dynamic-programming

Several years ago I took an algorithms course where we were giving the following problem (or one like it): There is a building of n floors with an elevator that can only go up 2 floors at a time and down 3 floors at a time. Using dynamic programming write a function that will compute the number of steps it takes the elevator to get from floor i to floor j . This is obviously easy using a stateful approach, you create an array n elements long and fill it up with the values. You could even use a technically non-stateful approach that involves accumulating a result as recursively passing it

I am practicing Dynamic Programming. I am focusing on the following variant of the coin exchange problem: Let S = [1, 2, 6, 12, 24, 48, 60] be a constant set of integer coin denominations. Let n be a positive integer amount of money attainable via coins in S . Consider two persons A and B . In how many different ways can I split n among persons A and B so that each person gets the same amount of coins (disregarding the actual amount of money each gets)? Example n = 6 can be split into 4 different ways per person: Person A gets {2, 2} and person B gets {1, 1}. Person A gets {2, 1} and person B

It's a bit immature, but I have to ask, The Bytelandian Gold coin problem mentioned here - http://www.codechef.com/problems/COINS/ , is said to be typical DP problem,even though I have read basics of DP & recursion, but I am finding hard to understand its solution, # include <stdio.h> # include <stdlib.h> long unsigned int costArray[30][19]; unsigned int amount; unsigned int currentValue(short int factor2,short int factor3) { int j; unsigned int current = amount >> factor2; for(j=0;j<factor3;j++) current /= 3; return current; } long unsigned int findOptimalAmount(short int factor2,short int

Suppose i have an array which contain n integers . How to find subset of size k such that the minimum distance between all pairs of integers in the subset is maximized , i mean they are at farthest distance . example : array a[]={1,2,6,7,10} and k=3 , subset = {1,6,10} , the minimum distance is 4 between 10 and 6 . Wrong subsets : {1,7,10} , minimum distance is 3 {1,2,6} , minimum distance is 1 I came up with a solution : 1) sort array 2) select a[0] , now find ceil(a[0]+ x ) = Y in array ....and then ceil(Y+ x ) and so on k-1 times , also kth element will be a[n-1] To find x : dp[i,j] be the

I have a problem in which we have an array of positive numbers and we have to make it strictly increasing by making zero or more changes to the array elements. We are asked the minimum number of changes required to make the array strictly increasing. Example if array is 1 2 9 10 3 15 so ans=1 if change 3 to some number between 12 to 14. if 1 2 2 2 3 4 5 ans=5 since changing 2 to 3 then 2 to 4 then 3 to 5 then 4 to 6 then 5 to 7 Constraints: Number of elements in array <= 10^6 Each element <= 10^9 Note: This is not a homework, it was asked in my interview and I was unable to give an algorithm

The following is a demo question from a coding interview site called codility: A prefix of a string S is any leading contiguous part of S. For example, "c" and "cod" are prefixes of the string "codility". For simplicity, we require prefixes to be non-empty. The product of prefix P of string S is the number of occurrences of P multiplied by the length of P. More precisely, if prefix P consists of K characters and P occurs exactly T times in S, then the product equals K * T. For example, S = "abababa" has the following prefixes: "a", whose product equals 1 * 4 = 4, "ab", whose product equals 2 *