g2101_2200.s2145_count_the_hidden_sequences.Solution Maven / Gradle / Ivy
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Java-based LeetCode algorithm problem solutions, regularly updated
package g2101_2200.s2145_count_the_hidden_sequences;
// #Medium #Array #Prefix_Sum #2022_06_07_Time_7_ms_(36.03%)_Space_111.3_MB_(13.23%)
/**
* 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
**/
public class Solution {
public int numberOfArrays(int[] diff, int lower, int upper) {
int n = diff.length;
if (lower == upper) {
for (int j : diff) {
if (j != 0) {
return 0;
}
}
}
int max = -(int) 1e9;
int min = (int) 1e9;
int[] hidden = new int[n + 1];
hidden[0] = 0;
for (int i = 1; i <= n; i++) {
hidden[i] = hidden[i - 1] + diff[i - 1];
}
for (int i = 0; i <= n; i++) {
if (hidden[i] > max) {
max = hidden[i];
}
if (hidden[i] < min) {
min = hidden[i];
}
}
int low = lower - min;
int high = upper - max;
if (low > high) {
return 0;
}
return (high - low) + 1;
}
}