dynamic-programming

I am trying to solve a variant of a problem I asked earlier: Given a string of parentheses (length <= 1,000,000) and a list of range queries, find the longest subsequence of balanced parentheses within each of the ranges for each of the <= 100,000 queries I found this other SO question that is similar but only has an O(N^3) algorithm. I believe that a DP solution of the form dp[i, j] = longest balanced subsequence in [i .. j] should work because once computed, this would enable to to answer all of the range queries just by querying the DP table. However, even an O(N^2) solution to this problem

From Codechef : A string is considered balanced if and only if all the characters occur in it equal number of times. You are given a string S ; this string may only contain uppercase English letters. You may perform the following operation any number of times (including zero): Choose one letter in S and replace it by another uppercase English letter. Note that even if the replaced letter occurs in S multiple times, only the chosen occurrence of this letter is replaced. Find the minimum number of operations required to convert the given string to a balanced string. Example: For input: ABCB Here

I recently found out about the technique called dynamic programming and I stumbled upon a problem which I can't figure out. You are given a list of arguments in the beginning and you need to do sums on as if you were cutting it. If the list has only one element, you don't sum it. If it has more, you sum the elements and cut it in every possible way. So if list has n elements, there are just n-1 ways to cut it. The picture will explain: I first wanted to sum up all of the sumable parts and I expected the result 20( 11 + 9 ) ( even thought the correct answer is 9 ), but I thought it would be a

This question already has an answer here : Dynamic programming for primitive calculator (1 answer) Closed 3 years ago . This assignment aims to implement a dynamic programming approach to a primitive calculator that can only add 1, multiply by 2 and multiply by 3. So with an input of n determine the minimum number of operations to reach n. I've implemented a very naive dp or what I think is a dp approach. It is not working. I have no-one else to ask. For an input of n = 5 the output of the below is: ([0, 1, 2, 2, 3, 4], [1, 1, 2, 3, 4, 5]) whereas there are two correct outputs for the list

A number N is given in the range 1 <= N <= 10^50 . A function F(x) is defined as the sum of all digits of a number x. We have to find the count of number of special pairs (x, y) such that: 1. 0 <= x, y <= N 2. F(x) + F(y) is prime in nature We have to count (x, y) and (y, x) only once. Print the output modulo 1000000000 + 7 My approach: Since the maximum value of sum of digits in given range can be 450 (If all the characters are 9 in a number of length 50, which gives 9*50 = 450 ). So, we can create a 2-D array of size 451*451 and for all pair we can store whether it is prime or not. Now, the