Number of Students Doing Homework at a Given Time - Problem

Array Easy

Given two integer arrays startTime and endTime and given an integer queryTime.

The ith student started doing their homework at the time startTime[i] and finished it at time endTime[i].

Return the number of students doing their homework at time queryTime. More formally, return the number of students where queryTime lies in the interval [startTime[i], endTime[i]] inclusive.

Input & Output

Example 1 — Basic Case

$ Input: startTime = [1,2,3], endTime = [3,4,7], queryTime = 4

› Output: 2

💡 Note: At time 4, students 1 and 2 are doing homework. Student 1: 2 ≤ 4 ≤ 4 (true), Student 2: 3 ≤ 4 ≤ 7 (true). Student 0 finished at time 3, so 1 ≤ 4 ≤ 3 is false.

Example 2 — Multiple Students

$ Input: startTime = [4], endTime = [4], queryTime = 4

› Output: 1

💡 Note: Student starts and ends at time 4, so at queryTime 4, they are still doing homework (inclusive interval).

Example 3 — No Active Students

$ Input: startTime = [4], endTime = [4], queryTime = 5

› Output: 0

💡 Note: Student finished at time 4, so at time 5 no one is doing homework.

Constraints

startTime.length == endTime.length
1 ≤ startTime.length ≤ 100
1 ≤ startTime[i] ≤ endTime[i] ≤ 1000
1 ≤ queryTime ≤ 1000

Visualization

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Asked in

A Amazon 15 G Google 12 🍎 Apple 8 M Microsoft 6

The key insight is that we need to check if queryTime falls within each student's [startTime[i], endTime[i]] interval. The optimal approach is a simple linear scan through all students, counting those whose intervals contain queryTime. Time: O(n), Space: O(1)

Common Approaches

✓ Linear Scan

⏱️ Time: O(n) Space: O(1)

Iterate through all students and count how many have queryTime within their [startTime[i], endTime[i]] interval. Since we need to check every student anyway, this is actually the optimal approach.

Single Pass with Early Insights

⏱️ Time: O(n) Space: O(1)

This is essentially the same approach as the brute force since we must examine every student. The only micro-optimization is to structure the conditional check efficiently, but the time complexity remains O(n).

Linear Scan — Algorithm Steps

Iterate through each student index i
Check if startTime[i] ≤ queryTime ≤ endTime[i]
If true, increment counter
Return final count

Visualization

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Step-by-Step Walkthrough

Input Arrays

startTime and endTime arrays with queryTime

Check Intervals

For each student, check if queryTime is in [start, end]

Count Active

Count students whose intervals contain queryTime

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int solution(int* startTime, int* endTime, int n, int queryTime) {
    int count = 0;
    for (int i = 0; i < n; i++) {
        if (startTime[i] <= queryTime && queryTime <= endTime[i]) {
            count++;
        }
    }
    return count;
}

int main() {
    char line[1000];
    
    // Read startTime array
    fgets(line, sizeof(line), stdin);
    int startTime[100];
    int n = 0;
    char* token = strtok(line, "[,]");
    while (token != NULL && n < 100) {
        if (strlen(token) > 0 && token[0] != '\n' && token[0] != ']') {
            startTime[n++] = atoi(token);
        }
        token = strtok(NULL, "[,]");
    }
    
    // Read endTime array
    fgets(line, sizeof(line), stdin);
    int endTime[100];
    int m = 0;
    token = strtok(line, "[,]");
    while (token != NULL && m < 100) {
        if (strlen(token) > 0 && token[0] != '\n' && token[0] != ']') {
            endTime[m++] = atoi(token);
        }
        token = strtok(NULL, "[,]");
    }
    
    int queryTime;
    scanf("%d", &queryTime);
    
    printf("%d\n", solution(startTime, endTime, n, queryTime));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single loop through n students to check each interval

✓ Linear Growth

Space Complexity

O(1)

Only using a counter variable, no extra data structures

✓ Linear Space

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Number of Students Doing Homework at a Given Time - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Linear Scan — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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