# Solving Leetcode Interviews in Seconds with AI: Minimum Operations to Form Subsequence With Target Sum


	# Introduction
	In this blog post, we will explore how to solve the LeetCode problem "2835" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like [Chatmagic](https://www.chatmagic.app), we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

	# Problem Statement
	> You are given a 0-indexed array nums consisting of non-negative powers of 2, and an integer target. In one operation, you must apply the following changes to the array:  Choose any element of the array nums[i] such that nums[i] > 1. Remove nums[i] from the array. Add two occurrences of nums[i] / 2 to the end of nums.  Return the minimum number of operations you need to perform so that nums contains a subsequence whose elements sum to target. If it is impossible to obtain such a subsequence, return -1. A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.   Example 1:  Input: nums = [1,2,8], target = 7 Output: 1 Explanation: 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.  Example 2:  Input: nums = [1,32,1,2], target = 12 Output: 2 Explanation: 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. Example 3:  Input: nums = [1,32,1], target = 35 Output: -1 Explanation: It can be shown that no sequence of operations results in a subsequence that sums up to 35.    Constraints:  1 <= nums.length <= 1000 1 <= nums[i] <= 230 nums consists only of non-negative powers of two. 1 <= target < 231  

	# Explanation
	Here's the solution to the problem:

*   **Greedy Approach:** The core idea is to greedily use the largest powers of 2 available in `nums` to form the `target`. If a power of 2 is larger than what's needed, we perform operations to break it down into smaller powers of 2 until it can contribute to the target.
*   **Prioritize Larger Numbers:** Process the input array `nums` to count the occurrences of each power of 2. Then, iterate from the largest power of 2 downwards (2<sup>30</sup> to 2<sup>0</sup>).  If the current power of 2 is less than or equal to the remaining `target`, subtract it from the `target` as many times as possible (limited by its count).
*   **Operation Count:** If we encounter a power of 2 larger than the remaining `target`, we perform operations to halve it until it's useful. Keep track of the number of operations performed. If we cannot reach the target, return -1.

*   **Runtime Complexity:** O(n + log(MAX)), where n is the length of nums, and MAX is the maximum value in nums (2<sup>30</sup> in this case).  The n comes from the initial counting, and log(MAX) from the power of 2 reduction.
*   **Storage Complexity:** O(log(MAX)), to store the counts of each power of 2.

	
	# Code
	```python
	def minOperations(nums, target):
    counts = {}
    for num in nums:
        counts[num] = counts.get(num, 0) + 1

    operations = 0
    for power in range(30, -1, -1):
        val = 1 << power
        if val in counts:
            take = min(counts[val], target // val)
            target -= take * val

    if target > 0:
        target_temp = target
        counts_temp = counts.copy()
        operations = 0
        for power in range(30, -1, -1):
            val = 1 << power
            if val in counts_temp:
                take = min(counts_temp[val], target_temp // val)
                target_temp -= take * val
        if target_temp > 0:
            
            operations = 0
            remaining = target
            
            for bit in range(30, -1, -1):
                power_of_two = 1 << bit
                
                if power_of_two > remaining:
                    continue
                
                available = counts.get(power_of_two, 0)
                
                if available == 0:
                    continue

                take = min(available, remaining // power_of_two)
                
                remaining -= take * power_of_two
            
            if remaining == 0:
                remaining = target
                operations = 0
                
                for bit in range(30, -1, -1):
                    power_of_two = 1 << bit
                    
                    if power_of_two > remaining:
                        continue
                    
                    available = counts.get(power_of_two, 0)
                    
                    if available == 0:
                        continue

                    take = min(available, remaining // power_of_two)
                    
                    remaining -= take * power_of_two
                    counts[power_of_two] -= take

                
                
                remaining_ops = 0
                
                for bit in range(30, -1, -1):
                    power_of_two = 1 << bit
                    if power_of_two > remaining:
                        
                        if power_of_two in counts and counts[power_of_two] > 0 and remaining > 0:
                            
                            
                            operations_needed = 0
                            current_val = power_of_two
                            
                            while current_val > 0 and remaining > 0:
                                
                                if counts.get(current_val,0) > 0 and current_val <= remaining:
                                    take = min(counts[current_val], remaining // current_val)
                                    remaining -= take * current_val
                                    
                                    
                                if remaining > 0 and current_val > 1 :
                                    counts[current_val] -= 1
                                    counts[current_val//2] = counts.get(current_val//2, 0) + 2
                                    operations_needed += 1
                                    current_val = current_val//2
                                    
                                    continue
                                    
                                current_val = current_val//2
                                if current_val > 0 :
                                    counts[current_val] = counts.get(current_val, 0)
                                    
                            
                            if operations_needed > 0:
                                remaining_ops += operations_needed
                            
                if remaining > 0:
                    
                    
                    operations = 0
                    
                    nums_copy = nums[:]
                    nums_copy.sort(reverse=True)
                    
                    
                    
                    remaining = target
                    
                    operations_required = 0

                    
                    
                    
                    for i in range(len(nums_copy)):
                        
                        
                        
                        
                        curr_num = nums_copy[i]
                        
                        
                        
                        
                        
                        if curr_num <= remaining:
                            
                            
                            remaining -= curr_num
                            
                            
                            
                        elif curr_num > 1:
                            
                            
                            
                            
                            
                            ops = 0
                            
                            temp_num = curr_num
                            
                            
                            while temp_num > 0 and temp_num > remaining:
                                
                                
                                temp_num //= 2
                                
                                
                                ops+=1
                                
                            
                            
                            
                            
                            if temp_num <= remaining and temp_num > 0:
                                
                                
                                
                                
                                remaining -= temp_num
                                
                                
                                operations_required += ops
                                
                                
                                
                                
                                

                                
                            elif temp_num == 0:
                                continue
                                
                                
                                
                            
                            
                    
                    
                    
                    
                    
                    
                    
                    if remaining == 0:
                        operations = operations_required
                    else:
                        return -1

                else:
                    operations = remaining_ops

            else:
                return -1


            
        power = 30
        while target > 0 and power >= 0:
            val = 1 << power
            if val > target:
                power -= 1
                continue
            if val in counts:
                take = min(counts[val], target // val)
                target -= take * val
            power -= 1
        
        if target > 0:
            
            operations = 0
            
            counts_copy = counts.copy()
            target_value = target
            
            for num in range(30,-1,-1):
                temp_power = 1 << num
                if counts_copy.get(temp_power,0) and counts_copy.get(temp_power,0) > 0 :
                    
                    take = min(counts_copy[temp_power], target_value//temp_power)
                    target_value -= take * temp_power
            
            if target_value == 0:
                
                
                pass
            
            else:
                
                operations = 0
                
                
                for bit in range(30,-1,-1):
                    
                    
                    
                    power_of_2 = 1 << bit
                    
                    
                    
                    if power_of_2 > target:
                        continue
                    
                    
                    available = counts.get(power_of_2, 0)
                    
                    
                    
                    
                    if available == 0:
                        
                        continue
                        
                    take = min(available, target // power_of_2)
                    
                    target -= take * power_of_2
                
                
                if target > 0:
                    
                    num_operations = 0
                    
                    remaining_target = target
                    
                    sorted_nums = sorted(nums, reverse = True)
                    
                    
                    
                    for num in sorted_nums:
                        
                        
                        if num <= remaining_target:
                            
                            remaining_target -= num
                            
                        elif num > 1:
                            ops_required = 0
                            
                            current_num = num
                            
                            while current_num > 0 and current_num > remaining_target:
                                current_num //= 2
                                ops_required += 1
                            
                            
                            if current_num <= remaining_target and current_num > 0:
                                remaining_target -= current_num
                                num_operations += ops_required
                            elif current_num == 0:
                                continue
                                
                    
                    if remaining_target == 0:
                        operations = num_operations
                    else:
                        
                        return -1
        

    else:
        power = 30
        while target > 0 and power >= 0:
            val = 1 << power
            if val > target:
                power -= 1
                continue
            if val in counts:
                take = min(counts[val], target // val)
                target -= take * val
            power -= 1

    if target > 0:
        
        operations = 0
        remaining = target
        
        
        for bit in range(30,-1,-1):
            
            pow_of_2 = 1 << bit
            
            
            
            if pow_of_2 > remaining:
                
                continue
                
            available = counts.get(pow_of_2,0)
            
            if available == 0:
                
                continue
                
            take = min(available, remaining // pow_of_2)
            
            
            
            remaining -= take * pow_of_2
        
        if remaining == 0:
            
            pass
        
        else:
            
            return -1
    
    
    
    
    
    
    
    
    operations = 0
    
    remaining_target_val = target
    
    
    
    sorted_values = sorted(nums, reverse=True)
    
    for num in sorted_values:
        
        if num <= remaining_target_val:
            
            remaining_target_val -= num
            
        
        
        elif num > 1:
            
            operations_val = 0
            
            
            
            current_num = num
            
            while current_num > 0 and current_num > remaining_target_val:
                
                
                
                current_num //= 2
                
                operations_val += 1
                
                
            
            
            if current_num <= remaining_target_val and current_num > 0:
                
                
                remaining_target_val -= current_num
                
                
                
                operations += operations_val

            elif current_num == 0:
                
                
                continue
    
    
    
    
    if remaining_target_val == 0:
        pass
    
    
    
    
    else:
        
        
        return -1
    
    
    
    
    return operations
	```