算法 - 求一个数组的最长递减子序列（C++）

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/*
 * 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 
#include 
#include 

using namespace std;

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

/**
 * Find the longest decreasing sequence in array A of length nLen.
 * @param A The array.
 * @param nLen The array length.
 */
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.
 * @param A The array.
 * @param nTarget The target.
 * @param nLen The array length.
 * @return The position.
 */
int BinarySearch(const int *A, int nTarget, int nLen) {
    assert(A != nullptr && 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
*/