Operation-Blue-Laminate-v2/BlueLaminate/BlueLaminate.Core/Tradeups/TradeupSelector.cs

namespace BlueLaminate.Core.Tradeups;

/// <summary>One candidate input copy, with its normalised fraction precomputed.</summary>
public readonly record struct SelectableInput(decimal Fraction, InputListing Listing);

/// <summary>
/// A persistent (shared-tail) singly-linked list of chosen listings. Travels with each
/// DP state so the winning selection is reconstructed for free — no fragile back-pointer
/// walk over a mutated cost table.
/// </summary>
public sealed record PickNode(InputListing Listing, PickNode? Previous)
{
    public IReadOnlyList<InputListing> ToList()
    {
        var items = new List<InputListing>();
        for (var node = this; node is not null; node = node.Previous)
        {
            items.Add(node.Listing);
        }

        items.Reverse();
        return items;
    }

    /// <summary>Exact total cost of the chosen copies (the DP minimises this in double).</summary>
    public decimal TotalCost()
    {
        var total = 0m;
        for (var node = this; node is not null; node = node.Previous)
        {
            total += node.Listing.Price;
        }

        return total;
    }
}

/// <summary>
/// The result of the selection DP: for every reachable summed-fraction bucket, the
/// cheapest way to pick exactly <see cref="ContractSize"/> distinct input copies whose
/// average fraction rounds (conservatively, upward) to that bucket. The finder reads
/// this once and evaluates output revenue across every bucket, which is equivalent to
/// solving the cheapest-inputs knapsack at every wear-boundary breakpoint at once.
/// </summary>
public sealed class TradeupSelection
{
    private readonly PickNode?[] _pickBySum;
    private readonly decimal _bucketWidth;

    internal TradeupSelection(PickNode?[] pickBySum, int contractSize, decimal bucketWidth)
    {
        _pickBySum = pickBySum;
        ContractSize = contractSize;
        _bucketWidth = bucketWidth;
    }

    public int ContractSize { get; }

    /// <summary>
    /// Every feasible full selection: the (conservative) average input fraction, the total
    /// input cost, and the exact copies to buy.
    /// </summary>
    public IEnumerable<(decimal AverageFraction, decimal Cost, PickNode Picks)> Selections()
    {
        for (var sum = 0; sum < _pickBySum.Length; sum++)
        {
            if (_pickBySum[sum] is { } picks)
            {
                var averageFraction = sum * _bucketWidth / ContractSize;
                yield return (averageFraction, picks.TotalCost(), picks);
            }
        }
    }
}

/// <summary>
/// Solves "pick exactly N distinct listings minimising total price, for each attainable
/// summed-fraction level". A bounded knapsack over the discretised fraction: O(items × N
/// × buckets). Fractions are bucketed by rounding UP, so the reported average float is an
/// upper bound — the conservative direction (it can only make an output look worse, never
/// better). Cost is minimised in <c>double</c> for speed; the exact decimal cost is
/// recovered from the reconstructed picks.
/// </summary>
public static class TradeupSelector
{
    public static TradeupSelection Solve(
        IReadOnlyList<SelectableInput> pool,
        int contractSize,
        decimal bucketWidth)
    {
        if (contractSize <= 0)
        {
            throw new ArgumentOutOfRangeException(nameof(contractSize));
        }

        if (bucketWidth <= 0m)
        {
            throw new ArgumentOutOfRangeException(nameof(bucketWidth));
        }

        // Buckets 0..maxBucketPerItem (fraction is clamped to [0,1]); summed across the
        // contract gives the DP's second dimension.
        var maxBucketPerItem = (int)Math.Ceiling(1m / bucketWidth);
        var maxSum = maxBucketPerItem * contractSize;

        var items = Trim(pool, bucketWidth, maxBucketPerItem, contractSize);

        // dp[c][s] = cheapest cost (double) to choose exactly c items whose bucket sum is s;
        // dpPick carries the actual copies so the winner is reconstructed exactly.
        var dpCost = new double[contractSize + 1, maxSum + 1];
        var dpPick = new PickNode?[contractSize + 1, maxSum + 1];
        for (var c = 0; c <= contractSize; c++)
        {
            for (var s = 0; s <= maxSum; s++)
            {
                dpCost[c, s] = double.PositiveInfinity;
            }
        }

        dpCost[0, 0] = 0d;

        foreach (var (bucket, listing, price) in items)
        {
            // Descending count + sum so each item is used at most once (0/1 knapsack).
            for (var c = contractSize - 1; c >= 0; c--)
            {
                for (var s = maxSum - bucket; s >= 0; s--)
                {
                    var baseCost = dpCost[c, s];
                    if (double.IsPositiveInfinity(baseCost))
                    {
                        continue;
                    }

                    var newCost = baseCost + price;
                    var ns = s + bucket;
                    if (newCost < dpCost[c + 1, ns])
                    {
                        dpCost[c + 1, ns] = newCost;
                        dpPick[c + 1, ns] = new PickNode(listing, dpPick[c, s]);
                    }
                }
            }
        }

        var pickBySum = new PickNode?[maxSum + 1];
        for (var s = 0; s <= maxSum; s++)
        {
            pickBySum[s] = dpPick[contractSize, s];
        }

        return new TradeupSelection(pickBySum, contractSize, bucketWidth);
    }

    // Within a single fraction bucket only the cheapest `contractSize` copies can ever be
    // part of an optimal selection, so drop the rest up front. This bounds the item count
    // regardless of how deep a popular skin's order book is.
    private static List<(int Bucket, InputListing Listing, double Price)> Trim(
        IReadOnlyList<SelectableInput> pool,
        decimal bucketWidth,
        int maxBucketPerItem,
        int contractSize)
    {
        var byBucket = new Dictionary<int, List<InputListing>>();
        foreach (var item in pool)
        {
            var bucket = BucketOf(item.Fraction, bucketWidth, maxBucketPerItem);
            if (!byBucket.TryGetValue(bucket, out var list))
            {
                list = new List<InputListing>();
                byBucket[bucket] = list;
            }

            list.Add(item.Listing);
        }

        var trimmed = new List<(int, InputListing, double)>();
        foreach (var (bucket, listings) in byBucket)
        {
            listings.Sort(static (a, b) => a.Price.CompareTo(b.Price));
            var take = Math.Min(contractSize, listings.Count);
            for (var i = 0; i < take; i++)
            {
                trimmed.Add((bucket, listings[i], (double)listings[i].Price));
            }
        }

        return trimmed;
    }

    // Round the fraction UP to a bucket index (conservative: never understates output float).
    private static int BucketOf(decimal fraction, decimal bucketWidth, int maxBucketPerItem)
    {
        var clamped = Math.Clamp(fraction, 0m, 1m);
        var bucket = (int)Math.Ceiling(clamped / bucketWidth);
        return Math.Clamp(bucket, 0, maxBucketPerItem);
    }

    /// <summary>
    /// One candidate input copy for the multi-collection search: its (already bucketed) float
    /// contribution and a per-item reward (its collection's average output value share minus
    /// its price, at a fixed output-float target).
    /// </summary>
    public readonly record struct RewardItem(int Bucket, double Reward, InputListing Listing);

    /// <summary>
    /// Picks exactly <paramref name="contractSize"/> copies that MAXIMISE total reward subject
    /// to the bucketed float sum not exceeding <paramref name="capBucket"/> (i.e. mean float
    /// ≤ the target). This is the multi-collection core: with each item's reward set to its
    /// collection's value share minus price, the optimum naturally mixes whichever collections
    /// pay off — no collection-subset enumeration. Returns the chosen copies, or null if the
    /// contract can't be filled within the cap.
    /// </summary>
    public static PickNode? SolveMaxReward(
        IReadOnlyList<RewardItem> items, int contractSize, int capBucket)
    {
        if (contractSize <= 0)
        {
            throw new ArgumentOutOfRangeException(nameof(contractSize));
        }

        var maxSum = Math.Max(0, capBucket);

        // dp[c][s] = max total reward for exactly c items with bucket sum s (≤ cap).
        var dpReward = new double[contractSize + 1, maxSum + 1];
        var dpPick = new PickNode?[contractSize + 1, maxSum + 1];
        for (var c = 0; c <= contractSize; c++)
        {
            for (var s = 0; s <= maxSum; s++)
            {
                dpReward[c, s] = double.NegativeInfinity;
            }
        }

        dpReward[0, 0] = 0d;

        foreach (var (bucket, reward, listing) in items)
        {
            if (bucket > maxSum)
            {
                continue; // a single copy already over the cap can't be in any valid contract
            }

            for (var c = contractSize - 1; c >= 0; c--)
            {
                for (var s = maxSum - bucket; s >= 0; s--)
                {
                    var baseReward = dpReward[c, s];
                    if (double.IsNegativeInfinity(baseReward))
                    {
                        continue;
                    }

                    var newReward = baseReward + reward;
                    var ns = s + bucket;
                    if (newReward > dpReward[c + 1, ns])
                    {
                        dpReward[c + 1, ns] = newReward;
                        dpPick[c + 1, ns] = new PickNode(listing, dpPick[c, s]);
                    }
                }
            }
        }

        PickNode? best = null;
        var bestReward = double.NegativeInfinity;
        for (var s = 0; s <= maxSum; s++)
        {
            if (dpReward[contractSize, s] > bestReward && dpPick[contractSize, s] is { } pick)
            {
                bestReward = dpReward[contractSize, s];
                best = pick;
            }
        }

        return best;
    }
}