) — the first DFS yield can be rejected by validate_path even though a SHA-256-only path exists in the same pool.

build_first_valid_path closes this gap: it iterates build_path_candidates and tries validate_path per yielded chain, returning the first chain that survives both passes.

Errors

• Error::NoPathFound — the underlying iterator yielded no candidates at all (no topologically valid chain through pool to any anchor). Matches build_path’s behaviour for that case.
• Error::DepthExceeded / Error::BudgetExceeded — propagated from build_path_candidates when the iterator surfaces them.
• Error::NoValidPath — at least one candidate was yielded but none passed validate_path. Carries tried (>= 1) and the last validate_path error rendering.

Out of scope

• Async / parallel candidate evaluation. Candidates are tried sequentially.
• Caching of validate_path failures across candidates. Each yielded chain is freshly validated.
• Promoting build_path itself to iterate. The single-shot helper is retained verbatim for backward compatibility; callers opt in to the iterating semantics by using this function.

Relationship to other path-builder entry points

Entry point	Verifier?	Returns
build_path	No	First DFS topological candidate (one-shot)
build_path_candidates	No	Iterator of topological candidates
build_first_valid_path	Yes	First candidate that passes validate_path