Question

$79$

Max. score: $20\mathrm{.}00$

Partitioning the Servers

A local cloud services provider CLTech offers On Demand Services $($ODS$)$ for customers to host their operations on CLTech$$s servers.

Customers send requests for resources to CLTech as and when they require them. Each request can be represented as a list of $3$ strings, $[$request$\_$id$,$ request$\_$start$\_$time, request$\_$end$\_$time$].$

Example Request

$["300\mathrm{.}11\mathrm{.}4380","03$:$34$:$49","05$:$23$:$11"]$

Description of Fields in a Request:

request$\_$id: A unique ID is given to each request, which is used to trace the origin of the request.

request $\_$start$\_$time: The time when the serving of the request needs to begin, if the request is served $($and not rejected$).$ The request is allocated a partition of the resources beginning at the time. Time is given in hh:mm:ss format.

request$\_$end$\_$time: The time when the serving of the request ends. The request occupies the resource till request$\_$end$\_$time, after which it is freed.$$Time is given in hh:mm:ss format.

Being a private organization, CLTech has limited resources $($memory and computational resources$),$ hence, it has to utilize them intelligently and efficiently.$$

Specifically, assume that a fixed amount of memory and processors are in possession of CLTech.$$

In order to meet the demands of its large customer base, it has to create partitions $($VMs or containers$)$ of the resources. At the beginning of each day, a certain number of partitions K are created, which will be used to serve all requests in the upcoming day. The number of partitions K is chosen to be the maximum number of concurrent requests that were served on the previous day. That is$,$ at max, K requests were served at a single instant on the previous day.

Note

A successful request is allotted the server from the request$\_$start$\_$time to the$$request$\_$end$\_$time inclusively.

Task

Given the successful requests $($that were served$)$ from yesterday, find K$,$ the number of partitions that CLTech must make today.

Example

Assumptions

N$=5$

$[["221\mathrm{.}005\mathrm{.}2333","04$:$02$:$31","06$:$03$:$32"],$

$["33\mathrm{.}145\mathrm{.}322","05$:$48$:$11","06$:$12$:$13"],$

$["106\mathrm{.}234\mathrm{.}42","04$:$15$:$55","07$:$11$:$48"],$

$["255\mathrm{.}67\mathrm{.}888","06$:$45$:$36","11$:$51$:$58"],$

$["655\mathrm{.}34\mathrm{.}899","09$:$12$:$00","12$:$34$:$29"]]$

Approach

The maximum concurrent requests that occur during a particular time duration are $3$ requests,$$ namely $1$st$,2$nd and $3$rd$.$ These occur in the time interval $["05$:$48$:$11",06$:$03$:$32"].$

So$,$ answer is $3.$

Function description

Complete the function$$solve$$provided in the editor. This function takes the following $2$parameters and returns the required answer:

N: An integer representing$$the number of requests

R:$$A list of N lists, where each list represents a successful request of the format$[$request$\_$id$,$ request$\_$start$\_$time, request$\_$end$\_$time$].$

Input format

Note: This is the input format that you must use to provide custom input $($available above the$$Compile and Test$$button$).$

The first line contains a single integer$$N$,$denoting the number of successful requests.

The next N lines contain the N requests. Each line contains $3$ space$-$separated integers request$\_$id$,$request$\_$start$\_$time, request$\_$end$\_$time which represent a request

Output format

Print K$,$ the$$number of partitions that CLTech must make today.

Constraints

$1$

$<=$

$$

$<=$

$2$

$$

$10$

$5$

$$

$$

$$

$($

$$

$[$

$$

$]$

$[$

$0$

$]$

$)$

$<=$

$50$

$,$

$$

$$

in

$[$

$0$

$,$

$$

$$

$1$

$]$

$($Length of request$\_$id is less than $51$ for each request$)$

Code snippets $($also called starter code$/$boilerplate code$)$

This question has code snippets for C$,$ CPP$,$ Java, and Python.

Sample input

$3$

$202$:$03$:$4405$:$06$:$07$

$22103$:$05$:$0006$:$07$:$11$

$222205$:$06$:$0806$:$00$:$00$

Sample output

$2$

Explanation

The maximum number of concurrent successful requests in the given input is $2.$ They occur between time intervals:$-[03$:$05$:$00,05$:$06$:$07],$ and also between time intervals:$-[05$:$06$:$08,06$:$00$:$00].$

So$,$ the answer is $2.$

The following test cases are the actual test cases of this question that may be used to evaluate your submission.

Sample input $1$

$84241$

$412\mathrm{.}455\mathrm{.}2113$:$42$:$3013$:$46$:$14$

$597\mathrm{.}336\mathrm{.}72609$:$39$:$2821$:$22$:$37$

$54\mathrm{.}589\mathrm{.}11006$:$38$:$2007$:$22$:$15$

$318\mathrm{.}188\mathrm{.}44914$:$22$:$4823$:$02$:$44$

$562\mathrm{.}856\mathrm{.}67113$:$19$:$4117$:$18$:$16$

$54\mathrm{.}47\mathrm{.}39810$:$56$:$5016$:$49$:$50$

$619\mathrm{.}262\mathrm{.}66408$:$20$:$2616$:$12$:$21$

$5\mathrm{.}781\mathrm{.}69003$:$54$:$3514$:$13$:$43$

$387\mathrm{.}303\mathrm{.}59723$:$09$:$1523$:$25$:$47$

Sample output $1$

$29757$

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Sample input $2$

$16838$

$219\mathrm{.}196\mathrm{.}91518$:$55$:$4618$:$55$:$49$

$812\mathrm{.}561\mathrm{.}28717$:$38$:$4422$:$36$:$37$

$922\mathrm{.}219\mathrm{.}47502$:$12$:$2809$:$53$:$21$

$429\mathrm{.}722\mathrm{.}18200$:$40$:$5600$:$52$:$07$

$81\mathrm{.}98\mathrm{.}94109$:$43$:$4114$:$38$:$39$

$737\mathrm{.}333\mathrm{.}3713$:$58$:$5819$:$23$:$17$

$282\mathrm{.}564\mathrm{.}28512$:$56$:$3912$:$58$:$19$

$77\mathrm{.}293\mathrm{.}70317$:$36$:$0919$:$33$:$54$

$949\mathrm{.}324\mathrm{.}9521$:$30$:$3521$:$46$:$58$

Sample output $2$

$6024$

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Note:

Your code must be able to print the sample output from the provided sample input. However, your code is run against multiple hidden test cases. Therefore, your code must pass these hidden test cases to solve the problem statement.

Limits

Time Limit: $5\mathrm{.}0$ sec$($s$)$ for each input file

MemoryQuestion

$79$

Max. score: $20\mathrm{.}00$

Partitioning the Servers

A local cloud services provider CLTech offers On Demand Services $($ODS$)$ for customers to ho