动态规划简单邮票分发

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文件名称：动态规划简单邮票分发

文件大小：17KB

文件格式：CPP

更新时间：2013-11-18 06:16:51

动态规划

DESCRIPTION: 1.Analyze Problem A : sorted stamps array A={ai} ai: one stamp element in array n: array size, that is number of elements in array r: desired value of stamps F(n,r):expected result, minimum number of stamps for a given value r from n size array. S: selected stamps array S={si} 2.Choose Algorithm a.Greedy algorithm seems to be a good choice, try to solve it in O(n), i try divide array into subarry B={bi}, r should larger than every elemnt in B that is r>bi and suppose bk is the smallest element in B, so that r= bk%r, f(i,r)=(bk/r), F(n,r)=∑f(i,r). The main idea is to choose the last element who larger than desired value each time. However,it can not give us optimal solution in some condition, like A={8,5,4,1}, if r=10, this algoritm will give a solution F(n,r)=3, S={8,1,1},but the optimal solution should be F(n,r)=2, S={5,5}. b.Full search so the straight forwards algorithm is to search for every solution in A for desired value directly.However, it will always take O(n!) to go through every combination. c.Dynamic programming, at last, I decide to choose dynamic programming. analyze optimal structure, suppose in A={ai}, for a specific stamp ak,there will be two cases it is choosen so that f(i,r)=1+f(i,r-ak) , 1<=i<=k, r>=ak it is not valid so that f(i,r)=f(i-1,r) 3.Design Dynamic programming optimal structure: Compute-opt(r)= 1 + Compute-opt(r-ai) value: Compute-opt(r) = ∞ (r < 0) Compute-opt(r) = 0 (r = 0) Compute-opt(r) = 1+{Compute-opt(r-ai)} ( 1=ai>0 ) Complexity :O(nr) Memory cost:O(n+r) Compute in a bottom-up style to recursive every desired value and array. store value of Compute-opt in memory for future use, so that we can easily get value from those memory in future recursive call, and avoid compute again, that is if the array is not change, you can easily fetch result any desired value j (j < r, r is the value using for compute ). 2.For User totally, I design a small command line for this machine list below 1.Manual Operation 2.Self Auto Testing 3.Check Results q.Quit Manual Operation: when select this machine will turn to be manual mode, ask person to input stamps and desired value; Self Auto Testing:when select this machine will turn to be auto mode, show the test case already design in code after that machine will quit automatically. Check Results: only be visiable in Manual Operation, people can check desired value for the array input before, the desired value should be no more than first time input. Quit, clean all the memory and quit system.