Buy and Sell Stock series

121. Best Time to Buy and Sell Stock

https://www.youtube.com/watch?v=8pVhUpF1INw
https://www.youtube.com/watch?v=76-CYD0jn7s

// time n^2 , space 1 
class Solution {
    public int maxProfit(int[] prices) {
      int max = 0;
      for(int i = 0; i < prices.length - 1; i++){
        for(int j = i + 1; j< prices.length; j++){
          int profit = prices[j] - prices[i];
          max = Math.max(profit, max);
        }
      }
      return max;
    }
}



// time n, space 1 
// keep a min price met so far, every time we see a new price., update min price if new price is smaller  , otherwise  check the diff, update the max profit if the new diff is bigger 

class Solution {
    public int maxProfit(int[] prices) {
      int max = 0; // max profit 
      int min = Integer.MAX_VALUE; // min_price so far 
      
      for(int i = 0; i < prices.length; i++){
        min = Math.min(min, prices[i]);
        if(prices[i] > min){
          int diff = prices[i] - min;
          max = Math.max(max, diff);
        }
      }
      return max;
    }
}

 

122


public class Solution {
    
    public int maxProfit(int[] prices) {
        int total = 0;
        for (int i=0; i< prices.length-1; i++) {
            if (prices[i+1]>prices[i]) total += prices[i+1]-prices[i];
        }
    
        return total;
    }
}


stock 1 2 3 ) 二要简单数学证明为啥贪心策略是对的

123. Best Time to Buy and Sell Stock III



Time o(n^ 2)


class Solution {
    public int maxProfit(int[] prices) {
        int res = 0;
        int left = 0;
        int right = 0;
        for(int i = 0; i < prices.length; i++){
            left = stock1(prices, 0, i);
            right = stock1(prices, i + 1, prices.length - 1);
            res = Math.max(left + right, res);
        }
        return res;
    }
    private int stock1(int[] prices, int start, int end){
        int res = 0;
        int min = Integer.MAX_VALUE;
        for(int i = start; i <= end; i++){
            min = Math.min(min, prices[i]);
            res = Math.max(res, prices[i] - min);
        }
        return res;
    }
}


Solution 
Time o(n)  ?

 121. 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.

Example 1:

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.

Example 2:

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





122. Best Time to Buy and Sell Stock II

Say you have an array for which the ith 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.






123. Best Time to Buy and Sell Stock III

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

Design an algorithm to find the maximum profit. You may complete at most two transactions.

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: [3,3,5,0,0,3,1,4]
Output: 6
Explanation: Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
             Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 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.