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

# Statement

Given a string `str1`, find the count of palindromic substrings in it.

A string is said to be a **palindrome** if it can be read the same backward and forward.
For example, "madam" is a palindrome because it can be read the same from left to right and right to left.

A **substring** is a sequence of consecutive characters from a string.
For example, "way" is a substring of "subway".

For example, if we have a string "aaa", the palindromic substrings and its count will be:

* "a", "a", "a", "aa", "aa", "aaa"
* Count of palindromic substrings will be equal to $6$

> **Note:** This problem has a direct application in bioinformatics. It is used in the analysis of DNA and RNA.

**Constraints:**

* $1 \leq$ `str1.length` $\leq 150$
* `str1` consists of the same case English letters.



# Examples



 


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# Try it yourself

Implement your solution in the following playground.

Help me debug only the function CountPalindromicSubstring.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 CountPalindromicSubstring function And Answer the following questions: Ensure that the Palindromic Subsequence  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 CountPalindromicSubstring.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 CountPalindromicSubstring.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.

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.*;

public class Main{
    public static Integer countPalindromicSubstring (String str1) {
        return 0;
    }
}

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : "abdbca"
    output: 
    - 1 : 7
  - name: "testcase 2"
    inputs:
    - 1: "cddpd"
    output:
    - 1 : 7
  - name: "testcase 3"
    inputs:
    - 1: "pqr"
    output:
    - 1 : 3
  - name: "testcase 4"
    inputs:
    - 1: "abaab"
    output:
    - 1 : 8
  - name: "testcase 5"
    inputs:
    - 1: "aaa"
    output:
    - 1 : 6
  - name: "testcase 6"
    inputs:
    - 1: "xkjkqlajprjwefilxgpdpebieswu"
    output:
    - 1 : 30
    

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : "abdbca"
    output: 
    - 1 : 7
  - name: "testcase 2"
    inputs:
    - 1: "cddpd"
    output:
    - 1 : 7
  - name: "testcase 3"
    inputs:
    - 1: "pqr"
    output:
    - 1 : 3
  - name: "testcase 4"
    inputs:
    - 1: "abaab"
    output:
    - 1 : 8
  - name: "testcase 5"
    inputs:
    - 1: "aaa"
    output:
    - 1 : 6

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)


>**Note:** If you clicked the "Submit" button and the code timed out, this means that your solution needs to be optimized in terms of running time.
>
>**Hint:** Use dynamic programming and see the magic.
# Solution
We will first explore the naive recursive solution to this problem and then see how it can be improved using the Palindromic Subsequence dynamic programming pattern.

## Naive approach

A naive approach to this problem is to process all the possible substrings, checking each substring if it is a palindrome or not, and maintaining the count of all palindromic substrings. A recursive solution that checks the substrings from the start and end of the string is explained below:

* Set two pointers `i` and `j` at the start and end index of the given string, respectively.

* If `i > j`, then we return $0$ as no substring is possible.

* If `i == j`, it means that the string has a single character and we know every single character is a palindromic substring of itself.

* Check if the substring from `i` to `j` is a palindrome or not. If yes, then:

  * Increment the count of palindromic substrings by $1$
  * Recursively check for the substrings from `i+1` to `j`
  * Recursively check for the substrings from `i` to `j-1`
  * Subtract the count of common palindromic substring from `i+1` to `j-1`

* If the substring from `i` to `j` is _not_ a palindrome, then:

  * Recursively check for the substrings from `i+1` to `j`
  * Recursively check for the substrings from `i` to `j-1`
  * Subtract the count of common palindromic substring from `i+1` to `j-1` 




Let’s implement the algorithm as discussed above:

Let's solve the  Count of Palindromic Substrings problem using Dynamic Programming.


Count of Palindromic Substrings

Let's solve the  Count of Palindromic Substrings problem using Dynamic Programming.

No.	str1	Palindromic Substrings	Count of Palindromic Substrings
1	pqr	"p", "q", "r"	3
2	aaa	"a", "a", "a", "aa", "aa", "aaa"	6

Getting Started

0/1 Knapsack

Unbounded Knapsack

Recursive Numbers

Longest Common Substring

Palindromic Subsequence

Conclusion

Count of Palindromic Substrings

Statement

Examples

Try it yourself

Solution

Naive approach