2145. 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 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 length 4 whose elements are in between 1 and 6 (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 than 6.
• [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.

class Solution {
public:
    int numberOfArrays(vector<int>& d, int lower, int upper) {
        long minD(min(0, d[0])), maxD(max(0, d[0])), cur(d[0]);
        for(int i = 1; i < d.size(); i++) {
            cur += d[i];
            minD = min(minD, cur);
            maxD = max(maxD, cur);
        }
        return max(upper - lower - maxD + minD + 1, 0L);
    }
};