256th Commit

Author: Shyam-Chen

README.md

@@ -253,15 +253,17 @@ Ace Coding Interview with 75 Qs
 [198]: ./src/page-2/198.%20House%20Robber/rob.ts
 [790]: ./src/page-8/790.%20Domino%20and%20Tromino%20Tiling/numTilings.ts
 
-| DP - Multidimensional                                     |                  |        |
-| --------------------------------------------------------- | ---------------- | ------ |
-| 62. Unique Paths                                          | [Solution][62]   | Medium |
-| 1143. Longest Common Subsequence                          | [Solution][1143] | Medium |
-| 714. Best Time to Buy and Sell Stock with Transaction Fee | Solution         | Medium |
-| 72. Edit Distance                                         | Solution         | Medium |
+| DP - Multidimensional                                     |                  |        |                         |
+| --------------------------------------------------------- | ---------------- | ------ | ----------------------- |
+| 62. Unique Paths                                          | [Solution][62]   | Medium | 詳解                    |
+| 1143. Longest Common Subsequence                          | [Solution][1143] | Medium | 詳解                    |
+| 714. Best Time to Buy and Sell Stock with Transaction Fee | [Solution][714]  | Medium | [詳解][714-explanation] |
+| 72. Edit Distance                                         | Solution         | Medium | 詳解                    |
 
 [62]: ./src/page-1/62.%20Unique%20Paths/uniquePaths.ts
 [1143]: ./src/page-11/1143.%20Longest%20Common%20Subsequence/longestCommonSubsequence.ts
+[714]: ./src/page-7/714.%20Best%20Time%20to%20Buy%20and%20Sell%20Stock%20with%20Transaction%20Fee/maxProfit.ts
+[714-explanation]: ./src/page-7/714.%20Best%20Time%20to%20Buy%20and%20Sell%20Stock%20with%20Transaction%20Fee/README.md
 
 | Bit Manipulation                              |                  |        |
 | --------------------------------------------- | ---------------- | ------ |

src/page-7/714. Best Time to Buy and Sell Stock with Transaction Fee/README.md

@@ -0,0 +1,125 @@
+# 714. 買賣股票的最佳時機含手續費 (Best Time to Buy and Sell Stock with Transaction Fee)
+
+給定一個整數陣列 `prices`，其中 `prices[i]` 表示第 `i` 天的股票價格；整數 `fee` 代表了交易股票的手續費。
+
+找出你能獲得的最大利潤。你可以完成任意數量的交易，但你需要為每筆交易支付手續費。
+
+注意：
+
+- 你不得同時進行多項交易 (即，您必須在再次購買之前出售股票)。
+- 每次買賣股票只收取一次手續費。
+
+## 解題
+
+使用動態規劃 (Dynamic Programming)
+
+`prices = [1,3,2,8,4,9], fee = 2`
+
+- cash：不持有股票時的最大利潤。
+- hold：持有股票時的最大利潤。
+
+i = 0, price = 1：
+
+- cash = 0
+- hold = -1，買入
+
+i = 1, price = 3：
+
+- cash = max(0, −1 + 3 − 2) = 0
+- hold = max(−1, 0 − 3) = −1
+
+i = 1, price = 2：
+
+- cash = max(0, −1 + 2 − 2) = 0
+- hold = max(−1, 0 − 2) = −1
+
+i = 1, price = 8：
+
+- cash = max(0, −1 + 8 − 2) = 5，賣出
+- hold = max(−1, 0 − 8) = −1
+
+i = 1, price = 4：
+
+- cash = max(5, -1 + 4 - 2) = 5
+- hold = max(−1, 5 − 4) = 1，買入
+
+i = 1, price = 9：
+
+- cash = max(5, 1 + 9 - 2) = 8，賣出
+- hold = max(1, 5 - 9) = 1
+
+```ts
+export const maxProfit: MaxProfit = (prices, fee) => {
+  const n = prices.length;
+  const dp: number[][] = Array(n).fill([0, 0]);
+
+  // 初始值
+  dp[0][0] = 0; // 第一天不持有股票，利潤為 0
+  dp[0][1] = -prices[0]; // 第一天持有股票，利潤為 -prices[0]
+
+  // 狀態轉移
+  for (let i = 1; i < n; i++) {
+    dp[i][0] = Math.max(dp[i - 1][0], dp[i - 1][1] + prices[i] - fee); // 不持有股票
+    dp[i][1] = Math.max(dp[i - 1][1], dp[i - 1][0] - prices[i]); // 持有股票
+  }
+
+  // 最後一天不持有股票的最大利潤
+  return dp[n - 1][0];
+};
+```
+
+```ts
+export const maxProfit: MaxProfit = (prices, fee) => {
+  const n = prices.length;
+  const cash = Array(n).fill(0);
+  const hold = Array(n).fill(0);
+
+  cash[0] = 0;
+  hold[0] = -prices[0];
+
+  for (let i = 1; i < n; i++) {
+    cash[i] = Math.max(cash[i - 1], hold[i - 1] + prices[i] - fee);
+    hold[i] = Math.max(hold[i - 1], cash[i - 1] - prices[i]);
+  }
+
+  return cash[n - 1];
+};
+```
+
+```ts
+export const maxProfit: MaxProfit = (prices, fee) => {
+  let cash = 0;
+  let hold = -prices[0];
+
+  for (let i = 1; i < prices.length; i++) {
+    cash = Math.max(cash, hold + prices[i] - fee);
+    hold = Math.max(hold, cash - prices[i]);
+  }
+
+  return cash;
+};
+```
+
+## 解題 2
+
+使用貪婪 (Greedy)
+
+```ts
+export const maxProfit2: MaxProfit = (prices, fee) => {
+  let profit = 0;
+  let prevPrice = prices[0];
+
+  for (let i = 0; i < prices.length; i++) {
+    if (prices[i] > prevPrice + fee) {
+      profit += prices[i] - prevPrice - fee;
+      prevPrice = prices[i] - fee;
+    }
+
+    if (prices[i] < prevPrice) {
+      prevPrice = prices[i];
+    }
+  }
+
+  return profit;
+};
+```

src/page-7/714. Best Time to Buy and Sell Stock with Transaction Fee/maxProfit.test.ts

@@ -0,0 +1,13 @@
+import { maxProfit, maxProfit2 } from './maxProfit';
+
+describe('714. Best Time to Buy and Sell Stock with Transaction Fee', () => {
+  test('maxProfit', () => {
+    expect(maxProfit([1, 3, 2, 8, 4, 9], 2)).toBe(8);
+    expect(maxProfit([1, 3, 7, 5, 10, 3], 3)).toBe(6);
+  });
+
+  test('maxProfit2', () => {
+    expect(maxProfit2([1, 3, 2, 8, 4, 9], 2)).toBe(8);
+    expect(maxProfit2([1, 3, 7, 5, 10, 3], 3)).toBe(6);
+  });
+});

src/page-7/714. Best Time to Buy and Sell Stock with Transaction Fee/maxProfit.ts

@@ -0,0 +1,37 @@
+type MaxProfit = (prices: number[], fee: number) => number;
+
+/**
+ * Accepted
+ */
+export const maxProfit: MaxProfit = (prices, fee) => {
+  let cash = 0;
+  let hold = -prices[0];
+
+  for (let i = 1; i < prices.length; i++) {
+    cash = Math.max(cash, hold + prices[i] - fee);
+    hold = Math.max(hold, cash - prices[i]);
+  }
+
+  return cash;
+};
+
+/**
+ * Accepted
+ */
+export const maxProfit2: MaxProfit = (prices, fee) => {
+  let profit = 0;
+  let prevPrice = prices[0];
+
+  for (let i = 0; i < prices.length; i++) {
+    if (prices[i] > prevPrice + fee) {
+      profit += prices[i] - prevPrice - fee;
+      prevPrice = prices[i] - fee;
+    }
+
+    if (prices[i] < prevPrice) {
+      prevPrice = prices[i];
+    }
+  }
+
+  return profit;
+};