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Minimum Days to Score Exactly N Points - Solution & Explanation

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Problem Statement

You are given an integer n representing a target score.

Your score starts at 0, and each day you either earn points or skip.

Points are earned during a streak. On the first day of a streak you earn 1 point, on the second day 2 points, on the third day 3 points, and so on. Skipping a day earns nothing and resets the streak, so the next time you earn points, you start from 1 again.

Return the minimum number of days, including any skipped days, needed to reach a score of exactly n.

 

Example 1:

Input: n = 2

Output: 3

Explanation:​​​​​​​

  • Day 1: earn 1 point. Score is 1.
  • Day 2: skip, which resets the streak. Earning here would add 2 points and take the score past n = 2.
  • Day 3: the streak has reset, so earning gives 1 point. Score is exactly n = 2 in 3 days.

Example 2:

Input: n = 9

Output: 6

Explanation:​​​​​​​

  • Days 1 to 3: earn 1, 2, and 3 points. Score is 1 + 2 + 3 = 6.
  • Day 4: skip, which resets the streak.
  • Days 5 and 6: earn 1 and 2 points. Score is exactly 6 + 1 + 2 = 9 in 6 days.

Example 3:

Input: n = 12

Output: 7

Explanation:​​​​​​​

  • Days 1 to 3: earn 1, 2, and 3 points. Score is 1 + 2 + 3 = 6.
  • Day 4: skip, which resets the streak.
  • Days 5 to 7: earn 1, 2, and 3 points. Score is exactly 6 + 1 + 2 + 3 = 12 in 7 days.

 

Constraints:

  • 1 <= n <= 105

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Video Solution

LeetCode 4050 | Biweekly Contest 191 Q3 | Minimum Days to Score Exactly N Points | Easy DP | C++ • CodeSprint • 352 views views

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