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//! Best Time to Buy and Sell Stock [leetcode: best_time_to_buy_and_sell_stock](https://leetcode.com/problems/best-time-to-buy-and-sell-stock/) //! //! Say you have an array for which the ith element is the price of a given stock on day *i*. //! //! If you were only permitted to complete at most one transaction (i.e., buy one and sell one share of the stock), design an algorithm to find the maximum profit. //! //! Note that you cannot sell a stock before you buy one. //! //! ***Example1:*** //! //! ``` //! Input: [7,1,5,3,6,4] //! Output: 5 //! Explanation: Buy on day 2 (price = 1) and sell on day 5 (price = 6), profit = 6-1 = 5. //! Not 7-1 = 6, as selling price needs to be larger than buying price. //! ``` //! //! ***Example2:*** //! //! ``` //! Input: [7,6,4,3,1] //! Output: 0 //! Explanation: In this case, no transaction is done, i.e. max profit = 0. //! ``` //! /// # Solutions /// /// # Approach 1: Dynamic Programming /// /// * Time complexity: O(3n) /// /// * Space complexity: O(n) /// /// * Runtime: 0 ms /// * Memory: 3.6 MB /// /// ```rust /// use std::cmp; /// /// impl Solution { /// pub fn max_profit(prices: Vec<i32>) -> i32 { /// if prices.len() < 2 { return 0; } /// /// let mut result = 0; /// let mut profits = vec![vec![0; 3]; prices.len()]; /// profits[0][1] = -prices[0]; /// /// for i in 1..prices.len() { /// profits[i][0] = profits[i - 1][0]; /// profits[i][1] = cmp::max(profits[i - 1][1], profits[i - 1][0] - prices[i]); /// profits[i][2] = profits[i - 1][1] + prices[i]; /// /// result = cmp::max(result, cmp::max(profits[i][0], cmp::max(profits[i][1], profits[i][2]))); /// } /// result /// } /// } /// ``` /// /// # Approach 2: Dynamic Programming /// /// * Time complexity: O(n) /// /// * Space complexity: O(n) /// /// * Runtime: 0 ms /// * Memory: 2.7 MB /// /// ```rust /// impl Solution { /// pub fn max_profit(prices: Vec<i32>) -> i32 { /// if prices.len() < 2 { return 0; } /// /// let mut profits = vec![0; prices.len()]; /// profits[0] = -prices[0]; /// for i in 1..prices.len() { /// if profits[i - 1] < 0 { profits[ i - 1] = 0; } /// /// profits[i] = profits[i - 1] - prices[i - 1] + prices[i]; /// } /// /// profits.sort(); /// *profits.last().unwrap() /// } /// } /// ``` /// /// # Approach 3: Dynamic Programming /// /// * Time complexity: O(n) /// /// * Space complexity: O(n) /// /// * Runtime: 0 ms /// * Memory: 2.6 MB /// /// ```rust /// use std::cmp; /// /// impl Solution { /// pub fn max_profit(prices: Vec<i32>) -> i32 { /// if prices.len() < 2 { return 0; } /// /// let mut profits = vec![0; prices.len()]; /// let mut max_profit = 0; /// let mut tmp_min = prices[0]; /// for i in 1..prices.len() { /// profits[i] = cmp::max(profits[i - 1], prices[i] - tmp_min); /// tmp_min = cmp::min(tmp_min, prices[i]); /// max_profit = cmp::max(profits[i], max_profit); /// } /// /// max_profit /// } /// } /// ``` /// /// # Approach 4: Dynamic Programming /// /// * Time complexity: O(n) /// /// * Space complexity: O(n) /// /// * Runtime: 0 ms /// * Memory: 2.6 MB /// /// ```rust /// use std::cmp; /// /// impl Solution { /// pub fn max_profit(prices: Vec<i32>) -> i32 { /// if prices.len() < 2 { return 0; } /// /// let mut profits = vec![0; 2]; /// let mut max_profit = 0; /// let mut tmp_min = prices[0]; /// for i in 1..prices.len() { /// let (x, y) = (i % 2, (i - 1) % 2); /// profits[x] = cmp::max(profits[y], prices[i] - tmp_min); /// tmp_min = cmp::min(tmp_min, prices[i]); /// max_profit = cmp::max(profits[x], max_profit); /// } /// /// max_profit /// } /// } /// ``` /// pub fn max_profit(prices: Vec<i32>) -> i32 { if prices.len() < 2 { return 0; } let mut profits = vec![0; prices.len()]; profits[0] = -prices[0]; for i in 1..prices.len() { if profits[i - 1] < 0 { profits[ i - 1] = 0; } profits[i] = profits[i - 1] - prices[i - 1] + prices[i]; } profits.sort(); *profits.last().unwrap() }