| | | 1 | | // -------------------------------------------------------------------------------- |
| | | 2 | | // Copyright (C) 2025 Eugene Eremeev (also known as Yevhenii Yeriemeieiv). |
| | | 3 | | // All Rights Reserved. |
| | | 4 | | // -------------------------------------------------------------------------------- |
| | | 5 | | // This software is the confidential and proprietary information of Eugene Eremeev |
| | | 6 | | // (also known as Yevhenii Yeriemeieiv) ("Confidential Information"). You shall not |
| | | 7 | | // disclose such Confidential Information and shall use it only in accordance with |
| | | 8 | | // the terms of the license agreement you entered into with Eugene Eremeev (also |
| | | 9 | | // known as Yevhenii Yeriemeieiv). |
| | | 10 | | // -------------------------------------------------------------------------------- |
| | | 11 | | |
| | | 12 | | namespace LeetCode.Algorithms.CanIWin; |
| | | 13 | | |
| | | 14 | | /// <inheritdoc /> |
| | | 15 | | public class CanIWinDynamicProgramming : ICanIWin |
| | | 16 | | { |
| | | 17 | | /// <summary> |
| | | 18 | | /// Time complexity - O(n * 2^n) |
| | | 19 | | /// Space complexity - O(2^n) |
| | | 20 | | /// </summary> |
| | | 21 | | /// <param name="maxChoosableInteger"></param> |
| | | 22 | | /// <param name="desiredTotal"></param> |
| | | 23 | | /// <returns></returns> |
| | | 24 | | public bool CanIWin(int maxChoosableInteger, int desiredTotal) |
| | 13 | 25 | | { |
| | 13 | 26 | | if (desiredTotal == 0) |
| | 2 | 27 | | { |
| | 2 | 28 | | return true; |
| | | 29 | | } |
| | | 30 | | |
| | 11 | 31 | | if (desiredTotal > maxChoosableInteger * (maxChoosableInteger + 1) / 2) |
| | 2 | 32 | | { |
| | 2 | 33 | | return false; |
| | | 34 | | } |
| | | 35 | | |
| | 9 | 36 | | return CanWinPlayer(maxChoosableInteger, 1, 0, desiredTotal, new int[1 << maxChoosableInteger]) == 1; |
| | 13 | 37 | | } |
| | | 38 | | |
| | | 39 | | private static int CanWinPlayer(int n, int player, int selectedMask, int rest, int[] dp) |
| | 120128 | 40 | | { |
| | 120128 | 41 | | if (dp[selectedMask] != 0) |
| | 90804 | 42 | | { |
| | 90804 | 43 | | return dp[selectedMask]; |
| | | 44 | | } |
| | | 45 | | |
| | 1034691 | 46 | | for (int i = 1, mask = 1; i <= n; i++, mask <<= 1) |
| | 333942 | 47 | | { |
| | 333942 | 48 | | if ((selectedMask & mask) > 0) |
| | 213165 | 49 | | { |
| | 213165 | 50 | | continue; |
| | | 51 | | } |
| | | 52 | | |
| | 120777 | 53 | | if (rest - i <= 0) |
| | 658 | 54 | | { |
| | 658 | 55 | | return dp[selectedMask] = player; |
| | | 56 | | } |
| | | 57 | | |
| | 120119 | 58 | | if (-player != CanWinPlayer(n, -player, selectedMask | mask, rest - i, dp)) |
| | 17711 | 59 | | { |
| | 17711 | 60 | | return dp[selectedMask] = player; |
| | | 61 | | } |
| | 102408 | 62 | | } |
| | | 63 | | |
| | 10955 | 64 | | return dp[selectedMask] = -player; |
| | 120128 | 65 | | } |
| | | 66 | | } |