By Dr Antonio Gulli
This ebook offers a set of Dynamic programming difficulties, their resolution, and the C++ code concerning them.
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Extra info for A Collection of Dynamic Programming Interview Questions Solved in C++
You can climb either one step or two steps at a time. How many different ways there are to climb the stair? g. 1 step, 1 step, or 2 steps); if we have three steps, then there are three ways. More examples are given in the following table: Steps #Confs Configurations 1 1 1 2 2 (1, 1); (2) 3 3 (1, 1, 1); (1, 2) ; (2, 1) 4 5 (1, 1, 1, 1); ( 2, 1, 1); (1, 2, 1); (1, 1, 2); (2, 2) 5 8 (1, 1, 1, 1, 1); ( 2, 1, 1, 1); (1, 2, 1, 1); (1, 1, 2, 1); (1, 1, 1, 2); (2, 2, 1); (1, 2, 2), (2, 1, 2) We notice that there is a pattern: at each step the number of configurations is the sum of the number of configurations of the previous and last steps but one.
Intuitively, the cost of the first word is and for the remaining words we can initially define. Also, let and consider the following recurrence, where we build the optimal cost for word, by considering the optimal cost for word: However this definition is not yet meeting our goal for two reasons. First, only considers the cost of the previous word, while it should consider all the words that can fit a line up to a maximal cost. Therefore we need to redefine in such a way to accumulate the cost of the previous words and stop before at the point where this cost becomes negative.
Jumping Array – Given an array of non-negative numbers, start at the first element and reach the end with a minimum number of jumps. A jump cannot exceed the length contained in the current position. 11. Dice -– Given n dice, count how many ways to get sum s. 12. Coin Change – Given dollars, how many different ways there are to make the change into a set of coins? 13. Longest Palindrome String – Given a string, compute the longest palindromic substring 14. String Palindromes -– Given a string, find the minimum number of characters to be inserted for converting the string into a palindrome 15.