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I came accross this question in a programming contest, i think it can be solved by DP but cannot think of any, so plz help. Here's the questn :

There are n stack of coins placed linearly, each labelled from 1 to n. You also have a sack of coins containing infinite coins with you. All the coins in the stacks and the sack are identical. All you have to do is to make the heights of coins non-decreasing.

You select two stacks i and j and place one coin on each of the stacks of coins from stack'i' to stack'j' (inclusive). This complete operations is considered as one move. You have to minimize the number of moves to make the heights non-decreasing. 

No. of Test Cases < 50  
1 <= n <= 10^5  
0 <= hi <= 10^9

Input Specification : There will be a number of test cases. Read till EOF. First line of each test case will contain a single integer n, second line contains n heights (h[i]) of stacks.

Output Specification : Output single integer denoting the number of moves for each test case. 

for eg: H={3,2,1}
     answer is 2
     step1: i=2, j=3, H = {3,3,2}   
     step2: i=3, j=3, H = {3,3,3}
ujjawal kumar
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    This is not the right place , Visit http://codegolf.stackexchange.com/ – Amarnath R Shenoy Mar 26 '14 at 06:11
  • That's a really, really boring problem... just draw a bit of an up-and-down line on graph paper and it's obvious that you have to fill them in from the bottom up, one horizontal run at a time (i.e. never any benefit to doing a fill that spans heights). The only other insight is that maintaining a stack of places the height decreases ensures that on finding an increase you can quickly work out where to start the fill(s). – Tony Delroy Mar 26 '14 at 06:45

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