Dynamic Programming Interview Questions

No. 03 - Maximum Sum of All Sub-arrays
A sub-array has one number of some continuous numbers. Given an integer array with positive numbers and negative numbers, get the maximum sum of all sub-arrays. Time complexity should be O(n).

For example, in the array {1, -2, 3, 10, -4, 7, 2, -5}, its sub-array {3, 10, -4, 7, 2} has the maximum sum 18.

No. 16 - Maximal Length of Incremental Subsequences

Given an unsorted array, find the max length of subsequence in which the numbers are in incremental order.

For example: If the input array is {7, 2, 3, 1, 5, 8, 9, 6}, a subsequence with the most numbers in incremental order is {2, 3, 5, 8, 9} and the expected output is 5.

No. 25 - Edit Distance

Implement a function which gets the edit distance of two input strings. There are three types of edit operations: insertion, deletion and substitution. Edit distance is the minimal number of edit operations to modify a string from one to the other.

No. 26 - Minimal Number of Coins for Change

Please implement a function which gets the minimal number of coins, whose value is v₁, v₂, …, v_n, to make change for an amount of money with value t. Any coin with value v_i may duplicate for any times to make change.

For example, the minimal number of coins to make change for 15 out of a set of coins with value 1, 3, 9, 10 is 3. We can choose two coins with value 3 and a coin with value 9. The number of coins for other choices should be greater than 3.

No. 44 - Dynamic Programming on Stolen Values

There are n houses built in a line, each of which contains some value in it. A thief is going to steal the maximal value in these houses, but he cannot steal in two adjacent houses because the owner of a stolen house will tell his two neighbors on the left and right side. What is the maximal stolen value?

No. 49 - Longest Substring without Duplication

Given a string, please get the length of the longest substring which does not have duplicated characters. Supposing all characters in the string are in the range from ‘a’ to ‘z’.

No. 52 - Maximal Product when Cutting Rope
Given a rope with length n, how to cut the rope into m parts with length n[0], n[1], ...,n[m-1], in order to get the maximal product of n[0]*n[1]* ... *n[m-1]? We have to cut once at least. Additionally, the length of the whole length of the rope, as well as the length of each part, are in integer value.

No. 56 - Maximal Value of Gifts

A board has n*m cells, and there is a gift with some value (value is greater than 0) in every cell. You can get gifts starting from the top-left cell, and move right or down in each step, and finally reach the cell at the bottom-right cell. What’s the maximal value of gifts you can get from the board?