Count the Hidden Sequences
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 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.
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 = 6Output
2The possible hidden sequences are [3, 4, 1, 5] and [4, 5, 2, 6], so the answer is 2.
Example 2
Input
differences = [3,-4,5,1,-2], lower = -4, upper = 5Output
4There are four possible hidden sequences: [-3, 0, -4, 1, 2, 0], [-2, 1, -3, 2, 3, 1], [-1, 2, -2, 3, 4, 2], and [0, 3, -1, 4, 5, 3].
Constraints
- n == differences.length
- 1 <= n <= 10^5
- -10^5 <= differences[i] <= 10^5
- -10^5 <= lower <= upper <= 10^5
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