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using System;
using System.Collections;
using System.Collections.Generic;
using AlgorithmCollection;
using UnityEngine;
// 递归与分治算法
namespace AlgorithmCollection.Recursion
{
public static class RecursionHelper
{
#region 全排列，返回数据的所有组合
public static void Permutations<T>(List<T> dataList, ref List<List<T>> perms)
{
List<List<T>> outPerms = new List<List<T>>(); // A B C D
List<T> temp = new List<T>(dataList.Count); // + A (BCD)
DNC( // + B (CD)
() => // init // + C(D)
{ // +D
DivisionDescriptor div = new DivisionDescriptor(); // + D(C)
div.userdata = -1; // +C
div.left = 0; // + C (BD)
div.right = dataList.Count - 1; // + B(D)
return div; // + D(B)
}, // + D (BC)
(DivisionDescriptor div, out DivisionDescriptor[] divs) => // 划分 // + B(C)
{ // + C(B)
int left = div.left; // 包含第一个元素在内的范围 // + B (ACD)
int right = div.right; // + C (ABD)
int pivot = (int)div.userdata; // 第一个元素在范围内的索引 // + D (ABC)
int l = left;
if (pivot != -1)
{
temp.Add(dataList[pivot]);
Algorithms.Swap(ref dataList, pivot, left);
l = left + 1;
}
divs = new DivisionDescriptor[right - l + 1];
int j = 0;
for (int i = l; i <= right; ++i)
{
divs[j].left = l;
divs[j].right = right;
divs[j].userdata = (int)i;
j++;
}
return l == right;
},
(DivisionDescriptor div) => // solve 最小子任务处理
{
temp.Add(dataList[div.left]);
List<T> newCompose = new List<T>(temp);
outPerms.Add(newCompose);
temp.RemoveAt(temp.Count - 1);
},
(DivisionDescriptor div) => //子任务后处理
{
int pivot = (int)div.userdata; // 第一个元素的索引
int left = div.left;
int right = div.right;
Algorithms.Swap(ref dataList, pivot, left);
temp.RemoveAt(temp.Count - 1);
}
);
perms = outPerms;
}
// 生成器形式，每次返回一个组合
public static IEnumerable Permutations<T>(List<T> data)
{
foreach (var perm in _Permutations(data, 0, data.Count - 1))
{
yield return perm;
}
}
// 计算start~end范围内的全排列
private static IEnumerable _Permutations<T>(List<T> data, int start, int end, List<T> perm = null)
{
if (perm == null)
perm = new List<T>(data.Count);
if (start == end)
{
perm.Add(data[start]);
yield return perm;
perm.RemoveAt(perm.Count - 1);
}
else
{
for (int i = start; i <= end; ++i)
{
perm.Add(data[i]);
Algorithms.Swap(ref data, start, i);
IEnumerator itor = _Permutations(data, start + 1, end, perm).GetEnumerator();
while (itor.MoveNext())
yield return itor.Current;
Algorithms.Swap(ref data, start, i);
perm.RemoveAt(perm.Count - 1);
}
}
}
#endregion
#region 分治
public delegate DivisionDescriptor Init();
public delegate void Solve(DivisionDescriptor division);
public delegate bool Divide(DivisionDescriptor division, out DivisionDescriptor[] divs);//返回值代表是否达到最小问题阈值
public delegate void Merge(DivisionDescriptor[] divisions);
public delegate void Postprocess(DivisionDescriptor div);
// 分治算法框架
public static void DNC(Init init, Divide divide, Solve solve, Postprocess postprocess = null, Merge merge = null)
{
DivisionDescriptor div = init();
_DivideAndConquer(div, solve, divide, merge, postprocess);
}
private static void _DivideAndConquer(DivisionDescriptor div, Solve solve, Divide divide, Merge merge, Postprocess postprocess)
{
DivisionDescriptor[] division;
bool bUnit = divide(div, out division);
if (!bUnit)
{
for(int i = 0; i < division.Length; ++i)
{
_DivideAndConquer(division[i], solve, divide, merge, postprocess);
postprocess?.Invoke(division[i]);
}
merge?.Invoke(division);
}
else
{
for(int i = 0; i < division.Length; ++i)
{
solve(division[i]);
}
}
}
#endregion
#region 动态规划
private static void DP()
{
}
#endregion
}
}
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