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 <= 10^5
1 <= arr[i] <= 10^6
0 <= target <= 10^7
// Similar to LC:898
// O(N*32)
class Solution {
public int closestToTarget(int[] arr, int target) {
int ans = Integer.MAX_VALUE;
Set<Integer> set = new HashSet<>();
for (int i = 0; i < arr.length; i++) {
Set<Integer> newSet = new HashSet<>();
newSet.add(arr[i]);
for (int x : set)
newSet.add(x & arr[i]);
for (int x : newSet)
ans = Math.min(ans, Math.abs(target - x));
set = newSet;
}
return ans;
}
}
// O(N*logN*logN)
// Fixing 'leftpointer' & searching for right pointer
// also using the fact that and & operation
// always results in <= value
class Solution {
static class SegmentTree {
int[] tree, arr;
int n;
SegmentTree(int[] arr) {
n = arr.length;
this.arr = arr;
tree = new int[4 * n];
buildTree(0, n - 1, 1);
}
private void buildTree(int start, int end, int index) {
if (start == end) {
tree[index] = arr[start];
return;
}
int mid = start + (end - start) / 2;
buildTree(start, mid, 2 * index);
buildTree(mid + 1, end, 2 * index + 1);
tree[index] = tree[2 * index] & tree[2 * index + 1];
}
public int query(int l, int r) {
return queryHelper(0, n - 1, 1, l, r);
}
private int queryHelper(int start, int end, int index, int L, int R) {
if (start > R || end < L)
return Integer.MAX_VALUE;
else if (start >= L && end <= R)
return tree[index];
int mid = start + (end - start) / 2;
return queryHelper(start, mid, 2 * index, L, R) & queryHelper(mid + 1, end, 2 * index + 1, L, R);
}
}
public int closestToTarget(int[] arr, int target) {
SegmentTree tree = new SegmentTree(arr);
int distance = Integer.MAX_VALUE;
for (int i = 0; i < arr.length; i++) {
int start = i, end = arr.length - 1;
while (start <= end) {
int mid = start + (end - start) / 2;
int AND = tree.query(i, mid);
if (AND == target)
return 0;
else if (AND > target)
start = mid + 1;
else
end = mid - 1;
distance = Math.min(distance, Math.abs(target - AND));
}
}
return distance;
}
}
