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This approach involves using recursion to explore all possible decisions by each player. With each choice, the players reduce the size of the array by selecting an element from either the start or end. Memoization is used to store intermediate results to minimize computational overhead by avoiding repeated calculations.
Time Complexity: O(n²) - Each state (i, j) is computed once.
Space Complexity: O(n²) - Intermediate results are stored in the memoization table.
1public class Solution {
2 public bool PredictTheWinner(int[] nums) {
3 int n = nums.Length;
4 int[,] memo = new int[n, n];
5 for (int i = 0; i < n; i++)
6 for (int j = 0; j < n; j++)
7 memo[i, j] = int.MinValue;
8 return Calculate(nums, 0, n - 1, memo) >= 0;
9 }
10
11 private int Calculate(int[] nums, int start, int end, int[,] memo) {
12 if (start == end) return nums[start];
13 if (memo[start, end] != int.MinValue) return memo[start, end];
14
15 int pickStart = nums[start] - Calculate(nums, start + 1, end, memo);
16 int pickEnd = nums[end] - Calculate(nums, start, end - 1, memo);
17 memo[start, end] = Math.Max(pickStart, pickEnd);
18
19 return memo[start, end];
20 }
21}The C# solution utilizes recursion along with memoization. The recursive function Calculate determines the optimal score a player can achieve given the current array slice, storing intermediate results in the memo table to improve efficiency.
This approach utilizes dynamic programming to solve the problem iteratively. Instead of recursion, it fills up a DP table where each entry represents the best possible score difference a player can achieve for a subarray defined by its boundaries.
Time Complexity: O(n²) - The table is filled once for every distinct range.
Space Complexity: O(n²) - The DP table consumes space proportional to n².
1
This Java solution constructs a 2D DP table where dp[i][j] represents the maximum advantageous score a player can ensure from the subarray nums[i...j]. Filling starts from single elements and progresses to larger subarrays, comparing feasible moves.