Leetcode
Dynamic Programming
122 Best Time to Buy and Sell Stock II

1. Question

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:
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Input: [7,1,5,3,6,4]
2
3
Output: 7
4
5
Explanation:
6
Buy on day 2 (price = 1) and sell on day 3 (price = 5), profit = 5-1 = 4.
7
Then buy on day 4 (price = 3) and sell on day 5 (price = 6), profit = 6-3 = 3.
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Example 2:
1
Input: [1,2,3,4,5]
2
3
Output: 4
4
5
Explanation:
6
Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.
7
Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are
8
engaging multiple transactions at the same time. You must sell before buying again.
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Example 3:
1
Input:
2
[7,6,4,3,1]
3
4
Output:
5
0
6
7
Explanation:
8
In this case, no transaction is done, i.e. max profit = 0.
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2. Implementation

(1) Greedy
1
class Solution {
2
public int maxProfit(int[] prices) {
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if (prices == null || prices.length == 0) {
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return 0;
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}
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int max = 0;
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int curMax = 0;
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for (int i = 1; i < prices.length; i++) {
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curMax = prices[i] > prices[i - 1] ? curMax + prices[i] - prices[i - 1] : curMax;
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max = Math.max(max, curMax);
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}
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return max;
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}
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}
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(2) DP
1
class Solution {
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public int maxProfit(int[] prices) {
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if (prices == null || prices.length == 0) {
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return 0;
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}
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int n = prices.length;
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int[] profits = new int[n];
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for (int i = 1; i < n; i++) {
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profits[i] = prices[i] > prices[i - 1] ? profits[i - 1] + prices[i] - prices[i - 1] : profits[i - 1];
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}
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return profits[n - 1];
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}
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}
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3. Time & Space Complexity

Greedy: 时间复杂度O(n), 空间复杂度O(1)
Dynamic Programming: 时间复杂度O(n), 空间复杂度O(n)