Find a Value of a Mysterious Function Closest to Target — LeetCode 1521 Python Solution

The problem

Winston was given the above mysterious function func. He has an integer array arr and an integer target and he wants to find the values l and r that make the value |func(arr, l, r) - target| minimum possible.

Example

Input

arr = [9,12,3,7,15], target = 5

Output

2

Explanation

Calling func with all the pairs of [l,r] = [[0,0],[1,1],[2,2],[3,3],[4,4],[0,1],[1,2],[2,3],[3,4],[0,2],[1,3],[2,4],[0,3],[1,4],[0,4]], Winston got the following results [9,12,3,7,15,8,0,3,7,0,0,3,0,0,0]. The value closest to 5 is 7 and 3, thus the minimum difference is 2.

Python solution

class Solution:
    def closestToTarget(self, arr: List[int], target: int) -> int:
        ans = abs(arr[0] - target)
        s = {arr[0]}
        for x in arr:
            s = {x & y for y in s} | {x}
            ans = min(ans, min(abs(y - target) for y in s))
        return ans

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 1521. Find a Value of a Mysterious Function Closest to Target is filed here because LeetCode tags it Bit Manipulation, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

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