g2101_2200.s2145_count_the_hidden_sequences

Class Solution

java.lang.Object

g2101_2200.s2145_count_the_hidden_sequences.Solution

public class Solution
extends Object

2145 - Count the Hidden Sequences.

Medium

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.

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

Constructor Summary

Constructors

Constructor and Description
Solution()

Method Summary

Modifier and Type	Method and Description
int	numberOfArrays(int[] diff, int lower, int upper)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Solution

public Solution()

Method Detail

numberOfArrays

public int numberOfArrays(int[] diff,
                          int lower,
                          int upper)