Say you have an array for which thei_thelement 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.
2. Implementation
(1) Greedy
class Solution {
public int maxProfit(int[] prices) {
if (prices == null || prices.length == 0) {
return 0;
}
int max = 0;
int curMax = 0;
for (int i = 1; i < prices.length; i++) {
curMax = prices[i] > prices[i - 1] ? curMax + prices[i] - prices[i - 1] : curMax;
max = Math.max(max, curMax);
}
return max;
}
}
(2) DP
class Solution {
public int maxProfit(int[] prices) {
if (prices == null || prices.length == 0) {
return 0;
}
int n = prices.length;
int[] profits = new int[n];
for (int i = 1; i < n; i++) {
profits[i] = prices[i] > prices[i - 1] ? profits[i - 1] + prices[i] - prices[i - 1] : profits[i - 1];
}
return profits[n - 1];
}
}