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DP Standard Problem Variations

Last Updated: 23 July 2025

When we solve Dynamic Programming problems, we try to find a pattern by matching pattern with a standard DP problem. This is generally recommended to solve new DP problems...read more

Count all ordered pairs (A, B) such that intersection of A and B becomes K

Last Updated: 26 February 2024

Given a positive integer k and an array arr[] of size n contains distinct elements, the task is to find the number of ordered pairs (A, B) that can be made where A and B a...read more

DSA

binomial coefficient

Geeks Premier League 2023

Find the number of ways to draw the last colored ball

Last Updated: 23 July 2025

Given an array balls[] representing the count of colored balls labeled from 1 to k, the task is to determine the number of ways to draw the last ball of color i before dra...read more

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DSA

combinatorics

Algorithms-Dynamic Programming

binomial coefficient

Geeks Premier League 2023

Stars and Bars Algorithms for Competitive Programming

Last Updated: 28 May 2026

The Stars and Bars (also known as Balls and Urns) technique is a widely used method in Combinatorics, which is the branch of mathematics dealing with counting and arrangem...read more

Geeks Premier League 2023

Number of ways to make N using product of M integers

Last Updated: 31 July 2023

Given two integers N (1 = N = 1e9) and M (M = 1e5), the task is to find the number of ways to represent the number N in terms of the product of M integers. Find the answer...read more

Permutation and Combination

binomial coefficient

Sum of binomial coefficients (nCr) in a given range

Last Updated: 07 November 2023

Given three values, N, L and R, the task is to calculate the sum of binomial coefficients (nCr) for all values of r from L to R.Examples:Input: N = 5, L = 0, R = 3Output: ...read more

Count of all possible combinations of K numbers that sums to N

Last Updated: 23 July 2025

Given a number N, the task is to count the combinations of K numbers from 1 to N having a sum equal to N, with duplicates allowed.Example:Input: N = 7, K = 3Output:15Expla...read more

DSA

binomial coefficient

Memoization

Remaining array element after repeated removal of last element and subtraction of each element from next adjacent element

Last Updated: 23 July 2025

Given an array arr[] consisting of N integers, the task is to find the remaining array element after subtracting each element from its next adjacent element and removing t...read more

Count odd and even Binomial Coefficients of N-th power

Last Updated: 23 July 2025

Given an integer N, the task is to count the number of even and odd binomial coefficients up to Nth power.Examples:Input: N = 4Output:Odd: 2Even: 3Explanation:The binomial...read more

Count sequences of given length having non-negative prefix sums that can be generated by given values

Last Updated: 23 July 2025

Given two integers M and X, the task is to find the number of sequences of length M that can be generated comprising X and -X such that their respective counts are equal a...read more

Permutation and Combination

binomial coefficient

Count permutations of given array that generates the same Binary Search Tree (BST)

Last Updated: 15 July 2025

Given an array, arr[] of size N consisting of elements from the range [1, N], that represents the order, in which the elements are inserted into a Binary Search Tree, the ...read more

Permutation and Combination

binomial coefficient

Count distinct regular bracket sequences which are not N periodic

Last Updated: 15 July 2025

Given an integer N, the task is to find the number of distinct bracket sequences that can be formed using 2 * N brackets such that the sequence is not N-periodic.A bracket...read more

Permutation and Combination

binomial coefficient

Sum of all products of the Binomial Coefficients of two numbers up to K

Last Updated: 15 July 2025

Given three integers N, M and K, the task is to calculate the sum of products of Binomial Coefficients C(N, i) and C(M, K - i), where i ranges between [0, K].\begin{*align...read more

DSA

Permutation and Combination

binomial coefficient

Central binomial coefficient

Last Updated: 15 July 2025

Given an integer N, the task is to find theN^{th}Central binomial coefficient.The first few Central binomial coefficients for N = 0, 1, 2, 3... are1, 2, 6, 20, 70, 252, 92...read more

Number of ways to color N-K blocks using given operation

Last Updated: 12 July 2025

Given N blocks, out of which K is colored. These K-colored blocks are denoted by an array arr[]. The task is to count the number of ways to color the remaining uncolored b...read more

DSA

Algorithms-Recursion

Permutation and Combination

binomial coefficient

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