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*/