- Difficulty: Hard
- Tags: LeetCode, Hard, Bit Manipulation, Segment Tree, Queue, Array, Binary Search, Dynamic Programming, leetcode-3117, O(n * m * logr), O(n + logr), Memoization, DP, RMQ, Sparse Table, Mono Deque, Two Pointers
Problem
You are given two arrays nums
and andValues
of length n
and m
respectively.
The value of an array is equal to the last element of that array.
You have to divide nums
into m
disjoint contiguous subarrays such that for the ith
subarray [li, ri]
, the bitwise AND
of the subarray elements is equal to andValues[i]
, in other words, nums[li] & nums[li + 1] & ... & nums[ri] == andValues[i]
for all 1 <= i <= m
, where &
represents the bitwise AND
operator.
Return the minimum possible sum of the values of the m
subarrays nums
is divided into. If it is not possible to divide nums
into m
subarrays satisfying these conditions, return -1
.
Example 1:
Input: nums = [1,4,3,3,2], andValues = [0,3,3,2]
Output: 12
Explanation:
The only possible way to divide nums
is:
[1,4]
as1 & 4 == 0
.[3]
as the bitwiseAND
of a single element subarray is that element itself.[3]
as the bitwiseAND
of a single element subarray is that element itself.[2]
as the bitwiseAND
of a single element subarray is that element itself.
The sum of the values for these subarrays is 4 + 3 + 3 + 2 = 12
.
Example 2:
Input: nums = [2,3,5,7,7,7,5], andValues = [0,7,5]
Output: 17
Explanation:
There are three ways to divide nums
:
[[2,3,5],[7,7,7],[5]]
with the sum of the values5 + 7 + 5 == 17
.[[2,3,5,7],[7,7],[5]]
with the sum of the values7 + 7 + 5 == 19
.[[2,3,5,7,7],[7],[5]]
with the sum of the values7 + 7 + 5 == 19
.
The minimum possible sum of the values is 17
.
Example 3:
Input: nums = [1,2,3,4], andValues = [2]
Output: -1
Explanation:
The bitwise AND
of the entire array nums
is 0
. As there is no possible way to divide nums
into a single subarray to have the bitwise AND
of elements 2
, return -1
.
Constraints:
1 <= n == nums.length <= 104
1 <= m == andValues.length <= min(n, 10)
1 <= nums[i] < 105
0 <= andValues[j] < 105