dynamic-programming

How would you use dynamic programming to find the list of positive integers in an array whose sum is closest to but not equal to some positive integer K? I'm a little stuck thinking about this. The usual phrasing for this is that you're looking for the value closest to, but not exceeding K. If you mean "less than K", it just means that your value of K is one greater than the usual. If you truly mean just "not equal to K", then you'd basically run through the algorithm twice, once finding the largest sum less than K, then again finding the smallest sum greater than K, then picking the one of

There's an array A containing (positive and negative) integers. Find a (contiguous) subarray whose elements' absolute sum is minimal, e.g.: A = [2, -4, 6, -3, 9] |(−4) + 6 + (−3)| = 1 <- minimal absolute sum I've started by implementing a brute-force algorithm which was O(N^2) or O(N^3) , though it produced correct results. But the task specifies: complexity: - expected worst-case time complexity is O(N*log(N)) - expected worst-case space complexity is O(N) After some searching I thought that maybe Kadane's algorithm can be modified to fit this problem but I failed to do it. My question is -

recently I have designed a puzzle for children to solve. However I would like to now the optimal solution. The problem is as follows: You have this figure made up off small squares You have to fill it in with larger squares and it is scored with the following table: | Square Size | 1x1 | 2x2 | 3x3 | 4x4 | 5x5 | 6x6 | 7x7 | 8x8 | |-------------|-----|-----|-----|-----|-----|-----|-----|-----| | Points | 0 | 4 | 10 | 20 | 35 | 60 | 84 | 120 | There are simply to many possible solutions to check them all. Some other people suggested dynamic programming, but I don't know how to divide the figure

Problem is "You are climbing a stair case. Each time you can either make 1 step or 2 steps. The staircase has n steps. In how many distinct ways can you climb the staircase?" Following is the code solution for this problem but I am having trouble understanding it. Can anybody explain me int stairs(int n) { if (n == 0) return 0; int a = 1; int b = 1; for (int i = 1; i < n; i++) { int c = a; a = b; b += c; } return b; } Thanks, Well, first you need to understand the recursive formula, and how we derived the iterative one from it. The recursive formula is: f(n) = f(n-1) + f(n-2) f(0) = f(1) = 1 (

I recently found a contest problem that asks you to compute the minimum number of characters that must be inserted (anywhere) in a string to turn it into a palindrome. For example, given the string: "abcbd" we can turn it into a palindrome by inserting just two characters: one after "a" and another after "d": "a d bcbd a ". This seems to be a generalization of a similar problem that asks for the same thing, except characters can only be added at the end - this has a pretty simple solution in O(N) using hash tables. I have been trying to modify the Levenshtein distance algorithm to solve this

I have done a bunch of research for finding the longest for M = 2 sequences, but I am trying to figure out how to do it for M ≥ 2 sequences I am being given N and M: M sequences, with N unique elements. N is the set of {1 - N}. I have thought about the dynamic programming approach, but I am still confused as to how to actually incorporate it. Example input 5 3 5 3 4 1 2 2 5 4 3 1 5 2 3 1 4 The max sequence here can be seen to be 5 3 1 Expected output Length = 3 A simple idea. For each number i between 1 and N , calculate the longest subsequence where the last number is i . (Let's call it a[i]