Description
We are given an array A of N lowercase letter strings, all of the same length.
Now, we may choose any set of deletion indices, and for each string, we delete all the characters in those indices.
For example, if we have an array A = ["babca","bbazb"] and deletion indices {0, 1, 4}, then the final array after deletions is ["bc","az"].
Suppose we chose a set of deletion indices D such that after deletions, the final array has every element (row) in lexicographic order.
For clarity, A[0] is in lexicographic order (ie. A[0][0] <= A[0][1] <= ... <= A[0][A[0].length - 1]), A[1] is in lexicographic order (ie. A[1][0] <= A[1][1] <= ... <= A[1][A[1].length - 1]), and so on.
Return the minimum possible value of D.length.
给定由 N 个小写字母字符串组成的数组 A，其中每个字符串长度相等。
选取一个删除索引序列，对于 A 中的每个字符串，删除对应每个索引处的字符。
比如，有 A = ["babca","bbazb"]，删除索引序列 {0, 1, 4}，删除后 A 为["bc","az"]。
假设，我们选择了一组删除索引 D，那么在执行删除操作之后，最终得到的数组的行中的每个元素都是按字典序排列的。
清楚起见，A[0] 是按字典序排列的（即，A[0][0] <= A[0][1] <= ... <= A[0][A[0].length - 1]），A[1] 是按字典序排列的（即，A[1][0] <= A[1][1] <= ... <= A[1][A[1].length - 1]），依此类推。
请你返回 D.length 的最小可能值。
题目链接：https://leetcode.com/problems/delete-columns-to-make-sorted-iii/
Difficulty: hard
Example 1:
Input: ["babca","bbazb"]
Output: 3
Explanation: After deleting columns 0, 1, and 4, the final array is A = ["bc", "az"].
Both these rows are individually in lexicographic order (ie. A[0][0] <= A[0][1] and A[1][0] <= A[1][1]).
Note that A[0] > A[1] - the array A isn't necessarily in lexicographic order.
Example 2:
Input: ["edcba"]
Output: 4
Explanation: If we delete less than 4 columns, the only row won't be lexicographically sorted.
Example 3:
Input: ["ghi","def","abc"]
Output: 0
Explanation: All rows are already lexicographically sorted.
Note:
- 1 <= A.length <= 100
- 1 <= A[i].length <= 100
分析
- updating（Solution）
参考代码
class Solution(object):
def minDeletionSize(self, A):
W = len(A[0])
dp = [1] * W
for i in xrange(W-2, -1, -1):
for j in xrange(i+1, W):
if all(row[i] <= row[j] for row in A):
dp[i] = max(dp[i], 1 + dp[j])
return W - max(dp)