The ultimate guide to dynamic programming interviews. Developed by FAANG engineers, it equips you with strategic DP skills, practice with real-world questions, and patterns for efficient solutions.

Some of the toughest questions in technical interviews require dynamic programming solutions. Dynamic programming (DP) is an advanced optimization technique applied to recursive solutions. However, DP is not a one-size-fits-all technique, and it requires practice to develop the ability to identify the underlying DP patterns. With a strategic approach, coding interview prep for DP problems shouldn’t take more than a few weeks.

This course starts with an introduction to DP and thoroughly discusses five DP patterns. You’ll learn to apply each pattern to several related problems, with a visual representation of the working of the pattern, and learn to appreciate the advantages of DP solutions over naive solutions.

After completing this course, you will have the skills you need to unlock even the most challenging questions, grok the coding interview, and level up your career with confidence.

This course is also available in C++, JavaScript, and Python—with more coming soon!

Grokking Dynamic Programming Interview

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import java.util.stream.*;
import java.util.*;

public class Solution{
    public static int findTargetSumWays(int[] arr, int T){
        
        // Write your code here

        return -1;
    }
}

Help me debug only the function FindTargetSumWays.I don't need the corrected code.I don't want explanations or code reviews. Just provide me the exact and to-the-point error that helps me run the code successfully on the test cases provided.

Please help me understand why this code failed for the last failed test case. Please don't give me the corrected code. Just provide me exact and to-the-point advice on how to correct the code so that it runs successfully on the test cases provided. 

Your current task is to review FindTargetSumWays function And Answer the following questions: Ensure that the 0/1 Knapsack  pattern used? Does the code follow proper language guidelines. At the end, review the code.

Please provide a brief time complexity analysis of the function FindTargetSumWays.While calculating time complexity, include the time complexity of built-in Java functions invoked by the code. The Answer should be to the point and in a few lines.

Please provide a brief Space complexity analysis of the function FindTargetSumWays.While calculating space complexity, include the space complexity of built-in Java functions invoked by the code. The Answer should be to the point and in a few lines.

OneD

import ds_v1.DataStructure.DataStructure;
import java.util.Arrays;
import java.io.IOException;
import com.fasterxml.jackson.databind.ObjectMapper;

public class OneD extends DataStructure {
    int[] values = {};


    public OneD() { }
    
    public OneD(int[] val){
        this.values = val.clone();
        
    }

    public String toString() {
        return Arrays.toString(values);
    }

    @Override
    public OneD construct(String new_value, Integer type_of_ds) {
        int[] array={};
        try {
            ObjectMapper mapper = new ObjectMapper();
            array = mapper.readValue(new_value, int[].class);
            
        } catch (IOException e) {
            e.printStackTrace();
        }
        return new OneD(array);
    }

    @Override
    public String traverse(Object input, Integer type_of_ds) {
        return input.toString();
    }
}

def evaluate_results(self) -> object:
        """
        self.__inputs is the list of inputs that are passed as input to function
        self.__actual_output is a list of outputs that is produced by the learner's code
        return : self.__edu__result object
        """
        # multiple outputs will be added at each index respectively for a single test_case
        expected_outputs = [] 
        # store the 1st expected output that should be displayed to the user 
        expected_outputs.append(self.__inputs[0] + self.__inputs[1])

        if json.dumps(self.__inputs[0] + self.__inputs[1]) == json.dumps(self.__actual_outputs[0]):
            self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
        else:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

        return self.__edu_result

import java.util.stream.*;
import java.util.*;

public class Main{
    public static int main(OneD arr, int T){
        return Solution.findTargetSumWays(arr.values, T);
    }
}

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [1]
    - 2 : 1
    output: 
    - 1 : 1
  - name: "testcase 2"
    inputs:
    - 1: [1, 1, 1, 1]
    - 2: 2
    output:
    - 1 : 4
  - name: "testcase 3"
    inputs:
    - 1: [8,48,11,47,26,12,16,39,38,50,21,12,34,1,28,1,3,9,17,50]
    - 2: 3
    output:
    - 1 : 6317
  - name: "testcase 4"
    inputs:
    - 1: [2, 3, 4, 6, 8, 12]
    - 2: 15
    output:
    - 1 : 2
  - name: "testcase 5"
    inputs:
    - 1: [38,21,23,36,1,36,18,3,37,27,29,29,35,47,16,0,2,42,46,6]
    - 2: 14
    output:
    - 1 : 6316
  - name: "testcase 6"
    inputs:
    - 1: [2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3]
    - 2: 42
    output:
    - 1 : 3176160

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [1]
    - 2 : 1
    output: 
    - 1 : 1
  - name: "testcase 2"
    inputs:
    - 1: [1, 1, 1, 1]
    - 2: 2
    output:
    - 1 : 4
  - name: "testcase 3"
    inputs:
    - 1: [8,48,11,47,26,12,16,39,38,50,21,12,34,1,28,1,3,9,17,50]
    - 2: 3
    output:
    - 1 : 6317
  - name: "testcase 4"
    inputs:
    - 1: [2, 3, 4, 6, 8, 12]
    - 2: 15
    output:
    - 1 : 2
  - name: "testcase 5"
    inputs:
    - 1: [38,21,23,36,1,36,18,3,37,27,29,29,35,47,16,0,2,42,46,6]
    - 2: 14
    output:
    - 1 : 6316  

def sum(input_1, input_2):
    return input_1+input_2

def validate_inputs(self) -> None:
        """
        self.__inputs is the list of inputs that are passed as input to function
        store the result using the self.store_result(error_msg, status)
        return : void
        """
        # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
        if self.__inputs[0] > 1000:
            self.store_result ("input 1 should be less than 1000", ValidationFunction.FAIL)
        elif self.__inputs[1] > 1000:
            self.store_result("input 2 should be less than 1000", ValidationFunction.FAIL)
        else:
            self.store_result("", ValidationFunction.PASS)


- $+2+1+2=5$
- $+2-1+2=3$
- $-2+1+2=1$
- $-2-1+2=-1$

- $+2+1-2=1$
- $+2-1-2=-1$
- $-2+1-2=-3$
- $-2-1-2=-5$

Let's solve the Target Sum problem using Dynamic Programming.

Expression	Sum
+ 1 + 1	2
+ 1 – 1	0
– 1 + 1	0
– 1 – 1	–2

No.	arr	T	Number of Expressions
1	[1, 2, 1]	0	2
2	[1, 1, 1, 1]	2	4

Getting Started

0/1 Knapsack

Unbounded Knapsack

Recursive Numbers

Longest Common Substring

Palindromic Subsequence

Conclusion

Target Sum

Statement

Examples

Try it yourself

Solution

Naive approach