算法 - 求一个数组的最长递减子序列（C++）

//****************************************************************************************************
//
// 求一个数组的最长递减子序列 - C++ - by Chimomo
//
// 题目： 求一个数组的最长递减子序列，比如{8, 14, 6, 2, 8, 14, 3, 2, 7, 4, 7, 2, 8, 101, 23, 6, 1, 2, 1, 1}的最长递减子序列为{14，8，3，2，1}。
//
// Answer: Scan from left to right, maintain a decreasing sequence. For each number, binary search in the decreasing sequence to see whether it can be substituted.
//
//****************************************************************************************************

#include <iostream>
#include <cassert>
#include <stack>

using namespace std ;

int BinarySearch(int *A, int nTarget, int nLen);

// Find the longest decreasing sequence in array A of length nLen.
void FindLongestDecreasingSequence(int *A, int nLen)
{
int *index = new int[nLen];
int *LDS = new int[nLen];
index[0] = A[0];
LDS[0] = 1;
int indexLen = 1;

for (int i = 1; i < nLen; i++)
{
int pos = BinarySearch(index, A[i], indexLen);
index[pos] = A[i];
LDS[i] = pos + 1;
if(pos >= indexLen)
{
indexLen++;
}
}

int ResultLen = indexLen;

for (int i = nLen; i >= 0; i--)
{
if(LDS[i] == ResultLen)
{
index[ResultLen - 1] = A[i];
ResultLen--;
}
}

for (int i = 0; i < indexLen; i++)
{
cout << index[i] << " ";
}

delete [] index;
}

// Binary search nTarget in array A of length nLen.
int BinarySearch(int *A, int nTarget, int nLen)
{
assert(A != NULL && nLen > 0);
int start = 0;
int end = nLen - 1;

while (start <= end)
{
int mid = (start + end) / 2;

if(nTarget > A[mid])
{
end=mid-1;
}
else if(nTarget<A[mid])
{
start=mid+1;
}
else
{
return mid;
}
}

return start;
}

int main()
{
int A[] = {8, 14, 6, 2, 8, 14, 3, 2, 7, 4, 7, 2, 8, 101, 23, 6, 1, 2, 1, 1};
int nLen = sizeof(A) / sizeof(int);
FindLongestDecreasingSequence(A, nLen);
return 0;
}

// Output:
/*
14 8 7 6 2 1
*/