122. Best Time to Buy and Sell Stock II.md

122. Best Time to Buy and Sell Stock II

---

leetcode-cn Daily Challenge on November 8th, 2020.

---

Difficulty : East

Related Topics : Array、Greedy

---

Say you have an array prices for which the i^th element is the price of a given stock on day i.

Design an algorithm to find the maximum profit. You may complete as many transactions as you like (i.e., buy one and sell one share of the stock multiple times).

Note

• You may not engage in multiple transactions at the same time (i.e., you must sell the stock before you buy again).

Example 1:

Input: [7,1,5,3,6,4]
Output: 7
Explanation: Buy on day 2 (price = 1) and sell on day 3 (price = 5), profit = 5-1 = 4.
             Then buy on day 4 (price = 3) and sell on day 5 (price = 6), profit = 6-3 = 3.

Example 2:

Input: [1,2,3,4,5]
Output: 4
Explanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.
             Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are
             engaging multiple transactions at the same time. You must sell before buying again.

Example 3:

Input: [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.

Constraints:

• 1 <= prices.length <= 3 * 10 ^ 4
• 0 <= prices[i] <= 10 ^ 4

---

Solution

• mine
  • Java

    // O(n) time  
    // O(1) space
    public int maxProfit(int[] prices) {
        int res = 0;
        for(int i = 1; i < prices.length; i++){
            res += Math.max(0, prices[i] - prices[i-1]);
        }
        return res;
    }
    

---

• other

  // O(n^2)time
  // O(n)space
  public int maxProfit(int[] prices) {
      return calculate(prices, 0);
  }
  
  public int calculate(int prices[], int s) {
      if (s >= prices.length)
          return 0;
      int max = 0;
      for (int start = s; start < prices.length; start++) {
          int maxprofit = 0;
          for (int i = start + 1; i < prices.length; i++) {
              if (prices[start] < prices[i]) {
                  int profit = calculate(prices, i + 1) + prices[i] - prices[start];
                  if (profit > maxprofit)
                      maxprofit = profit;
              }
          }
          if (maxprofit > max)
              max = maxprofit;
      }
      return max;
  }
  

---

• the most votes

  //O(n)time  O(1)space
  public int maxProfit(int[] prices) {
      int i = 0;
      int valley = prices[0];
      int peak = prices[0];
      int maxprofit = 0;
      while (i < prices.length - 1) {
          while (i < prices.length - 1 && prices[i] >= prices[i + 1])
              i++;
          valley = prices[i];
          while (i < prices.length - 1 && prices[i] <= prices[i + 1])
              i++;
          peak = prices[i];
          maxprofit += peak - valley;
      }
      return maxprofit;
  }
  

---

more

---