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////  求一個數組的最長遞減子序列 - C++ - by Chimomo////  題目： 求一個數組的最長遞減子序列，比如{8, 14, 6, 2, 8, 14, 3, 2, 7, 4, 7, 2, 8, 101, 23, 6, 1, 2, 1, 1}的最長遞減子序列為{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*/

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