LeetCode——Best Time to Buy and Sell Stock IV

Description：

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 k transactions.

Note:
You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.

动态规划，有递推式：参考：http://blog.csdn.net/feliciafay/article/details/45128771

local[i][j]=max(global[i-1][j-1]+max(diff,0),local[i-1][j]+diff)，

global[i][j]=max(local[i][j],global[i-1][j])

public class Solution {
    public int maxProfit(int k, int[] prices) {
        
        int len = prices.length;
        
        if(len < 2) {
            return 0;
        }
        
        if(k > len) {
            return bigProfit(prices);
        }
        
        int[] local = new int[k+1];
        int[] global = new int[k+1];
        
        Arrays.fill(local, 0);
        Arrays.fill(global, 0);
        
        for(int i=0; i<len-1; i++) {
            int diff = prices[i+1] - prices[i];
            for(int j=k; j>=1; j--) {
                local[j] = Math.max(global[j-1]+(diff>0?diff:0), local[j]+diff);
                global[j] = Math.max(global[j], local[j]);
            }
        }
        
        return global[k];
    }
    
    
    public int bigProfit(int[] prices) {
        
        int res = 0;
        for(int i=0; i<prices.length-1; i++) {
            if(prices[i] < prices[i+1]) {
                res += prices[i+1] - prices[i];
            }
        }
        
        return res;
        
    }
    
}