2026-03-29 23:42

Author: SilverRainZ

src/p/leetcode/best-time-to-buy-and-sell-stock-ii/go.mod

@@ -0,0 +1,3 @@
+module best-time-to-buy-and-sell-stock-ii
+
+go 1.26.1

src/p/leetcode/best-time-to-buy-and-sell-stock-ii/main.go

@@ -0,0 +1,23 @@
+package main
+
+import "fmt"
+
+func maxProfit(prices []int) int {
+	if len(prices) <= 1 {
+		return 0
+	}
+	profit := 0
+	low := prices[0]
+
+	for i := 0; i < len(prices); i++ {
+		if prices[i] > low {
+			profit += prices[i] - low
+		}
+		low = prices[i]
+	}
+	return profit
+}
+
+func main() {
+	fmt.Println(maxProfit([]int{7,1,5,3,6,4}))
+}

src/p/leetcode/best-time-to-buy-and-sell-stock/go.mod

@@ -0,0 +1,3 @@
+module best-time-to-buy-and-sell-stock
+
+go 1.26.1

src/p/leetcode/best-time-to-buy-and-sell-stock/main.go

@@ -0,0 +1,27 @@
+package main
+
+import "fmt"
+
+func maxProfit(prices []int) int {
+	if len(prices) <= 1 {
+		return 0
+	}
+	maxProfit := 0
+	lowPrice := prices[0]
+	for i := 1; i < len(prices); i++ {
+		if prices[i] - lowPrice > maxProfit {
+			maxProfit = prices[i] - lowPrice
+		}
+		if lowPrice > prices[i] {
+			lowPrice = prices[i]
+		}
+	}
+	return maxProfit
+}
+
+func main() {
+	fmt.Println(maxProfit([]int{0}))
+	fmt.Println(maxProfit([]int{1}))
+	fmt.Println(maxProfit([]int{7,1,5,3,6,4}))
+	fmt.Println(maxProfit([]int{7,6,4,3,1}
+}

src/p/leetcode/best-time-to-buy-and-sell-stock/src/lib.rs

@@ -14,12 +14,11 @@ impl Solution {
         return max
     }
 
-    // DP1
     pub fn max_profit2(prices: Vec<i32>) -> i32 {
         let mut max = 0;
         let mut profit = vec![0; prices.len()];
         for i in 1..prices.len() {
-            for j in (0..i).rev() {
+            for j in (0..i).rev() { // 很关键，保证新的低价格被考虑到
                 if prices[i] >= prices[j] {
                     profit[i] = profit[j] + (prices[i] - prices[j]);
                     if profit[i] > max {
@@ -59,5 +58,7 @@ mod tests {
 
         assert_eq!(Solution::max_profit2(vec![1, 2, 3]), 2);
         assert_eq!(Solution::max_profit2(vec! [7,1,5,3,6,4]), 5);
+        assert_eq!(Solution::max_profit2(vec! [9, 100, 1, 101]), 100);
+        assert_eq!(Solution::max_profit3(vec! [9, 100, 1, 101]), 100);
     }
 }

src/p/leetcode/index.rst

@@ -247,26 +247,32 @@ Best Time to Buy and Sell Stock
    :id: best-time-to-buy-and-sell-stock
    :diffculty: Easy
    :language: rust
-   :key: 动态规划
-   :date: 2021-07-07
+   :key: 数组
+   :date: 2021-07-07 2026-03-29
    :reference: https://leetcode-cn.com/problems/best-time-to-buy-and-sell-stock/solution/bao-li-mei-ju-dong-tai-gui-hua-chai-fen-si-xiang-b/
 
 写了三个版本：
 
 暴力
    TLE，每次 `i+1..prices.len()` 的回溯有大量荣誉计算，复杂度为 :math:`O(n!)`
 
-DP1
-   其实不太算 DP，参考里给出了非常 DP 的解法。 
-   `profit[i]` 第 i 天卖出股票的最大正收益（亏本不卖）。以为状态转移方程是 `profit[i] = profit[j] + (prices[i] - prices[j])`, where `j < i && prices[j] <= prices[i]` 。复杂度依然为 :math:`O(n!)` ，只是有几率避免冗余计算，勉强 AC 但时间上只超过了 8% 的选手，有问题。
+暴力 + 稍微剪枝
+   内层循环的 `(0..i).rev()` 很重要，确保新出现的低价被计算到。
+   复杂度依然为 :math:`O(n!)` ，只是有几率避免冗余计算，勉强 AC 但时间上只超过了 8% 的选手，有问题。
 
    .. note:: 实际上 `profit[i]` 可以只从 `profit[i-1]` 推断，见下
 
-DP2
+DP
    更好的状态转移方程是 `profit[i] = max(profit[i-1] + (prices[i] - prices[i-1]), 0)` 。复杂度为 :math:`O(n)` ，超过了 85%+ 的选手，够了。
 
    从题意上看，方程的意思是：在第 i-1 天我们已经取得了能取得的最大收益，那第 i 天也应该参考第 i-1 天的购入时机，如果亏本了，则不购入。
 
+   2026-03-29: 看起来不太对。
+
+记录低价
+   只买卖一次，所以记录下 maxProfit 和 lowPrice，每次只看
+   max(maxProfit, price[i] - lowPrice) 即可，遇到 `price[i] < lowPrice` 要及时更新。
+
 Invert Binary Tree
 ------------------
 
@@ -286,12 +292,12 @@ Best Time to Buy and Sell Stock II
 
 .. leetcode:: _
    :id: best-time-to-buy-and-sell-stock-ii
-   :diffculty: Easy
+   :diffculty: Medium
    :language: rust
-   :key: 动态规划
-   :date: 2021-07-07
+   :key: 贪心
+   :date: 2021-07-07 2026-03-29
 
-:leetcode:`Best Time to Buy and Sell Stock` 的一个简单变体，允许多次买卖，没啥好说。
+:leetcode:`Best Time to Buy and Sell Stock` 的一个简单变体，允许多次买卖，贪心即可，每次有价差则卖出。
 
 Best Time to Buy and Sell Stock III
 -----------------------------------
@@ -965,3 +971,29 @@ i 位置的元素往右挪动 k 个位置，被修改的下标序列会组成一
 `[i, (i+k)%n (i+2k)%n, ... i]`。存在 `(i+x*k)%n == i`，即 `(x*k)%n == 0`。
 
 .. todo:: 环的数目为 `gcd(n, k)`
+
+Jump Game
+---------
+
+.. leetcode:: _
+   :id: jump-game
+   :diffculty: Easy
+   :language: go
+   :key: 贪心
+   :date: 2026-03-29
+
+Jump Game II
+------------
+
+.. leetcode:: _
+   :id: jump-game-ii
+   :diffculty: Medium
+   :language: go
+   :key: 贪心
+   :date: 2026-03-29
+
+`解法 1 <https://medium.com/@william31525/leetcode-45-jump-game-2-294a21f5baba>`_
+   非常好懂，`for i in (0..n)` 找出能越过终点（`i+nums[i]>=n-1`）的地方，那里就是最小步数再 + 1 就能达到终点的地方。时间复杂度稍高
+
+解法 2
+   其实和 1 一样，但利用 `farest` 和 `end` 两个变量配合消除了内部循环，保证 `O(n)`

src/p/leetcode/jump-game-ii/go.mod

@@ -0,0 +1,3 @@
+module jump-game-ii
+
+go 1.26.1

src/p/leetcode/jump-game-ii/main.go

@@ -0,0 +1,77 @@
+package main
+
+import (
+	"fmt"
+)
+
+// https://medium.com/@william31525/leetcode-45-jump-game-2-294a21f5baba
+func jump(nums []int) int {
+	if len(nums) <= 2 {
+		return len(nums) - 1
+	}
+
+	var footprints []int
+	for {
+		lastStep := -1
+		for i := 0; i < len(nums); i++ {
+			if i + nums[i] >= len(nums) - 1 {
+				lastStep = i
+				footprints = append(footprints, lastStep)
+				break
+			}
+		}
+		if lastStep == 0 {
+			break
+		}
+		nums = nums[:lastStep+1]
+	}
+	return len(footprints)
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
+
+func jump2(nums []int) int {
+	if len(nums) <= 2 {
+		return len(nums) - 1
+	}
+
+	farest := 0
+	end := 0
+	step := 0
+
+	for i := 0; i < len(nums); i++ {
+		farest = max(farest, i+nums[i])
+		if i == end {
+			end = farest
+			step++
+		}
+		if end >= len(nums) - 1 {
+			break
+		}
+	}
+	return step
+}
+
+
+func main() {
+	fmt.Println(jump([]int{2,3,1,1,4}))
+	fmt.Println(jump([]int{1,1,1,1,1}))
+	fmt.Println(jump([]int{3,1,0}))
+	fmt.Println(jump([]int{2,3,1}))
+	fmt.Println(jump([]int{2,3,1,4}))
+	fmt.Println(jump([]int{2,3,1,1,4}))
+
+	fmt.Println("===")
+
+	fmt.Println(jump2([]int{2,3,1,1,4}))
+	fmt.Println(jump2([]int{1,1,1,1,1}))
+	fmt.Println(jump2([]int{3,1,0}))
+	fmt.Println(jump2([]int{2,3,1}))
+	fmt.Println(jump2([]int{2,3,1,4}))
+	fmt.Println(jump2([]int{2,3,1,1,4}))
+}

src/p/leetcode/jump-game/go.mod

@@ -0,0 +1,3 @@
+module jump-game
+
+go 1.26.1

src/p/leetcode/jump-game/main.go

@@ -0,0 +1,23 @@
+package main
+
+import "fmt"
+
+func canJump(nums []int) bool {
+	if len(nums) <= 1 {
+		return true
+	}
+	max := 0;
+	for i := 0; i < len(nums); i++ {
+		if max < i {
+			break
+		}
+		if max < i+nums[i] {
+			max = i+nums[i] 
+		}
+	}
+	return max >= len(nums) - 1
+}
+
+func main() {
+	fmt.Println(canJump([]int{3,2,1,0,4}))
+}