Cielonos/Assets/Scripts/SLSUtilities/General/StableProbability.cs

using UnityEngine;
using System;

namespace SLSUtilities.General
{
    /// <summary>
    /// 伪随机分布 (Pseudo-Random Distribution, PRD) 计算器。
    /// 给定目标概率 P，算法会得出一个常数 C。
    /// 第一次判定的概率为 C，第二次为 2C，第 N 次为 NC。
    /// 在判定成功后，概率回归为 C。
    /// </summary>
    [Serializable]
    public class StableProbability
    {
        [SerializeField, Range(0, 1)] 
        private float _probability;
        
        /// <summary>
        /// 设定的目标概率 (0.0 ~ 1.0)。
        /// 每次更改时将自动重新计算常量 C。
        /// </summary>
        public float Probability
        {
            get => _probability;
            set
            {
                float clamped = Mathf.Clamp01(value);
                if (Mathf.Abs(_probability - clamped) > 0.0001f)
                {
                    _probability = clamped;
                    C = GetCFromP(_probability);
                    //Reset();
                }
            }
        }

        public float C { get; private set; }
        public int N { get; private set; } = 1;

        public StableProbability()
        {
            _probability = 0f;
            C = 0f;
            N = 1;
        }

        public StableProbability(float probability)
        {
            _probability = Mathf.Clamp01(probability);
            C = GetCFromP(_probability);
            N = 1;
        }

        /// <summary>
        /// 进行一次概率判定。
        /// </summary>
        /// <param name="retainRealProbability">如果为 true，则在失败时不增加 N，从而保持每次判定的实际概率不变；如果为 false，则在失败时增加 N，使得每次判定的实际概率逐渐接近 1。</param>
        /// <returns>判定是否成功。如果成功，累积次数归 1；如果失败，次数递增。</returns>
        public bool Roll(bool retainRealProbability = false)
        {
            if (_probability <= 0f) return false;
            if (_probability >= 1f) return true;

            float currentProb = N * C;
            if (UnityEngine.Random.value <= currentProb)
            {
                N = 1;
                return true;
            }
            else
            {
                if (!retainRealProbability) N++;
                return false;
            }
        }

        /// <summary>
        /// 重置当前的失败次数积累。
        /// </summary>
        public void Reset()
        {
            N = 1;
        }

        /// <summary>
        /// 强制重新计算自身的C值（通常用于反序列化之后）
        /// </summary>
        public void RecalculateC()
        {
            C = GetCFromP(_probability);
        }

        /// <summary>
        /// 基于目标概率 P 计算常量 C。(基于二分查找算法)
        /// </summary>
        public static float GetCFromP(float p)
        {
            if (p <= 0f) return 0f;
            if (p >= 1f) return 1f;

            float low = 0f;
            // C 的绝对上限不能超过 P 本身
            float high = p;
            float mid = 0f;

            // 20次迭代二分查找精度足够
            for (int i = 0; i < 20; i++)
            {
                mid = (low + high) / 2f;
                float pTested = SimulatePFromC(mid);

                if (Mathf.Abs(pTested - p) < 0.0001f)
                    break;

                if (pTested < p)
                    low = mid;
                else
                    high = mid;
            }
            return mid;
        }

        /// <summary>
        /// 给定常量 C，计算出整体期望表现出的概率 P。
        /// </summary>
        private static float SimulatePFromC(float C)
        {
            if (C <= 0f) return 0f;

            float expectedTrials = 0f;
            float waitProbability = 1f; // 到目前为止仍然未触发的概率

            int maxN = Mathf.CeilToInt(1f / C);
            for (int n = 1; n <= maxN; n++)
            {
                float pSuccess = Mathf.Min(n * C, 1f);
                float pSuccessOnN = pSuccess * waitProbability;
                waitProbability *= (1f - pSuccess);

                expectedTrials += n * pSuccessOnN;
            }
            
            return 1f / expectedTrials;
        }
    }
}