Free Timed practice lessonsTimed practice · Stage 1 · Timed set 2 · Step 5
Pairs that fill up a k
Count pairs whose sum is a multiple of k. About 12 minutes.
Shrink the numbers first
When only divisibility matters, a big number can be swapped for its remainder. Songs of 150 seconds and 30 seconds behave the same when you're checking for whole minutes: both leave 30 seconds over.
Once every value is small, the question often turns into one you've already solved. Ask what each item needs from its partner.
Try: ask what each item needs from its partner.
nums = [10, 50, 70, 20, 40], k = 30
10
020
110
220
310
4i
- seen
- {}
- pairs
- 0
Only remainders matter, so shrink every value mod 30: 10, 20, 10, 20, 10.
Move 1 of 6
k = 60. A song lasts 150 seconds (remainder 30). Which partner remainders make a multiple of 60?
- A30
- B0
- C90
Show the answer
30. 30 + 30 = 60.
Pairs that fill up a k
Count the pairs of positions i < j where nums[i] + nums[j] is divisible by k.
nums = [30, 20, 150, 100, 40], k = 60 → 3
0 ≤ n ≤ 1,000,000 · 0 ≤ each value ≤ 10^9 · 1 ≤ k ≤ 100,000 · return a long
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