rosalind练习题二十四

# Problem
# A subsequence of a permutation is a collection of elements of the permutation in the order that they appear. For example, (5, 3, 4) is a subsequence of (5, 1, 3, 4, 2).
# A subsequence is increasing if the elements of the subsequence increase, and decreasing if the elements decrease. For example, given the permutation (8, 2, 1, 6, 5, 7, 4, 3, 9), an increasing subsequence is (2, 6, 7, 9), and a decreasing subsequence is (8, 6, 5, 4, 3). You may verify that these two subsequences are as long as possible.

# Given: A positive integer n≤10000 followed by a permutation π of length n.
# Return: A longest increasing subsequence of π, followed by a longest decreasing subsequence of π.

# Sample Dataset
# 5
# 5 1 4 2 3
# Sample Output
# 1 2 3
# 5 4 2

# 对于一个给定的长度为 n 的排列 π，求它的最长上升子序列和最长下降子序列。

n = 5
a = [5, 1, 4, 2, 3]

dp1 = [1] * n  # 最长上升子序列
pre1 = [-1] * n  # 记录前驱，方便输出
for i in range(n):
    for j in range(i):
        if a[j] < a[i]:
            if dp1[j] + 1 > dp1[i]:
                dp1[i] = dp1[j] + 1
                pre1[i] = j

dp2 = [1] * n  # 最长下降子序列
pre2 = [-1] * n
for i in range(n):
    for j in range(i):
        if a[j] > a[i]:
            if dp2[j] + 1 > dp2[i]:
                dp2[i] = dp2[j] + 1
                pre2[i] = j

# 输出最长上升子序列
idx1 = dp1.index(max(dp1))
ans1 = []
while idx1 != -1:
    ans1.append(a[idx1])
    idx1 = pre1[idx1]
print(*ans1[::-1])  # 注意倒序输出

# 输出最长下降子序列
idx2 = dp2.index(max(dp2))
ans2 = []
while idx2 != -1:
    ans2.append(a[idx2])
    idx2 = pre2[idx2]
print(*ans2[::-1])