You are given a 0-indexed array of n
integers differences
, which describes the differences between each pair of consecutive integers of a hidden sequence of length (n + 1)
. More formally, call the hidden sequence hidden
, then we have that differences[i] = hidden[i + 1] - hidden[i]
.
You are further given two integers lower
and upper
that describe the inclusive range of values [lower, upper]
that the hidden sequence can contain.
- For example, given
differences = [1, -3, 4]
,lower = 1
,upper = 6
, the hidden sequence is a sequence of length4
whose elements are in between1
and6
(inclusive).-
[3, 4, 1, 5]
and[4, 5, 2, 6]
are possible hidden sequences. -
[5, 6, 3, 7]
is not possible since it contains an element greater than6
. -
[1, 2, 3, 4]
is not possible since the differences are not correct.
-
Return the number of possible hidden sequences there are. If there are no possible sequences, return 0
.
Example 1:
Input: differences = [1,-3,4], lower = 1, upper = 6
Output: 2
Explanation: The possible hidden sequences are:
- [3, 4, 1, 5]
- [4, 5, 2, 6] Thus, we return 2.
Example 2:
Input: differences = [3,-4,5,1,-2], lower = -4, upper = 5
Output: 4
Explanation: The possible hidden sequences are:
- [-3, 0, -4, 1, 2, 0]
- [-2, 1, -3, 2, 3, 1]
- [-1, 2, -2, 3, 4, 2]
- [0, 3, -1, 4, 5, 3] Thus, we return 4.
Example 3:
Input: differences = [4,-7,2], lower = 3, upper = 6
Output: 0
Explanation: There are no possible hidden sequences. Thus, we return 0.
Constraints:
-
n == differences.length
-
1 <= n <= 105
-
-105 <= differences[i] <= 105
-
-105 <= lower <= upper <= 105
SOLUTION:
class Solution:
def numberOfArrays(self, differences: List[int], lower: int, upper: int) -> int:
pos = [0]
for d in differences:
pos.append(pos[-1] + d)
least = min(pos)
pos = [p + lower - least for p in pos]
return max(upper - max(pos) + 1, 0)
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