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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.
1function PredictTheWinner(nums) {
2 const length = nums.length;
3 const memo = Array.from({ length }, () => Array(length).fill(null));
4
5 const calculate = (i, j) => {
6 if (i === j) return nums[i];
7 if (memo[i][j] !== null) return memo[i][j];
8 const pickI = nums[i] - calculate(i + 1, j);
9 const pickJ = nums[j] - calculate(i, j - 1);
10 memo[i][j] = Math.max(pickI, pickJ);
11 return memo[i][j];
12 };
13
14 return calculate(0, length - 1) >= 0;
15}The JavaScript solution employs a recursive function calculate that considers choices at both ends of the array for the current player. The result of the best strategic choice by a player is stored in a memo array to prevent recomputation of the same state.
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.
1The Python solution involves initializing a 2D array dp where dp[i][j] stores the maximum score difference a player can achieve for nums[i...j]. We fill this table bottom-up, considering all possibilities by iterating over lengths of subarrays and their starting indices.