23:I[344796,["/_next/static/chunks/083cs_iw_ie0y.js","/_next/static/chunks/2sk2f47durg8o.js","/_next/static/chunks/00mfjk9z2ewie.js","/_next/static/chunks/2q9x6spyz4qxv.js","/_next/static/chunks/1wo5i8je1ygp5.js","/_next/static/chunks/1h4l04ysuholp.js","/_next/static/chunks/2qcnia-og0qh0.js","/_next/static/chunks/40webkzfr6rcp.js"],"default"] 28:I[27201,["/_next/static/chunks/083cs_iw_ie0y.js","/_next/static/chunks/2sk2f47durg8o.js","/_next/static/chunks/00mfjk9z2ewie.js","/_next/static/chunks/2q9x6spyz4qxv.js","/_next/static/chunks/1wo5i8je1ygp5.js","/_next/static/chunks/1h4l04ysuholp.js","/_next/static/chunks/2qcnia-og0qh0.js"],"IconMark"] 24:T125e,

Container Limit Changes

A resource manager keeps a log of limit changes for a set of containers. You are given n update records. The i-th record consists of three values:

container[i] — the name of a container.
timestamp[i] — the time at which an update occurred.
limit[i] — the new limit assigned to that container at that time.

Each record means: the limit of container[i] was set to limit[i] at time timestamp[i].

For every container, consider its own updates in increasing order of time. Count the number of containers that satisfy both of the following conditions:

1. The container's limit increased at least once compared to a previous update (some update set a strictly larger limit than an earlier update of the same container). 2. The container's limit decreased at least once compared to a previous update (some update set a strictly smaller limit than an earlier update of the same container).

The increase and the decrease may occur in any order.

Input Format

The first line contains a single integer n — the number of update records.
Each of the next n lines contains a container name and two integers: container[i], timestamp[i] and limit[i], separated by single spaces.

Output Format

Print a single integer — the number of containers that experienced both at least one increase and at least one decrease across their updates.

Constraints

1 ≤ n ≤ 2 * 10^5
container[i] is a non-empty string of at most 20 characters consisting of lowercase English letters and digits. (character set and length bound inferred; the source only states "container[i] is a string")
1 ≤ limit[i] ≤ 10^9
1 ≤ timestamp[i] ≤ 10^9
For a given container, all of its update timestamps are distinct, so the order of its updates in time is unambiguous. (inferred; the source does not describe ties, and this guarantee removes the only ordering ambiguity)

Examples

Example 1

Input:

5
apple 1 5
apple 2 8
apple 3 4
beta 1 3
beta 2 7

Output:

Explanation: Container apple has limits 5, 8, 4 over time — it increased (5 → 8) and later decreased (8 → 4), so it qualifies. Container beta has limits 3, 7 — it only increased and never decreased, so it does not. The answer is 1.

Example 2

Input:

7
db 10 3
db 5 3
db 8 6
cache 1 2
cache 2 2
api 3 9
api 1 4

Output:

Explanation: Ordering each container by time — db has limits 3, 6, 3 (times 5, 8, 10): it increased (3 → 6) and decreased (6 → 3), so it qualifies. cache has limits 2, 2: unchanged, so neither condition holds. api has limits 4, 9 (times 1, 3): only an increase. The answer is 1.

Example 3

Input:

Output:

Explanation: x has limits 1, 5, 2: increased then decreased — qualifies. y has limits 10, 3, 8: decreased then increased — qualifies. z has a single update, so it can neither increase nor decrease. The answer is 2.

Notes

A container qualifies only when it has both a strictly increasing step and a strictly decreasing step somewhere in its time-ordered sequence of limits. Equivalently, its time-ordered limit sequence is neither non-decreasing nor non-increasing.
Comparisons are strict: two consecutive equal limits count as neither an increase nor a decrease.
Several records may refer to the same container; the records for different containers may be interleaved arbitrarily in the input.
A container that appears in only one record can never qualify.
Container names are case-sensitive: two names are the same container only if they are identical strings.

25:T816,import java.io.DataInputStream; import java.io.IOException; public class Main { static long countVolatileContainers(int n, String[] container, long[] timestamp, long[] limit) { // Write your code here return 0; } public static void main(String[] args) throws IOException { FastReader in = new FastReader(); int n = in.nextInt(); String[] container = new String[n]; long[] timestamp = new long[n]; long[] limit = new long[n]; for (int i = 0; i < n; i++) { container[i] = in.nextToken(); timestamp[i] = in.nextLong(); limit[i] = in.nextLong(); } System.out.println(countVolatileContainers(n, container, timestamp, limit)); } static class FastReader { private final DataInputStream din = new DataInputStream(System.in); private final byte[] buffer = new byte[1 << 16]; private int pointer = 0, bytesRead = 0; String nextToken() throws IOException { StringBuilder sb = new StringBuilder(); int b = read(); while (b <= ' ') b = read(); while (b > ' ') { sb.append((char) b); b = read(); } return sb.toString(); } long nextLong() throws IOException { long ret = 0; int b = read(); while (b <= ' ') b = read(); boolean neg = b == '-'; if (neg) b = read(); while (b >= '0' && b <= '9') { ret = ret * 10 + (b - '0'); b = read(); } return neg ? -ret : ret; } int nextInt() throws IOException { return (int) nextLong(); } private int read() throws IOException { if (pointer == bytesRead) { bytesRead = din.read(buffer, 0, buffer.length); pointer = 0; if (bytesRead == -1) return -1; } return buffer[pointer++]; } } } 26:Te77,# Container Limit Changes A resource manager keeps a log of limit changes for a set of containers. You are given `n` update records. The `i`-th record consists of three values: - `container[i]` — the name of a container. - `timestamp[i]` — the time at which an update occurred. - `limit[i]` — the new limit assigned to that container at that time. Each record means: the limit of `container[i]` was set to `limit[i]` at time `timestamp[i]`. For every container, consider its own updates in increasing order of time. Count the number of containers that satisfy **both** of the following conditions: 1. The container's limit **increased** at least once compared to a previous update (some update set a strictly larger limit than an earlier update of the same container). 2. The container's limit **decreased** at least once compared to a previous update (some update set a strictly smaller limit than an earlier update of the same container). The increase and the decrease may occur in any order. ## Input Format - The first line contains a single integer `n` — the number of update records. - Each of the next `n` lines contains a container name and two integers: `container[i]`, `timestamp[i]` and `limit[i]`, separated by single spaces. ## Output Format Print a single integer — the number of containers that experienced both at least one increase and at least one decrease across their updates. ## Constraints - `1 ≤ n ≤ 2 * 10^5` - `container[i]` is a non-empty string of at most `20` characters consisting of lowercase English letters and digits. *(inferred; the source only states "container[i] is a string")* - `1 ≤ limit[i] ≤ 10^9` - `1 ≤ timestamp[i] ≤ 10^9` - For a given container, all of its update timestamps are distinct, so the order of its updates in time is unambiguous. *(inferred; the source does not describe ties, and this guarantee removes the only ordering ambiguity)* ## Examples ### Example 1 Input: ``` 5 apple 1 5 apple 2 8 apple 3 4 beta 1 3 beta 2 7 ``` Output: ``` 1 ``` Explanation: Container `apple` has limits `5, 8, 4` over time — it increased (`5 → 8`) and later decreased (`8 → 4`), so it qualifies. Container `beta` has limits `3, 7` — it only increased and never decreased, so it does not. The answer is `1`. ### Example 2 Input: ``` 7 db 10 3 db 5 3 db 8 6 cache 1 2 cache 2 2 api 3 9 api 1 4 ``` Output: ``` 1 ``` Explanation: Ordering each container by time — `db` has limits `3, 6, 3` (times `5, 8, 10`): it increased (`3 → 6`) and decreased (`6 → 3`), so it qualifies. `cache` has limits `2, 2`: unchanged, so neither condition holds. `api` has limits `4, 9` (times `1, 3`): only an increase. The answer is `1`. ### Example 3 Input: ``` 7 x 1 1 x 2 5 x 3 2 y 1 10 y 2 3 y 3 8 z 1 4 ``` Output: ``` 2 ``` Explanation: `x` has limits `1, 5, 2`: increased then decreased — qualifies. `y` has limits `10, 3, 8`: decreased then increased — qualifies. `z` has a single update, so it can neither increase nor decrease. The answer is `2`. ## Notes - A container qualifies only when it has **both** a strictly increasing step and a strictly decreasing step somewhere in its time-ordered sequence of limits. Equivalently, its time-ordered limit sequence is neither non-decreasing nor non-increasing. - Comparisons are strict: two consecutive equal limits count as neither an increase nor a decrease. - Several records may refer to the same container; the records for different containers may be interleaved arbitrarily in the input. - A container that appears in only one record can never qualify. - Container names are case-sensitive: two names are the same container only if they are identical strings.27:Tbb7,# Container Limit Changes ## Overview We are given `n` update records, each naming a container, a timestamp, and the new limit set at that time. For every container we must decide whether, across its own updates ordered by time, its limit both increased at least once and decreased at least once. The answer is the number of containers for which both happened. ## Key Insight The two conditions ("increased compared to a previous update" and "decreased compared to a previous update") depend only on the relative order of a container's limits in time — not on which specific earlier update we compare against. A container has an increase somewhere iff its time-ordered limit sequence is **not** non-increasing, and it has a decrease somewhere iff that sequence is **not** non-decreasing. So a container qualifies exactly when its time-ordered limit sequence is neither non-decreasing nor non-increasing. It is enough to scan consecutive pairs: comparing each limit to any earlier one gives the same verdict as comparing it to the immediately preceding one, because a sequence with any out-of-order pair must also have an adjacent out-of-order pair. ## Approach Group the records by container name using a hash map from name to a list of `(timestamp, limit)` pairs. For each container, sort its list by timestamp so the updates are in chronological order. Walk the sorted limits, keeping the previous limit: if the current limit is strictly greater than the previous one, mark that an increase occurred; if it is strictly smaller, mark that a decrease occurred. After the walk, if both flags are set, the container counts. Sum these across all containers and print the total. ## Why This Works Sorting by timestamp reconstructs each container's true chronological limit history. Detecting a single strictly increasing adjacent step is equivalent to the existence of some update whose limit exceeds an earlier update's limit, and likewise for a strictly decreasing step — an inversion in a sequence always implies an adjacent inversion. Strict comparisons correctly treat two equal consecutive limits as neither an increase nor a decrease, matching the problem's wording. ## Complexity Let `n` be the total number of records. Grouping is `O(n)`. Sorting each container's list costs `O(k log k)` for a container with `k` records, and the sum of all `k` is `n`, so total sorting is `O(n log n)`. The scan is `O(n)`. Overall time is `O(n log n)` and space is `O(n)`. ## Common Pitfalls - Forgetting to sort each container's updates by timestamp — the records may arrive interleaved and out of time order. - Using non-strict comparisons (`>=` / `<=`), which wrongly treats an unchanged limit as both an increase and a decrease. - Requiring the increase to come before the decrease; the two events may occur in either order. - Counting qualifying records or updates instead of distinct qualifying containers. - Treating all records as one global stream rather than grouping per container.1c:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"LearningResource\",\"learningResourceType\":\"Coding Question\",\"name\":\"Container Limit Changes\",\"description\":\"Container Limit Changes A resource manager keeps a log of limit changes for a set of containers. You are given n update records. The i -th record consists of three values: container[i] — the name of a container. timestamp[i] — the time at which an update occurred. limit[i] — the new limit assigned to that container at that time. Each record means: the limit of container[i] was set to limit[i] at time timestamp[i] . For every container, consider its own updates in increasing order of time. 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