<p>You are given an array <code>target</code> that consists of <strong>distinct</strong> integers and another integer array <code>arr</code> that <strong>can</strong> have duplicates.</p>

<p>In one operation, you can insert any integer at any position in <code>arr</code>. For example, if <code>arr = [1,4,1,2]</code>, you can add <code>3</code> in the middle and make it <code>[1,4,<u>3</u>,1,2]</code>. Note that you can insert the integer at the very beginning or end of the array.</p>

<p>Return <em>the <strong>minimum</strong> number of operations needed to make </em><code>target</code><em> a <strong>subsequence</strong> of </em><code>arr</code><em>.</em></p>

<p>A <strong>subsequence</strong> of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the remaining elements&#39; relative order. For example, <code>[2,7,4]</code> is a subsequence of <code>[4,<u>2</u>,3,<u>7</u>,2,1,<u>4</u>]</code> (the underlined elements), while <code>[2,4,2]</code> is not.</p>

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

<pre>
<strong>Input:</strong> target = [5,1,3], <code>arr</code> = [9,4,2,3,4]
<strong>Output:</strong> 2
<strong>Explanation:</strong> You can add 5 and 1 in such a way that makes <code>arr</code> = [<u>5</u>,9,4,<u>1</u>,2,3,4], then target will be a subsequence of <code>arr</code>.
</pre>

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

<pre>
<strong>Input:</strong> target = [6,4,8,1,3,2], <code>arr</code> = [4,7,6,2,3,8,6,1]
<strong>Output:</strong> 3
</pre>

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

<ul>
	<li><code>1 &lt;= target.length, arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= target[i], arr[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>target</code> contains no duplicates.</li>
</ul>

class Solution {
public:
    int minOperations(vector<int>& target, vector<int>& arr) {
        std::ios_base::sync_with_stdio(false);
        cin.tie(0);
        cout.tie(0);
        
        int len_t = target.size();
        int len_a = arr.size();

        map<int, int> targetMap;
        for(int i = 0; i < len_t; i++) targetMap[target[i]] = i;

        vector<int> ind_arr(len_a, 1e9);
        for(int i = 0; i < len_a; i++) {
            if(targetMap.count(arr[i]) != 0) {
                ind_arr[i] = targetMap[arr[i]];
            }
        }

        vector<int> dp_arr(len_a + 1, 1e9);
        dp_arr[0] = -1e9;
        for(int i = 0; i < len_a; i++) {
            int lower_index = lower_bound(dp_arr.begin(), dp_arr.end(), ind_arr[i]) - dp_arr.begin();
            dp_arr[lower_index] = ind_arr[i];
        }

        int minMoves = 0;
        for(int i = 1; i <= len_a; i++) {
            if(dp_arr[i] < 1e9) minMoves = i;
        }

        minMoves = max(0, len_t - minMoves);
        return minMoves;
    }
};
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