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| 1 | +/** |
| 2 | + * Title: Can I Win |
| 3 | + * Description: In the "100 game" two players take turns adding, to a running total, any integer from 1 to 10. The player who first causes the running total to reach or exceed 100 wins. |
| 4 | + * Author: Hasibul Islam |
| 5 | + * Date: 06/05/2023 |
| 6 | + */ |
| 7 | + |
| 8 | +/** |
| 9 | + * @param {number} maxChoosableInteger |
| 10 | + * @param {number} desiredTotal |
| 11 | + * @return {boolean} |
| 12 | + */ |
| 13 | +function canIWin(maxChoosableInteger, desiredTotal) { |
| 14 | + if (desiredTotal === 0) return true; |
| 15 | + if ((maxChoosableInteger * (maxChoosableInteger + 1)) / 2 < desiredTotal) |
| 16 | + return false; |
| 17 | + |
| 18 | + const initialChoices = Math.pow(2, maxChoosableInteger) - 1; |
| 19 | + |
| 20 | + const dp = []; |
| 21 | + |
| 22 | + function DP(choices, total) { |
| 23 | + if (total <= 0) return false; |
| 24 | + |
| 25 | + if (dp[choices] !== undefined) { |
| 26 | + return dp[choices]; |
| 27 | + } |
| 28 | + |
| 29 | + let pow = 0; |
| 30 | + let choicesCopy = choices; |
| 31 | + |
| 32 | + dp[choices] = false; |
| 33 | + |
| 34 | + while (choicesCopy > 0) { |
| 35 | + if (choicesCopy % 2 && !DP(choices - (1 << pow), total - pow - 1)) { |
| 36 | + dp[choices] = true; |
| 37 | + break; |
| 38 | + } |
| 39 | + choicesCopy >>= 1; |
| 40 | + pow++; |
| 41 | + } |
| 42 | + |
| 43 | + return dp[choices]; |
| 44 | + } |
| 45 | + |
| 46 | + return DP(initialChoices, desiredTotal); |
| 47 | +} |
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