recurrence

问题 Assume today is Feb 21, 2011 ( Monday ). It is the third Monday of this month. If date is given as input, How can I know how many Mondays have passed before it? In PHP, how to know how many mondays have passed in this month uptil today? 回答1: $now=time() + 86400; if (($dow = date('w', $now)) == 0) $dow = 7; $begin = $now - (86400 * ($dow-1)); echo "Mondays: ".ceil(date('d', $begin) / 7)."<br/>"; works for me.... EDIT: includes today's monday too 回答2: That sounds like a pretty straightforward

问题 I'm studying recursive logic that one of the problems is subset sum. AFAI read, there are overlaps when it is run by recursion. But, I cannot figure out how there are. Also, I read that to overcome the issue DP can be used but I want to comprehend how the recursion overcome the problem. Could you picturize an example with overlapping? Pseudo-code, def hasSum( array, start, sum): if sum == 0: return true if start > array.length - 1: return false; return hasSum(array, start + 1, sum - array

问题 This question already has answers here : Big O of Recursive Methods (2 answers) Closed 5 years ago . How to find the Big O for the following recursive function using the recursive method: T(n)=(n-1)T(n-1)+(n-1)T(n-2) 回答1: Anyway, I tried to solve this case using the classic recursive relation methodology. It's all about observing if a pattern exists: Very expensive algorithm (Enemies of computer science are factorial and exponential orders of growth). 来源： https://stackoverflow.com/questions

问题 I was solving a coding question, and found out the following relation to find the number of possible arrangements: one[1] = two[1] = three[1] = 1 one[i] = two[i-1] + three[i-1] two[i] = one[i-1] + three[i-1] three[i] = one[i-1] + two[i-1] + three[i-1] I could have easily used a for loop to find out the values of the individual arrays till n , but the value of n is of the order 10^9 , and I won't be able to iterate from 1 to such a huge number. For every value of n , I need to output the value

问题 I'm tried to figure out how to do it for quite of time and its not working as intended; I'm writing a code where there is 1 to k numbers, I need to find all possible combination without repeats. e.g. for 3: 1, 2, 3, 12, 13. Example for counting 4-digits numbers with 1, 2, 3, 4, 5. int k = 5; for (int p = 0; p < k; p++) { for (int i = p+1; i < k; i++) { for (int j = i + 1; j < k; j++) { for (int h = j + 1; h < k; h++) { cout << p + 1 << i + 1 << j + 1 << h + 1 << endl; } } } } And there is

问题 I have a collection of DateTime objects. I need to "parse" out subcollections from this original list to grab related items based on recurrence. So I need to take this single original collection: var collectionOfDateTime = GetDateTimeCollection(); and translate that into a list of DateTime collections where each collection includes a set of dates from the first list that following a specific recurrence pattern. In my examples below I am not including time but in the real requirement, these

问题 I am having trouble with this recurrence relation. T(n) = 2T(n/2) + 1 Can anyone help me in explaining how one would go about solving this to get to the answer of O(n) ? 回答1: Let's assume for simplicity that n is a power of 2. For example, if n = 8 and the base case T(0) = 0 then the tree of recursive call looks like that: 1 n = 8, depth 0 / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ 1 1 n = 4, depth 1 / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ 1 1 1 1 n = 2, depth 2 / \ / \ / \ / \ / \ / \ / \ /

问题 Lately I have been interested in algorithms and I have been watching a video series published by MIT. I encountered some problems regarding recurrence though. https://www.youtube.com/watch?v=-EQTVuAhSFY The attached link is the source of the video. At 07:10, the professor mentioned that it's fine to use T(n/2) in T(n) = 2T(n/2) + theta(1) due to a certain theorem, despite that it would be more accurate to use T(the floor of n/2) or T(the ceiling of n/2) . What exactly is this theorem?

问题 I have a set of events that reoccur. I need to be able to calculate when these events occur with the next 5 weeks or so. This system will inform the user that within this month, these events will occur.. For example: Event1 Date Started = Monday 19th Dec 2011 Recurrence Pattern = Monday/Fortnightly Event2 Date Started = Thursday 3rd Feb 2012 Recurrence Pattern = Thursday/Every Three Weeks It's now 22 March - within the next 5 weeks what dates will Events 1 & 2 fall on. It would also be useful

问题 I tried recursion tree method since the master method is not applicable for this recurrence but it seems that it is not the right method also, any help would be appreciated ! 回答1: Either I have an error somewhere in my derivation or there is an error in your statement. You do this by unrolling the recursion: T(n) = T(n/2) + T(n/4) = 2T(n/4) + T(n/8) T(n) = 3T(n/8) + 2T(n/16) T(n) = 5T(n/16) + 3T(n/32) .... T(n) = F(i + 1)T(n/2^(i-1)) + F(i)T(n/2^i) where F(i) if a Fibonacci number. Using