1521. Find a Value of a Mysterious Function Closest to Target

Description

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

 

Solutions

Solution: Bit Manipulation

• Time complexity: O(nlog*Max(arr))
• Space complexity: O(log*Max(arr))

 

JavaScript

/**
 * @param {number[]} arr
 * @param {number} target
 * @return {number}
 */
const closestToTarget = function (arr, target) {
  let prevValueSet = new Set();
  let result = Number.MAX_SAFE_INTEGER;

  for (const num of arr) {
    const valueSet = new Set();

    valueSet.add(num);

    for (const value of prevValueSet) {
      valueSet.add(num & value);
    }

    for (const value of valueSet) {
      const difference = Math.abs(target - value);

      result = Math.min(difference, result);
    }

    prevValueSet = valueSet;
  }

  return result;
};