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Count ways to express ‘n’ as sum of odd integers in C++

Sunidhi Bansal
Sunidhi Bansal
Updated on 11-Mar-2026 415 Views

Given an integer n as input. The goal is to find the number of ways in which we can represent ‘n’ as the sum of odd integers. For example, if n is 3 it can be represented as sum ( 1+1+1 ) and (3) so total 2 ways.For ExampleInputn=6OutputCount of ways to express ‘n’ as sum of odd integers are: 8ExplanationThe ways in which we can express ‘n’ as sum of odd integers − 1. 1+1+1+1+1+1 2. 3+1+1+1 3. 1+3+1+1 4. 1+1+3+1 5. 1+1+1+3 6. 3+3 7. 1+5 8. 5+1Inputn=9OutputCount of ways to express ‘n’ as sum of odd integers ...

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Find if given matrix is Toeplitz or not in C++

sudhir sharma
sudhir sharma
Updated on 11-Mar-2026 301 Views

In this problem, we are given a 2D square matrix mat[][] of size n*n. Our task is to find if the given matrix is Toeplitz or not.Toeplitz matrix also known as diagonal matrix is a matrix in which the elements at the diagonal start from top-left corner to bottom-right corner.Let’s take an example to understand the problem, Input:          Mat[][] = {{3, 5, 1},                            {4, 3 ,2},                            {1, 2, 3}}Output: YesExplanation:  Diagonal : ...

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Program to find minimum number of roads we have to make to reach any city from first one in C++

Arnab Chakraborty
Arnab Chakraborty
Updated on 11-Mar-2026 802 Views

Suppose we have two lists costs_from and costs_to of same size where each index i represents a city. It is making a one-way road from city i to j and their costs are costs_from[i] + costs_to[j]. We also have a list of edges where each edge contains [x, y] indicates there is already a one-way road from city x to y. If we want to go to any city from city 0, we have to find the minimum cost to build the necessary roads.So, if the input is like costs_from = [6, 2, 2, 12] costs_to = [2, 2, 3, ...

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Program to check whether first player can take more candies than other or not in Python

Arnab Chakraborty
Arnab Chakraborty
Updated on 11-Mar-2026 217 Views

Suppose we have a list of numbers called candies and two persons are racing to collect the most number of candies. Here the race is turn based, person 1 is starting first, and in each turn he can pick up candies from the front or from the back. We have to check whether person 1 can collect more candies than other or not.So, if the input is like candies = [1, 4, 3, 8], then the output will be True, as person 1 can take 8 candies in the first round and regardless of whether second person picks 1 or ...

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How to create horizontal legend using ggplot2 in R?

Nizamuddin Siddiqui
Nizamuddin Siddiqui
Updated on 11-Mar-2026 7K+ Views

The default legend direction is vertical but it can be changed to horizontal as well and for this purpose we can use legend.direction argument of theme function of ggplot2 package. For example, if we want to create a bar chart with x as categories and y as frequencies tjat are contained in a data frame df then the bar chart with horizontal legends for categories in x can be created as −ggplot(df, aes(x, y, fill=x))+geom_bar(stat="identity")+theme(legend.direction="horizontal")ExampleConsider the below data frame −> x y df dfOutputx y 1 A 27 2 B 25 3 C 28Loading ggplot2 package and creating the bar ...

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Check if frequency of all characters can become same by one removal in Python

Arnab Chakraborty
Arnab Chakraborty
Updated on 11-Mar-2026 657 Views

Suppose we have a lowercase string s. We have to check whether the frequency of all characters are same after deleting one character or not.So, if the input is like s = "abbc", then the output will be True as we can delete one b to get string "abc" where frequency of each element is 1.To solve this, we will follow these steps −occurrence := a map with all characters of s and their frequenciesif occurrences of all characters in s are same, thenreturn Truefor each char in s, dooccurrence[char] := occurrence[char] - 1if occurrences of all characters in s ...

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Find if given number is sum of first n natural numbers in C++

sudhir sharma
sudhir sharma
Updated on 11-Mar-2026 427 Views

In this problem, we are given a number num. Our task is to find if the given number is the sum of first n natural numbers.  Problem Description: Here, we need to check whether the given number is the sum of first n natural numbers.Let’s take an example to understand the problem, Input: num = 55Output: yes, 10Explanation:55 is the sum of the first 10 natural numbers, 1+2+3+4+5+6+7+8+9+10.Solution Approach: A simple approach to solving the problem is finding the sum of n natural numbers until it becomes equal to or greater than num.If the sum is equal to num, return n.If at any value of ...

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Program to check how many ways we can choose empty cells of a matrix in python

Arnab Chakraborty
Arnab Chakraborty
Updated on 11-Mar-2026 274 Views

Suppose we have a N x N binary matrix where 0 is for empty cells and 1 is a blocked cells, we have to find the number of ways to choose N empty cells such that every row and every column has at least one chosen cells. If the answer is very large return result mod 10^9 + 7So, if the input is like000000010then the output will be 4, as we have following configurations (where x is a selected cell) −To solve this, we will follow these steps −n := size of matrixDefine a function f() . This will take ...

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Program to check person 1 can win the candy game by taking maximum score or not in Python

Arnab Chakraborty
Arnab Chakraborty
Updated on 11-Mar-2026 379 Views

Suppose two players are playing a game. Where several candies placed on a line, and person 1 is given a list of numbers called nums that is representing the point value of each candy. On each person's turn, they can pick 1, 2, or 3 candies from the front of the line, then delete them from list, and get the sum of their points added to their score. This game will end when all the candies are deleted and the person with the higher score will be the winner. We have to check person 1 can win this game or ...

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Count ways to express a number as sum of consecutive numbers in C++

Sunidhi Bansal
Sunidhi Bansal
Updated on 11-Mar-2026 981 Views

Given an integer n as input. The goal is to find the number of ways in which we can represent ‘num’ as the sum of two or more consecutive natural numbers. For example, if n is 3 it can be represented as sum ( 1+2 ) so total 1 way.For ExampleInputnum=6OutputCount of ways to express a number as sum of consecutive numbers are: 1ExplanationThe ways in which we can express ‘num’ as sum of consecutive natural numbers: 1+2+3Inputnum=19OutputCount of ways to express a number as sum of consecutive numbers are: 1ExplanationThe ways in which we can express ‘num’ as sum ...

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