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/**
* MaxOrderedSubsequence.cpp
* @Author Tu Yongce <yongce (at) 126 (dot) com>
* @Created 2008-4-26
* @Modified 2008-4-26
* @Version 0.1
*/
#include <iostream>
#include <vector>
#include <iterator>
#include <algorithm>
using namespace std;
/*
* 计算最长有序子序列（子序列不必连续）
* note: 算法时间复杂度为O(nlgn)，空间复杂度也为O(n)
*/
template <typename T>
struct ArrayIndexCompare
{
const T *arr_;
ArrayIndexCompare(const T *arr): arr_(arr) { }
bool operator() (int lhs, int rhs) const {
return arr_[lhs] < arr_[rhs];
}
};
template <typename T>
void MaxOrderedSubsequence(const T arr[], size_t num, vector<int> &subseqIndices)
{
vector<int> m;
vector<int> pre(num, -1);
m.push_back(-1); // 哨兵
for (int i = 0; static_cast<size_t>(i) < num; ++i) {
// 二分搜索
vector<int>::iterator it = upper_bound(m.begin() + 1, m.end(), i, ArrayIndexCompare<T>(arr));
--it; // 在数组m中二分查找元素m[j]，使arr[m[j]] ≤ arr[i]且j最大
pre[i] = *it; // 记下arr[i]的前驱元素下标
if (it == m.end() - 1)
m.push_back(i); // 比m中对应的元素都大，当前最大子序列增长
else if (arr[i] < arr[*++it])
*it = i; // 长为j + 1的最大子序列的最大值有更小值，需要更新
}
// 将最大有序子序列的数组下标输出
subseqIndices.resize(m.size() - 1);
int indexIn = m[m.size() - 1];
int indexOut = subseqIndices.size() - 1;
while (indexOut >= 0) {
subseqIndices[indexOut--] = indexIn;
indexIn = pre[indexIn];
}
}
void MaxOrderedSubSequenceTest()
{
// 示例1
//int arr[] = {1, 7, 3, 5, 9, 4, 8};
int arr[] = {3, 7, 1, 5, 9, 3};
const size_t NUM = sizeof(arr) / sizeof(arr[0]);
vector<int> subseq;
MaxOrderedSubsequence(arr, NUM, subseq);
cout << "序列：";
copy(arr, arr + NUM, ostream_iterator<int>(cout, " "));
cout << "\n最长有序子序列长度为：" << subseq.size();
cout << "\n最长有序子序列下标为：";
copy(subseq.begin(), subseq.end(), ostream_iterator<int>(cout, " "));
cout << "\n最长有序子序列为：";
for (size_t i = 0; i < subseq.size(); ++i)
cout << arr[subseq[i]] << ' ';
cout << endl;
// 示例2
char arr2[] = {'D', 'A', 'E', 'K', 'T', 'Q', 'H'};
const size_t NUM2 = sizeof(arr2) / sizeof(arr2[0]);
MaxOrderedSubsequence(arr2, NUM2, subseq);
cout << "\n序列：";
copy(arr2, arr2 + NUM2, ostream_iterator<char>(cout, " "));
cout << "\n最长有序子序列长度为：" << subseq.size();
cout << "\n最长有序子序列下标为：";
copy(subseq.begin(), subseq.end(), ostream_iterator<int>(cout, " "));
cout << "\n最长有序子序列为：";
for (size_t i = 0; i < subseq.size(); ++i)
cout << arr2[subseq[i]] << ' ';
cout << endl;
}
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