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This approach uses Dynamic Programming to determine if Alice can win given n stones. We can maintain a boolean array dp where dp[i] represents whether Alice can win with i stones. A state is winning if there's any move that leaves the opponent in a losing state.
Time Complexity: O(n*sqrt(n)), Space Complexity: O(n)
1using System;
2
3public class Solution {
4 public bool WinnerSquareGame(int n) {
5 bool[] dp = new bool[n + 1];
6 for (int i = 1; i <= n; i++) {
7 for (int k = 1; k * k <= i; k++) {
8 if (!dp[i - k * k]) {
9 dp[i] = true;
10 break;
11 }
12 }
13 }
14 return dp[n];
15 }
16}This approach is similar across various languages where we use a boolean array to track winning positions. A position is winning if removing a square leads to a losing opponent state.
This approach involves a recursive solution with memoization to cache previously computed results. If n is already solved, we return the cached result. Otherwise, we recursively check if any move leaves the opponent in a losing position.
Time Complexity: O(n*sqrt(n)), Space Complexity: O(n)
1var This JavaScript recursive solution uses a helper function for checking state results. The memo stores previous outcomes to avoid duplicate work, iterating over possible square removals to identify winning moves.