944. Delete Columns to Make Sorted

1. Description

You are given an array of n strings strs, all of the same length.
The strings can be arranged such that there is one on each line, making a grid.

• For example, strs = [“abc”, “bce”, “cae”] can be arranged as follows:

abc
bce
cae

You want to delete the columns that are not sorted lexicographically. In the above example (0-indexed), columns 0 (‘a’, ‘b’, ‘c’) and 2 (‘c’, ‘e’, ‘e’) are sorted, while column 1 (‘b’, ‘c’, ‘a’) is not, so you would delete column 1.
Return the number of columns that you will delete.

2. Example

Example 1:
Input: strs = [“cba”,“daf”,“ghi”]
Output: 1
Explanation: The grid looks as follows:
cba
daf
ghi
Columns 0 and 2 are sorted, but column 1 is not, so you only need to delete 1 column.

Example 2:
Input: strs = [“a”,“b”]
Output: 0
Explanation: The grid looks as follows:
a
b
Column 0 is the only column and is sorted, so you will not delete any columns.

Example 3:
Input: strs = [“zyx”,“wvu”,“tsr”]
Output: 3
Explanation: The grid looks as follows:
zyx
wvu
tsr
All 3 columns are not sorted, so you will delete all 3.

3. Constraints

• n == strs.length
• 1 <= n <= 100
• 1 <= strs[i].length <= 1000
• strs[i] consists of lowercase English letters.

4. Solutions

Loop

n = strs.size() * strs[0].size()
Time complexity: O(n)
Space complexity: O(1)

class Solution {
public:
    int minDeletionSize(const vector<string> &strs) {
        const int columns = strs[0].size();
        int result = 0;
        for (int i = 0; i < columns; ++i) {
            bool is_sorted = true;
            for (int j = 1; j < strs.size(); ++j) {
                if (strs[j][i] < strs[j - 1][i]) {
                    is_sorted = false;
                    break;
                }
            }

            result += !is_sorted;
        }

        return result;
    }
};