146 lines
4.3 KiB
C#
146 lines
4.3 KiB
C#
using UnityEngine;
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using System;
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namespace SLSUtilities.General
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{
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/// <summary>
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/// 伪随机分布 (Pseudo-Random Distribution, PRD) 计算器。
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/// 给定目标概率 P，算法会得出一个常数 C。
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/// 第一次判定的概率为 C，第二次为 2C，第 N 次为 NC。
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/// 在判定成功后，概率回归为 C。
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/// </summary>
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[Serializable]
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public class StableProbability
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{
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[SerializeField, Range(0, 1)]
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private float _probability;
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/// <summary>
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/// 设定的目标概率 (0.0 ~ 1.0)。
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/// 每次更改时将自动重新计算常量 C。
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/// </summary>
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public float Probability
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{
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get => _probability;
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set
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{
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float clamped = Mathf.Clamp01(value);
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if (Mathf.Abs(_probability - clamped) > 0.0001f)
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{
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_probability = clamped;
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C = GetCFromP(_probability);
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//Reset();
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}
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}
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}
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public float C { get; private set; }
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public int N { get; private set; } = 1;
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public StableProbability()
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{
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_probability = 0f;
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C = 0f;
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N = 1;
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}
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public StableProbability(float probability)
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{
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_probability = Mathf.Clamp01(probability);
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C = GetCFromP(_probability);
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N = 1;
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}
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/// <summary>
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/// 进行一次概率判定。
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/// </summary>
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/// <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>
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/// <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>
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public bool Roll(bool retainRealProbability = false)
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{
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if (_probability <= 0f) return false;
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if (_probability >= 1f) return true;
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float currentProb = N * C;
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if (UnityEngine.Random.value <= currentProb)
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{
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N = 1;
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return true;
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}
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else
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{
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if (!retainRealProbability) N++;
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return false;
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}
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}
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/// <summary>
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/// 重置当前的失败次数积累。
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/// </summary>
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public void Reset()
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{
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N = 1;
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}
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/// <summary>
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/// 强制重新计算自身的C值（通常用于反序列化之后）
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/// </summary>
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public void RecalculateC()
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{
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C = GetCFromP(_probability);
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}
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/// <summary>
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/// 基于目标概率 P 计算常量 C。(基于二分查找算法)
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/// </summary>
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public static float GetCFromP(float p)
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{
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if (p <= 0f) return 0f;
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if (p >= 1f) return 1f;
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float low = 0f;
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// C 的绝对上限不能超过 P 本身
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float high = p;
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float mid = 0f;
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// 20次迭代二分查找精度足够
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for (int i = 0; i < 20; i++)
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{
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mid = (low + high) / 2f;
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float pTested = SimulatePFromC(mid);
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if (Mathf.Abs(pTested - p) < 0.0001f)
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break;
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if (pTested < p)
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low = mid;
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else
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high = mid;
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}
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return mid;
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}
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/// <summary>
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/// 给定常量 C，计算出整体期望表现出的概率 P。
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/// </summary>
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private static float SimulatePFromC(float C)
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{
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if (C <= 0f) return 0f;
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float expectedTrials = 0f;
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float waitProbability = 1f; // 到目前为止仍然未触发的概率
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int maxN = Mathf.CeilToInt(1f / C);
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for (int n = 1; n <= maxN; n++)
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{
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float pSuccess = Mathf.Min(n * C, 1f);
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float pSuccessOnN = pSuccess * waitProbability;
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waitProbability *= (1f - pSuccess);
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expectedTrials += n * pSuccessOnN;
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}
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return 1f / expectedTrials;
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}
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}
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} |