为什么我要找最长的递增子序列，而不是最长的递减子序列？

Question

我试图在O（nlogn）中寻找数组中最长的递减子序列。不确定这是否真的需要O（nlogn），但无论如何，它返回最长递增子序列的长度，而不是最长递减子序列的长度。有人能帮忙吗？！？你知道吗

def binary_search(L, l, r, key): 
    while (r - l > 1): 
        m = l + (r - l)//2
        if (L[m] >= key): 
            r = m 
        else: 
            l = m 
    return r 

def LongestDecreasingSubsequenceLength(L, size): 
    tailTable = [0 for i in range(size + 1)] 
    len = 0 
    tailTable[0] = L[0] 
    len = 1
    for i in range(1, size): 
        if (L[i] < tailTable[0]): 
            # new smallest value 
            tailTable[0] = L[i] 
        elif (L[i] > tailTable[len-1]): 
            tailTable[len] = L[i] 
            len+= 1
        else: 
            tailTable[binary_search(tailTable, -1, len-1, L[i])] = L[i]
    return len

L = [ 38, 20, 15, 30, 90, 14, 6, 7] 
n = len(L) 


print("Length of Longest Decreasing Subsequence is ", 
   LongestDecreasingSubsequenceLength(L, n))

Answer 1

如果您愿意以任何方式来看待它，Wikipedia有一些伪代码，可以很容易地转换到Python中，并翻转以减少子序列。你知道吗

N = len(X)
P = np.zeros(N, dtype=np.int)
M =  np.zeros(N+1, dtype=np.int)

L = 0
for i in range(0, N-1):
    # Binary search for the largest positive j ≤ L
    # such that X[M[j]] <= X[i]
    lo = 1
    hi = L
    while lo <= hi:
        mid = (lo+hi)//2

        if X[M[mid]] >= X[i]:
            lo = mid+1
        else:
            hi = mid-1
    # After searching, lo is 1 greater than the
    # length of the longest prefix of X[i]
    newL = lo

    # The predecessor of X[i] is the last index of 
    # the subsequence of length newL-1
    P[i] = M[newL-1]
    M[newL] = i
    #print(i)
    if newL > L:
        # If we found a subsequence longer than any we've
        # found yet, update L
        L = newL

# Reconstruct the longest increasing subsequence
S = np.zeros(L, dtype=np.int)
k = M[L]
for i in range(L-1, -1, -1):
    S[i] = X[k]
    k = P[k]

S

它给出了你想要的序列

array([38, 20, 15, 14,  6])