Minimum Operations to Form Subsequence With Target Sum
<p>You are given a <strong>0-indexed</strong> array <code>nums</code> consisting of <strong>non-negative</strong> powers of <code>2</code>, and an integer <code>target</code>.</p>

<p>In one operation, you must apply the following changes to the array:</p>

<ul>
	<li>Choose any element of the array <code>nums[i]</code> such that <code>nums[i] &gt; 1</code>.</li>
	<li>Remove <code>nums[i]</code> from the array.</li>
	<li>Add <strong>two</strong> occurrences of <code>nums[i] / 2</code> to the <strong>end</strong> of <code>nums</code>.</li>
</ul>

<p>Return the <em><strong>minimum number of operations</strong> you need to perform so that </em><code>nums</code><em> contains a <strong>subsequence</strong> whose elements sum to</em> <code>target</code>. If it is impossible to obtain such a subsequence, return <code>-1</code>.</p>

<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,8], target = 7
<strong>Output:</strong> 1
<strong>Explanation:</strong> In the first operation, we choose element nums[2]. The array becomes equal to nums = [1,2,4,4].
At this stage, nums contains the subsequence [1,2,4] which sums up to 7.
It can be shown that there is no shorter sequence of operations that results in a subsequnce that sums up to 7.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,32,1,2], target = 12
<strong>Output:</strong> 2
<strong>Explanation:</strong> In the first operation, we choose element nums[1]. The array becomes equal to nums = [1,1,2,16,16].
In the second operation, we choose element nums[3]. The array becomes equal to nums = [1,1,2,16,8,8]
At this stage, nums contains the subsequence [1,1,2,8] which sums up to 12.
It can be shown that there is no shorter sequence of operations that results in a subsequence that sums up to 12.</pre>

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

<pre>
<strong>Input:</strong> nums = [1,32,1], target = 35
<strong>Output:</strong> -1
<strong>Explanation:</strong> It can be shown that no sequence of operations results in a subsequence that sums up to 35.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 2<sup>30</sup></code></li>
	<li><code>nums</code> consists only of non-negative powers of two.</li>
	<li><code>1 &lt;= target &lt; 2<sup>31</sup></code></li>
</ul>
Greedy; Bit Manipulation; Array
class Solution {
public:
    int minOperations(vector<int>& nums, int target) {
        long long s = 0;
        int cnt[32]{};
        for (int x : nums) {
            s += x;
            for (int i = 0; i < 32; ++i) {
                if (x >> i & 1) {
                    ++cnt[i];
                }
            }
        }
        if (s < target) {
            return -1;
        }
        int i = 0, j = 0;
        int ans = 0;
        while (1) {
            while (i < 32 && (target >> i & 1) == 0) {
                ++i;
            }
            if (i == 32) {
                return ans;
            }
            while (j < i) {
                cnt[j + 1] += cnt[j] / 2;
                cnt[j] %= 2;
                ++j;
            }
            while (cnt[j] == 0) {
                cnt[j] = 1;
                ++j;
            }
            ans += j - i;
            --cnt[j];
            j = i;
            ++i;
        }
    }
};