What is the optimal approach and complexity for Best Team With No Conflicts?

Sort by age, then score; best[i] = score[i] + the best earlier player whose score is not higher with optimal time complexity O(N²) and space complexity O(N).

How do you identify the pattern for Best Team With No Conflicts?

Look for key signals in the prompt: "no conflicts" indicates A rule between two players: the younger one must not score strictly more than the older one.; "highest overall score" indicates A maximum of a sum, not a count. Each chosen player adds their score to the total.; "same age never conflicts" indicates Equal ages can be in any order. So the sort breaks ties by score, and the check is `≤`, not `<`..

Best Team With No Conflicts

Q: What is the brute force approach and complexity for Best Team With No Conflicts?

Try every team: each player is in or out, and a player joins only when they do not conflict with the team with time complexity O(N · 2^N) and space complexity O(N).

Medium·LeetCode #1626 Pro OnlySlight Variation

LeetCode

Problem Statement

You manage a basketball team. Every player has a score and an age. The team's total is the sum of its players' scores.

The team must have no conflicts. A conflict happens when a younger player has a strictly higher score than an older player. Two players of the same age never conflict.

Choose the players so that the total score is as high as possible, and return that total.

Input

Two lists of the same length: scores and ages. scores[i] and ages[i] describe player i.

Output

The highest total score of a team with no conflicts.

Example 1

Input: scores = [1, 3, 5, 10, 15], ages = [1, 2, 3, 4, 5]

Output: 34

Scores go up with age, so nobody conflicts. Take everyone: 1 + 3 + 5 + 10 + 15 = 34.

Example 2

Input: scores = [4, 5, 6, 5], ages = [2, 1, 2, 1]

Output: 16

Take the last three players: scores 5, 6 and 5. The two age-1 players do not conflict with each other, and the age-2 player with score 6 is not beaten by any younger player. Total 16.

Example 3

Input: scores = [1, 2, 3, 5], ages = [8, 9, 10, 1]

Output: 6

Take the first three players: 1 + 2 + 3 = 6. Adding the youngest player (score 5) would conflict, because 5 is higher than the score of every older player.

Constraints

• 1 ≤ scores.length ≤ 1000
• scores.length == ages.length
• 1 ≤ scores[i] ≤ 10^6
• 1 ≤ ages[i] ≤ 1000

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“no conflicts”

→ A rule between two players: the younger one must not score strictly more than the older one.

“highest overall score”

→ A maximum of a sum, not a count. Each chosen player adds their score to the total.

“same age never conflicts”

→ Equal ages can be in any order. So the sort breaks ties by score, and the check is `≤`, not `<`.

Approach Complexity Ladder

Brute Force — add or leave out each playerO(N · 2^N)O(N)

Try every team: each player is in or out, and a player joins only when they do not conflict with the team

Optimal — sort by (age, score), then the run of scoresO(N²)O(N)

Sort by age, then score; best[i] = score[i] + the best earlier player whose score is not higher

Brute Force Intuition

Go through the players in input order. For each one, leave them out, or add them when they do not conflict with anyone already in the team. At the end, add up the scores. Keep the best total over all choices.

Recognition rule for this sub-pattern:

Sort by one dimension (ties broken carefully), then run LIS on the other.

Remember this · DP — Longest Increasing Subsequence

Trigger

Longest chain where each item must be bigger/fit inside the previous one (numbers, pairs, envelopes, words).

Think

Does each element extend the best chain ending at some smaller earlier element?

Key question

Sort first? Then what does "increasing" mean for these items?

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