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1521. Find a Value of a Mysterious Function Closest to Target (Hard)

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.

Return the minimum possible value of |func(arr, l, r) - target|.

Notice that func should be called with the values l and r where 0 <= l, r < arr.length.

 

Example 1:

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.

Example 2:

Input: arr = [1000000,1000000,1000000], target = 1
Output: 999999
Explanation: Winston called the func with all possible values of [l,r] and he always got 1000000, thus the min difference is 999999.

Example 3:

Input: arr = [1,2,4,8,16], target = 0
Output: 0

 

Constraints:

• 1 <= arr.length <= 105
• 1 <= arr[i] <= 106
• 0 <= target <= 107

Related Topics

[Array] [Binary Search] [Bit Manipulation] [Segment Tree]

Hints

Hint 1

If the and value of sub-array arr[i...j] is ≥ the and value of the sub-array arr[i...j+1].

Hint 2

For each index i using binary search or ternary search find the index j where |target - AND(arr[i...j])| is minimum, minimize this value with the global answer.