188. Best Time to Buy and Sell Stock IV Leetcode Java

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).

Solution:

Actually, in problem 123.Best Time to Buy and Sell Stock III, I already solved this problem. So please see that problem for full analysis. Basically, this is the general problem of all buy and sell stock problems. The trick part for any k transactions is that if k>prices.length/2, which basically means we can do as many as transactions for all n days.Because there is no meaning for buying and selling the stock on the same day, buy and sell on different days, which makes when k> length/2, it is the same as problem 122. Best Time to Buy and Sell Stock II. Other than that it is the same as problem 123. 

All relevant problems:

188. Best Time to Buy and Sell Stock IV 

123.Best Time to Buy and Sell Stock III

122. Best Time to Buy and Sell Stock II

121. Best Time to Buy and Sell Stock I

 public int maxProfit(int k, int[] prices) {  
    if(prices==null || prices.length==0 || k==0) return 0;  
    if(k>=prices.length/2){  
      int res=0;  
      for(int i=1;i<prices.length;i++){  
        res+=Math.max(prices[i]-prices[i-1],0);  
      }  
      return res;  
    }  
    int[] local=new int[k+1];
     int[] global=new int[k+1];
     int res=0;
     for(int i=1;i<prices.length;i++){
         for(int j=1;j<=k;j++){
             local[j]=Math.max(local[j]+prices[i]-prices[i-1],global[j-1]);
             global[j]=Math.max(global[j],local[j]);
             res=Math.max(res,global[j]);
         }
     }
     return res;
   }