onenoughtone
Code Implementation
Best Team With No Conflicts Implementation
Below is the implementation of the best team with no conflicts:
solution.js
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112/** * Find the highest overall score of all possible basketball teams. * Dynamic Programming (Longest Increasing Subsequence Variation) approach. * * @param {number[]} scores - Array of player scores * @param {number[]} ages - Array of player ages * @return {number} - Highest overall score */function bestTeamScore(scores, ages) { const n = scores.length; // Create a list of pairs [age, score] const players = []; for (let i = 0; i < n; i++) { players.push([ages[i], scores[i]]); } // Sort by age (and by score if ages are equal) players.sort((a, b) => { if (a[0] !== b[0]) { return a[0] - b[0]; // Sort by age } return a[1] - b[1]; // Sort by score if ages are equal }); // Initialize DP array const dp = new Array(n); for (let i = 0; i < n; i++) { dp[i] = players[i][1]; // Initialize with the player's score } // Fill DP array for (let i = 0; i < n; i++) { for (let j = 0; j < i; j++) { if (players[j][1] <= players[i][1]) { // If score of player j <= score of player i dp[i] = Math.max(dp[i], dp[j] + players[i][1]); } } } // Return the maximum score return Math.max(...dp);} /** * Find the highest overall score of all possible basketball teams. * Binary Indexed Tree (Fenwick Tree) approach. * * @param {number[]} scores - Array of player scores * @param {number[]} ages - Array of player ages * @return {number} - Highest overall score */function bestTeamScoreBIT(scores, ages) { const n = scores.length; // Create a list of pairs [age, score] const players = []; for (let i = 0; i < n; i++) { players.push([ages[i], scores[i]]); } // Sort by age (and by score if ages are equal) players.sort((a, b) => { if (a[0] !== b[0]) { return a[0] - b[0]; // Sort by age } return a[1] - b[1]; // Sort by score if ages are equal }); // Find the maximum score const maxScore = Math.max(...scores); // Initialize BIT const bit = new Array(maxScore + 1).fill(0); // Helper function to query BIT function query(idx) { let result = 0; while (idx > 0) { result = Math.max(result, bit[idx]); idx -= idx & -idx; // Remove the least significant bit } return result; } // Helper function to update BIT function update(idx, val) { while (idx <= maxScore) { bit[idx] = Math.max(bit[idx], val); idx += idx & -idx; // Add the least significant bit } } // Fill BIT for (let i = 0; i < n; i++) { const score = players[i][1]; const maxPrevScore = query(score); update(score, maxPrevScore + score); } // Return the maximum score return query(maxScore);} // Test casesconsole.log(bestTeamScore([1, 3, 5, 10, 15], [1, 2, 3, 4, 5])); // 34console.log(bestTeamScore([4, 5, 6, 5], [2, 1, 2, 1])); // 16console.log(bestTeamScore([1, 2, 3, 5], [8, 9, 10, 1])); // 6 console.log(bestTeamScoreBIT([1, 3, 5, 10, 15], [1, 2, 3, 4, 5])); // 34console.log(bestTeamScoreBIT([4, 5, 6, 5], [2, 1, 2, 1])); // 16console.log(bestTeamScoreBIT([1, 2, 3, 5], [8, 9, 10, 1])); // 6Step-by-Step Explanation
Let's break down the implementation:
- Create Player Pairs: Create a list of pairs [age, score] for each player to keep track of both attributes together.
- Sort Players: Sort the players by age in ascending order (and by score in ascending order if ages are equal) to ensure we only consider valid teams.
- Initialize DP Array: Initialize a DP array where dp[i] represents the maximum score we can achieve by considering the first i players and including the i-th player.
- Fill DP Array: For each player, consider all previous players with scores less than or equal to the current player's score, and update the DP array accordingly.
- Find Maximum Score: Return the maximum value in the DP array as the highest overall score of all possible basketball teams.
String Problems
Learning Objective
Implement the best team with no conflicts solution in different programming languages.
Best Team With No Conflicts Implementation
Below is the implementation of the best team with no conflicts in different programming languages. Select a language tab to view the corresponding code.
solution.js
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112/** * Find the highest overall score of all possible basketball teams. * Dynamic Programming (Longest Increasing Subsequence Variation) approach. * * @param {number[]} scores - Array of player scores * @param {number[]} ages - Array of player ages * @return {number} - Highest overall score */function bestTeamScore(scores, ages) { const n = scores.length; // Create a list of pairs [age, score] const players = []; for (let i = 0; i < n; i++) { players.push([ages[i], scores[i]]); } // Sort by age (and by score if ages are equal) players.sort((a, b) => { if (a[0] !== b[0]) { return a[0] - b[0]; // Sort by age } return a[1] - b[1]; // Sort by score if ages are equal }); // Initialize DP array const dp = new Array(n); for (let i = 0; i < n; i++) { dp[i] = players[i][1]; // Initialize with the player's score } // Fill DP array for (let i = 0; i < n; i++) { for (let j = 0; j < i; j++) { if (players[j][1] <= players[i][1]) { // If score of player j <= score of player i dp[i] = Math.max(dp[i], dp[j] + players[i][1]); } } } // Return the maximum score return Math.max(...dp);} /** * Find the highest overall score of all possible basketball teams. * Binary Indexed Tree (Fenwick Tree) approach. * * @param {number[]} scores - Array of player scores * @param {number[]} ages - Array of player ages * @return {number} - Highest overall score */function bestTeamScoreBIT(scores, ages) { const n = scores.length; // Create a list of pairs [age, score] const players = []; for (let i = 0; i < n; i++) { players.push([ages[i], scores[i]]); } // Sort by age (and by score if ages are equal) players.sort((a, b) => { if (a[0] !== b[0]) { return a[0] - b[0]; // Sort by age } return a[1] - b[1]; // Sort by score if ages are equal }); // Find the maximum score const maxScore = Math.max(...scores); // Initialize BIT const bit = new Array(maxScore + 1).fill(0); // Helper function to query BIT function query(idx) { let result = 0; while (idx > 0) { result = Math.max(result, bit[idx]); idx -= idx & -idx; // Remove the least significant bit } return result; } // Helper function to update BIT function update(idx, val) { while (idx <= maxScore) { bit[idx] = Math.max(bit[idx], val); idx += idx & -idx; // Add the least significant bit } } // Fill BIT for (let i = 0; i < n; i++) { const score = players[i][1]; const maxPrevScore = query(score); update(score, maxPrevScore + score); } // Return the maximum score return query(maxScore);} // Test casesconsole.log(bestTeamScore([1, 3, 5, 10, 15], [1, 2, 3, 4, 5])); // 34console.log(bestTeamScore([4, 5, 6, 5], [2, 1, 2, 1])); // 16console.log(bestTeamScore([1, 2, 3, 5], [8, 9, 10, 1])); // 6 console.log(bestTeamScoreBIT([1, 3, 5, 10, 15], [1, 2, 3, 4, 5])); // 34console.log(bestTeamScoreBIT([4, 5, 6, 5], [2, 1, 2, 1])); // 16console.log(bestTeamScoreBIT([1, 2, 3, 5], [8, 9, 10, 1])); // 6Step-by-Step Explanation
1Create Player Pairs
Create a list of pairs [age, score] for each player to keep track of both attributes together.
2Sort Players
Sort the players by age in ascending order (and by score in ascending order if ages are equal) to ensure we only consider valid teams.
3Initialize DP Array
Initialize a DP array where dp[i] represents the maximum score we can achieve by considering the first i players and including the i-th player.
4Fill DP Array
For each player, consider all previous players with scores less than or equal to the current player's score, and update the DP array accordingly.
5Find Maximum Score
Return the maximum value in the DP array as the highest overall score of all possible basketball teams.
Language-Specific Notes
javascript
- JavaScript's Array.push() method is used to add elements to an array.
- The sort() method with a custom comparator is used to sort the players by age and score.
- Math.max() is used to find the maximum value in an array or between multiple values.
- The spread operator (...) is used to pass all elements of an array as arguments to Math.max().
- Bitwise operators (&, -) are used in the Binary Indexed Tree implementation for efficient queries and updates.
python
- Python's list comprehension [(ages[i], scores[i]) for i in range(n)] is used to create a list of pairs.
- The sort() method is used to sort the players by age and score (Python's sort automatically sorts tuples by their first element, then second).
- The max() function is used to find the maximum value in a list.
- List initialization [0] * n is used to create and initialize arrays.
- Nested functions (query and update) are defined within the main function in the BIT approach.
java
- Java's Arrays.sort() with a lambda comparator is used to sort the players by age and score.
- Math.max() is used to find the maximum of two values.
- The enhanced for loop (for-each) is used to iterate through arrays.
- Private static helper methods are used for the BIT query and update operations.
- Arrays are initialized with a specific size using new int[n].
cpp
- C++'s std::vector and std::pair are used to store player information.
- std::sort with the default comparator is used to sort pairs (which compares first element, then second).
- std::max_element is used to find the maximum element in a vector.
- Lambda functions [&] are used to define the query and update operations for the BIT.
- Initializer lists {1, 3, 5, 10, 15} are used to create vectors in the test cases.
Key Takeaways
- This problem can be solved using dynamic programming, specifically a variation of the Longest Increasing Subsequence (LIS) algorithm.
- Sorting the players by age (and by score if ages are equal) is crucial to ensure we only consider valid teams.
- The DP approach has a time complexity of O(n²), which can be optimized to O(n log n) using a Binary Indexed Tree.
- The key insight is to recognize that after sorting, we only need to ensure that the scores are non-decreasing as we include players in our team.
- The Binary Indexed Tree approach is more efficient for large inputs, but the DP approach is simpler to understand and implement.
Try It Yourself
Modify the code to implement an alternative approach and test it with the same examples.
Challenge:
Implement a function that solves the best team with no conflicts problem using a different approach than shown above.
Common Edge Cases
All Players Same Age
Handle the case where all players have the same age, in which case we can include all players in our team.
scores = [1, 2, 3, 4, 5], ages = [1, 1, 1, 1, 1]
Decreasing Scores with Increasing Ages
Handle the case where scores decrease as ages increase, in which case we can only include one player in our team.
scores = [5, 4, 3, 2, 1], ages = [1, 2, 3, 4, 5]
Multiple Players with Same Age and Score
Handle the case where multiple players have the same age and score, in which case we can include all of them in our team.
scores = [3, 3, 3, 3, 3], ages = [2, 2, 2, 2, 2]