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| 1 | +// Approach 2: Dynamic Programming |
| 2 | +// // Time Complexity: O(amout * n), where n is the number of coins |
| 3 | +// // Space Complexity: O(amount) |
| 4 | + |
| 5 | +function coinChange(coins: number[], amount: number): number { |
| 6 | + |
| 7 | + // input: coins = [2, 3, 5], amount = 7 |
| 8 | + |
| 9 | + // initial state dp |
| 10 | + // 0: 0 |
| 11 | + // 1: amount + 1 = 8 |
| 12 | + // 2: 8 |
| 13 | + // 3: 8 |
| 14 | + // 4: 8 |
| 15 | + // 5: 8 |
| 16 | + // 6: 8 |
| 17 | + // 7: 8 |
| 18 | + |
| 19 | + // using coin 2 |
| 20 | + // 0: 0 |
| 21 | + // 1: 8 |
| 22 | + // 2: 8 -> 8 vs dp[2-2] + 1 = 1 -> 1 |
| 23 | + // 3: 8 -> 8 vs dp[3-2] + 1 = 9 -> 8 |
| 24 | + // 4: 8 -> 8 vs dp[4-2] + 1 = 2 -> 2 |
| 25 | + // 5: 8 -> 8 vs dp[5-2] + 1 = 9 -> 8 |
| 26 | + // 6: 8 -> 8 vs dp[6-2] + 1 = 3 -> 3 |
| 27 | + // 7: 8 -> 8 vs dp[7-2] + 1 = 9 -> 8 |
| 28 | + |
| 29 | + const dp = Array.from({ length: amount + 1 }, () => amount + 1); |
| 30 | + dp[0] = 0 |
| 31 | + |
| 32 | + for (const coin of coins) { |
| 33 | + for (let currentTotal = coin; currentTotal <= amount; currentTotal++) { |
| 34 | + dp[currentTotal] = Math.min(dp[currentTotal - coin] + 1, dp[currentTotal]) |
| 35 | + } |
| 36 | + } |
| 37 | + |
| 38 | + return dp[amount] > amount ? -1 : dp[amount] |
| 39 | +}; |
| 40 | + |
| 41 | + |
| 42 | +// // Approach 1: BFS Traversal |
| 43 | +// // Time Complexity: O(amout * n), where n is the number of coins |
| 44 | +// // Space Complexity: O(amount) |
| 45 | + |
| 46 | +// function coinChange(coins: number[], amount: number): number { |
| 47 | +// // queue: [[number of coints, current total]] |
| 48 | +// let queue = [[0, 0]]; |
| 49 | +// let visited = new Set(); |
| 50 | + |
| 51 | +// while (queue.length > 0) { |
| 52 | +// const [cnt, total] = queue.shift()!; |
| 53 | + |
| 54 | +// if (total === amount) { |
| 55 | +// return cnt; |
| 56 | +// } |
| 57 | + |
| 58 | +// if (visited.has(total)) { |
| 59 | +// continue; |
| 60 | +// } |
| 61 | +// visited.add(total); |
| 62 | + |
| 63 | +// for (const coin of coins) { |
| 64 | +// if (total + coin <= amount) { |
| 65 | +// queue.push([cnt + 1, total + coin]); |
| 66 | +// } |
| 67 | +// } |
| 68 | +// } |
| 69 | + |
| 70 | +// return -1; |
| 71 | +// } |
| 72 | + |
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