<p>You are given an array of <code>n</code> strings <code>strs</code>, all of the same length.</p>

<p>We may choose any deletion indices, and we delete all the characters in those indices for each string.</p>

<p>For example, if we have <code>strs = [&quot;abcdef&quot;,&quot;uvwxyz&quot;]</code> and deletion indices <code>{0, 2, 3}</code>, then the final array after deletions is <code>[&quot;bef&quot;, &quot;vyz&quot;]</code>.</p>

<p>Suppose we chose a set of deletion indices <code>answer</code> such that after deletions, the final array has <strong>every string (row) in lexicographic</strong> order. (i.e., <code>(strs[0][0] &lt;= strs[0][1] &lt;= ... &lt;= strs[0][strs[0].length - 1])</code>, and <code>(strs[1][0] &lt;= strs[1][1] &lt;= ... &lt;= strs[1][strs[1].length - 1])</code>, and so on). Return <em>the minimum possible value of</em> <code>answer.length</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> strs = [&quot;babca&quot;,&quot;bbazb&quot;]
<strong>Output:</strong> 3
<strong>Explanation:</strong> After deleting columns 0, 1, and 4, the final array is strs = [&quot;bc&quot;, &quot;az&quot;].
Both these rows are individually in lexicographic order (ie. strs[0][0] &lt;= strs[0][1] and strs[1][0] &lt;= strs[1][1]).
Note that strs[0] &gt; strs[1] - the array strs is not necessarily in lexicographic order.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> strs = [&quot;edcba&quot;]
<strong>Output:</strong> 4
<strong>Explanation:</strong> If we delete less than 4 columns, the only row will not be lexicographically sorted.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> strs = [&quot;ghi&quot;,&quot;def&quot;,&quot;abc&quot;]
<strong>Output:</strong> 0
<strong>Explanation:</strong> All rows are already lexicographically sorted.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == strs.length</code></li>
	<li><code>1 &lt;= n &lt;= 100</code></li>
	<li><code>1 &lt;= strs[i].length &lt;= 100</code></li>
	<li><code>strs[i]</code> consists of lowercase English letters.</li>
</ul>

<ul>
	<li>&nbsp;</li>
</ul>

class Solution {
    bool isPossible(vector<string>& strs, int idx, int prev) {
        int n = strs.size();
    
        for (int i = 0; i < n; i++) {
            if (strs[i][idx] < strs[i][prev])
               return false;
           
        }
      
        return true;
    }
    int helper(vector<string>& strs, int idx, int prev,vector<vector<int>> &dp) {
        int n = strs[0].size();
        if(idx==n)
        return 0;
        int cnt = 200;
        if(prev!=-1 && dp[idx][prev]!=-1)
        return dp[idx][prev];

        if ((prev==-1)||(isPossible(strs, idx,prev))) {
            cnt = helper(strs,idx+1,idx,dp);
        }
        cnt = min(cnt, 1+helper(strs, idx + 1, prev,dp));
        if(prev!=-1)
        dp[idx][prev]=cnt;
        return cnt;
    }

public:
    int minDeletionSize(vector<string>& strs) {
        int n = strs.size();
        vector<vector<int>> dp(105,vector<int>(105,-1));
        return helper(strs, 0, -1,dp);
    }
};
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