Knowee
Questions
Features
Study Tools

You are given two positive integers n and limit.Return the total number of ways to distribute n candies among 3 children such that no child gets more than limit candies. Example 1:Input: n = 5, limit = 2Output: 3Explanation: There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1).Example 2:Input: n = 3, limit = 3Output: 10Explanation: There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0).

Question

You are given two positive integers n and limit.Return the total number of ways to distribute n candies among 3 children such that no child gets more than limit candies. Example 1:Input: n = 5, limit = 2Output: 3Explanation: There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1).Example 2:Input: n = 3, limit = 3Output: 10Explanation: There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0).

...expand
🧐 Not the exact question you are looking for?Go ask a question

Solution

This problem can be solved using dynamic programming. Here are the steps to solve this problem:

  1. Create a 4D array dp[i][j][k][l] where i is the total number of candies, j is the number of candies the first child has, k is the number of candies the second child has, and l is the number of candies the third child has. Initialize all values in the array to 0.

  2. Set dp[0][0][0][0] = 1 because there is one way to distribute 0 candies among 3 children such that no child gets more than limit candies.

  3. Iterate over all possible values of i, j, k, and l. For each combination, if j, k, or l is greater than the limit, set dp[i][j][k][l] = 0 because it's not possible to distribute more than limit candies to a child. Otherwise, add the values of dp[i-1][j-1][k][l], dp[i-1][j][k-1][l], and dp[i-1][j][k][l-1

This problem has been solved

Similar Questions

Candy Distribution for StudentsIn a school, there is a row of  N students, each with their own academic rating. The teachers want to reward the students with candies, but they have specific rules:Minimum Candy Rule: Every student must receive at least one candy.Higher Rating, More Candies: Students with a higher academic rating should receive more candies than their neighbors.What is the minimum number of candies you must give?Input FormatThe first and only argument is an integer array A representing the rating of children.Output FormatReturn an integer representing the minimum candies to be given.Example InputsInput 1: A = [1, 2]Input 2: A = [1, 5, 2, 1]Example OutputsOutput 1: 3Output 2: 7Problem Constraints1 <= N <= 105-109 <= A[i] <= 109Write Your Code

Five chocolates of different flavours are to be distributed in three different children such that any child get at least 1 chocolate. What is the maximum number of different ways in which this can be distributed?

There are three friends and a total of 𝑁N candies.There will be a fight amongst the friends if all of them do not get the same number of candies.Chef wants to divide all the candies such that there is no fight. Find whether such distribution is possible.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of a single integer 𝑁N - the number of candies.Output FormatFor each test case, output YES, if we can distribute all the candies between the three friends equally. Otherwise output NO.You can output each character of the answer in uppercase or lowercase. For example, the strings yEs, yes, Yes, and YES are considered the same.Constraints1≤𝑇≤1001≤T≤1001≤𝑁≤1001≤N≤100Sample 1:InputOutput43426YESNONOYESExplanation:Test case 11: Chef can distribute all 33 candies such that each friend gets 11 candy. Since all three friends have same number of candies, there is no fight.Test case 22: There exist no way of distributing all candies such that all three friends have same number of candies.Test case 33: There exist no way of distributing all candies such that all three friends have same number of candies.Test case 44: Chef can distribute all 66 candies such that each friend gets 22 candies. Since all three friends have same number of candies, there is no fight.Did you like the problem statement?113 users found this helpful

Every New Year's Day, Darnel brings 4 candies for each of his grandchildren and 8 more candies for the adults to share.Let g represent the number of Darnel's grandchildren and c represent the total number of candies he brings.Complete the table using the equation c=4g+8.g c1 3 5 287

Candy DistributionChef has 𝑁N candies. He has to distribute them to exactly 𝑀M of his friends such that each friend gets equal number of candies and each friend gets even number of candies. Determine whether it is possible to do so.NOTE: Chef will not take any candies himself and will distribute all the candies.Input FormatFirst line will contain 𝑇T, number of test cases. Then the test cases follow.Each test case contains of a single line of input, two integers 𝑁N and 𝑀M, the number of candies and the number of friends.Output FormatFor each test case, the output will consist of a single line containing Yes if Chef can distribute the candies as per the conditions and No otherwise.You may print each character of the string in uppercase or lowercase (for example, the strings yes, Yes, yEs, and YES will all be treated as identical).

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.