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| 1 | +/** |
| 2 | + * Title: Guess Number Higher or Lower II |
| 3 | + * Description: Given a particular n, return the minimum amount of money you need to guarantee a win regardless of what number I pick. |
| 4 | + * Author: Hasibul Islam |
| 5 | + * Date: 06/05/2023 |
| 6 | + */ |
| 7 | + |
| 8 | +/** |
| 9 | + * @param {number} n |
| 10 | + * @return {number} |
| 11 | + */ |
| 12 | +var getMoneyAmount = function (n) { |
| 13 | + // Memo |
| 14 | + this.memo = new Map(); |
| 15 | + |
| 16 | + return dp(n, 0, n); |
| 17 | +}; |
| 18 | + |
| 19 | +var dp = function (n, start, end) { |
| 20 | + let key = `${start}_${end}`; |
| 21 | + |
| 22 | + // Base, there is only 1 node on this side of the leg, which mean our guess is always correct and it cost nothing so return 0 |
| 23 | + if (end - start < 2) { |
| 24 | + return 0; |
| 25 | + } |
| 26 | + |
| 27 | + // Base, there are only 2 nodes on this side of the leg, which mean we only need to pick cheapest guess |
| 28 | + if (end - start === 2) { |
| 29 | + // The `start` will always be smaller so pick `start`, add 1 to account for 0 index |
| 30 | + return start + 1; |
| 31 | + } |
| 32 | + |
| 33 | + // Return from memo |
| 34 | + if (this.memo.has(key) === true) { |
| 35 | + return this.memo.get(key); |
| 36 | + } |
| 37 | + |
| 38 | + // Minimum cost |
| 39 | + let minCost = Infinity; |
| 40 | + |
| 41 | + // Try to arrange the tree's left and right leg and find the cost of each leg |
| 42 | + for (let i = start; i < end; i++) { |
| 43 | + let left = dp(n, start, i); |
| 44 | + let right = dp(n, i + 1, end); |
| 45 | + |
| 46 | + // Cost of current guess, add 1 to account for 0 index |
| 47 | + let curr = i + 1; |
| 48 | + |
| 49 | + // Update cost of current guess, which is the max of left or right leg |
| 50 | + curr = Math.max(left + curr, right + curr); |
| 51 | + |
| 52 | + // Then update the minimum cost for entire tree |
| 53 | + minCost = Math.min(minCost, curr); |
| 54 | + } |
| 55 | + |
| 56 | + // Set memo |
| 57 | + this.memo.set(key, minCost); |
| 58 | + |
| 59 | + return minCost; |
| 60 | +}; |
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