You have three independent coding tasks: A) Date normalization and business-day delta - Input: a list of strings with mixed, possibly ambiguous date/time formats, e.g., ["2025/02/28 23:59 PST", "28-02-2025", "02/03/25", "2025-02-29", "Mar 1, 2025 01:30 +0530"]. Normalize each to strict UTC ISO 8601 "YYYY-MM-DDTHH:MM:SSZ". - Disambiguation rules: if a date is of the form dd/mm/yy or mm/dd/yy, treat as dd/mm/yy when the first number > 12; otherwise default to mm/dd/yy. Two‑digit years map 00–68 → 2000–2068, 69–99 → 1969–1999. Validate leap years. If a timezone is absent, assume local time is UTC−08:00; then convert to UTC. - Then, given any two normalized instants, compute business-day difference between their dates (ignore time-of-day), excluding weekends and a provided holiday set H = {2025-01-01, 2025-07-04, 2025-12-25}. Return an integer that can be negative. - Edge cases to handle: invalid dates (return an error with the offending token), Feb 29 on non‑leap years, zero-length input, and timezone offsets like +05:45. B) Arbitrary shopping with bundles (DP/memoization) - You are given: target quantities T over up to 6 item types, unit prices P, and a list of special bundles (each bundle is a vector of item counts plus a bundle price). Compute the minimum total cost to satisfy T exactly; if impossible, return −1. Also return one optimal combination of bundles and leftover unit purchases. - Example: T = {A:3, B:2}, P = {A:5, B:4} Bundles = [b1: {A:2, B:1} @ 12, b2: {A:3, B:0} @ 13] Output: min_cost and a decomposition (e.g., b1×1 + unit A×1 + unit B×1). - Constraints: 0 ≤ T[i] ≤ 6, 1 ≤ |Bundles| ≤ 20, prices are nonnegative integers. Require a solution with pruning and memoization over states; state space must not exceed 7^k for k item types. - Edge cases: zero-cost bundles, dominated bundles, and bundles that oversupply (not allowed). C) Circle‑relationship classifier with numerics - Implement a function relate((x1, y1, r1), (x2, y2, r2), eps=1e-9) that returns one of: {"separate", "externally_tangent", "intersecting", "internally_tangent", "contained_no_touch", "concentric_equal", "concentric_distinct"}. - Use squared distances to avoid precision loss; treat values within eps as equal. Radii may be zero. If "intersecting", also return the two intersection points (ordered by x then y), or one point if tangency detected within eps. - Edge cases: coincident centers, one or both radii zero, very large coordinates (|x|,|y| ≤ 1e9), and near‑tangency scenarios where |d − (r1±r2)| < eps.