All Tracks Data Structures Advanced Data Structures Problem
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Counting the number of intervals
Problem
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You are given a sequence of \(N\) integers \(a_1, a_2, \dots, a_N\) and an integer \(K\). Your task is to count the number of intervals \([l, r] \) such that \(a_l + a_r + min(a_l, a_{l + 1}, \dots, a_r) \le K\).
Input format
- First line: Two space-separated integers \(N, K\)
- Second line: \(N\) space-separated integers denoting the elements of the sequence
Output format
- Print the answer in a single line.
Constraints
\(1 \le N \le 5\times10^5\), \(80\%\) test cases \(N \le 2\times 10^5\)
\(1 \le K \le 10^{18}\)
\(1 \le a_i \le 10^{18}\)
Explanation
There are five intervals satisfy the condition:
- [1, 1]: \(a_1 + min(a_1) + a_1 = 3\)
- [1, 2]: \(a_1 + min(a_1, a_2) + a_2 = 4\)
- [1, 3]: \(a_1 + min(a_1, a_2, a_3) + a_3 = 5\)
- [1, 4]: \(a_1 + min(a_1, a_2, a_3, a_4) + a_4 = 6\)
- [2, 2]: \(a_2 + min(a_2, a_2) + a_2 = 6\)
Time Limit:
3.0 sec(s)
for each input file.
Memory Limit:
512 MB
Source Limit:
1024 KB
Marking Scheme:
Marks are awarded when all the testcases pass.
Allowed Languages:
Bash,
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PHP,
Python,
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Swift,
Swift-4.1,
TypeScript,
Visual Basic
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Algorithms > Searching
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