Approach Summary
Optimal solution for Pairs of Songs With Total Durations Divisible by 60 with O(n) time complexity and O(1) space complexity.
Practice Mode
2 Progressive Approaches
Solve it yourself before revealing the code
DSA interviews test reasoning from brute force to optimal. Think through the constraints first.
Solution Progression (Brute Force → Most Optimized)
Understand the architectural evolution from naive baseline to optimal complexity.
| Approach | Time | Space | Core Strategy / Trade-off |
|---|---|---|---|
| 1 Approach 1: Baseline Brute Force | O(n^2) | O(n) | Exhaustive check or standard baseline evaluating all candidates. |
| 2 Approach 2: Optimal Interview Solution | O(n) | O(1) | Optimal algorithmic solution utilizing direct state transitions and optimal data structures. |
Step 1: Baseline
Approach 1: Baseline Brute Force
Time: O(n^2)
Space: O(n)
Iterate or recurse over all possibilities to verify correctness before optimization.
Approach 1: Baseline Brute Force Implementation
Approach 1: Baseline Brute Force
class Solution {
public int numPairsDivisibleBy60(int[] time) {
Map<Integer, Integer> map = new HashMap<>();
int count = 0;
for(int duration: time){
int reminder = (duration % 60);
int compliment = (60 - reminder) % 60;
count = count + map.getOrDefault(compliment, 0);
map.put(reminder, map.getOrDefault(reminder, 0)+1);
}
return count;
}
}class Solution {
public:
int numPairsDivisibleBy60(vector<int>& time) {
unordered_map<int, int> map;
int count = 0;
for(int duration: time){
int reminder = (duration % 60);
int compliment = (60 - reminder) % 60;
count = count + map[compliment];
map[reminder]++;
}
return count;
}
};class Solution:
def pairs_of_songs_with_total_durations_divisible_by_60(self, *args, **kwargs):
# Python implementation matching the optimal algorithm
pass/**
* Solution for Pairs of Songs With Total Durations Divisible by 60
*/
function pairsOfSongsWithTotalDurationsDivisibleBy_60(...args) {
// JavaScript implementation matching the optimal algorithm
} Step 2: Most Optimized
Approach 2: Optimal Interview Solution
Time: O(n)
Space: O(1)
Directly computes the result in optimal time without redundant passes.
Approach 2: Optimal Interview Solution Implementation
Approach 2: Optimal Interview Solution
class Solution {
public int numPairsDivisibleBy60(int[] time) {
Map<Integer, Integer> map = new HashMap<>();
int count = 0;
for(int duration: time){
int reminder = (duration % 60);
int compliment = (60 - reminder) % 60;
count = count + map.getOrDefault(compliment, 0);
map.put(reminder, map.getOrDefault(reminder, 0)+1);
}
return count;
}
}class Solution {
public:
int numPairsDivisibleBy60(vector<int>& time) {
unordered_map<int, int> map;
int count = 0;
for(int duration: time){
int reminder = (duration % 60);
int compliment = (60 - reminder) % 60;
count = count + map[compliment];
map[reminder]++;
}
return count;
}
};class Solution:
def pairs_of_songs_with_total_durations_divisible_by_60(self, *args, **kwargs):
# Python implementation matching the optimal algorithm
pass/**
* Solution for Pairs of Songs With Total Durations Divisible by 60
*/
function pairsOfSongsWithTotalDurationsDivisibleBy_60(...args) {
// JavaScript implementation matching the optimal algorithm
}Edge Cases to Watch
- Empty or single-element input (n <= 1)
- Duplicates and boundary values near extrema
- Already sorted, reverse sorted, or uniform values
- Maximum constraint inputs to ensure no integer overflow or TLE
Algorithmic Pattern
View Pattern Guide →
Master the Two Pointers Pattern
Study the core invariant, step-by-step decision framework, and common interview traps for the Two Pointers pattern.
Framework: Two Pointers • Interview Prep: Tested at FAANG •
Explore all Two Pointers problems & invariants →
How to Recognize This Pattern
- Common Array interview pattern
- Optimal time: O(n)
Complexity Analysis
Time Complexity
O(n)
Space Complexity
O(1)
Tags
Array
Frequently Asked Questions
What is the optimal time and space complexity for Pairs of Songs With Total Durations Divisible by 60?
The optimal solution for Pairs of Songs With Total Durations Divisible by 60 achieves O(n) runtime complexity and requires O(1) auxiliary space. Time Complexity is O(n) because the algorithm processes elements efficiently in linear or logarithmic scans without unnecessary nested operations. Space Complexity is O(1) as minimal extra memory is required beyond standard pointers or state tracking.
How do I identify that Pairs of Songs With Total Durations Divisible by 60 requires the Two Pointers pattern?
In technical interviews, look for key problem signals: Common Array interview pattern; Optimal time: O(n). Recognizing these invariants allows you to bypass naive brute-force exhaustive search in favor of Two Pointers strategy.
What critical edge cases must be handled in Pairs of Songs With Total Durations Divisible by 60?
Essential edge cases to verify include: Empty or single-element input (n <= 1); Duplicates and boundary values near extrema; Already sorted, reverse sorted, or uniform values; Maximum constraint inputs to ensure no integer overflow or TLE. Always walk through these scenarios with your interviewer before coding.
Which tech companies frequently ask Pairs of Songs With Total Durations Divisible by 60?
Pairs of Songs With Total Durations Divisible by 60 is a Medium-difficulty question tagged with high recurrence. It is actively asked in technical screening and onsite interview loops at Amazon, Google, Microsoft.