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Dynamic Programming Articles
Page 11 of 14
Minimum number of squares whose sum equals to given number
Any numbers can be represented by the sum of some perfect square numbers. In this problem, we need to find that how many minimum numbers of perfect square terms are needed to represent the given value.let the value is 94, so 95 = 92 + 32 + 22 + 12. so the answer will be 4The idea is to start from 1, we move further to get perfect squared numbers. When the value is 1 to 3, they must be formed with only 1s.Input and OutputInput: An integer number. Say 63. Output: Number of squared terms. Here the answer is ...
Read MoreBreak Number Into 3 parts to find max sum
A number is given. Our task is to break the number three times by n/2, n/3, and n/4 and find maximum sum we can make by dividing the number into three parts.For an example, 50 can be divided into {25, 16, 12}, now break each of the set {25, 16, 12}, into three divisions again, and so on. After completing the division up to 3 times, we will calculate the sum to find the maximum of them.This program can be solved in a recursive way, but in the recursive approach, we need to find the same results for multiple times, ...
Read MoreMobile Numeric Keypad Problem
In this problem, a Numeric mobile keypad is given. We can only press top, bottom, right and left buttons of the current button, diagonal keys are not Allowed. We also cannot press the * and # buttons in the keypad.A digit is given, we have to find the number of possible numbers of given digits can be formed, using the keypad, maintaining given rules.Input and OutputInput: Digit count. Say 3 digit numbers. Output: Number of possible 3 digit numbers, that can be formed with the given conditions. Here the answer is 138.AlgorithmgetCount(n)Input: number of digits n.Output: Possible ways to type n ...
Read MoreFriend Pairing Problem
In a group, there is n number of friends. Each person can remain single or be paired with some other friend. Find the total number of ways, in which friends can remain single or can be paired up.If one pair has two friends’ p and q, then (p, q) or (q, p) are same. For a group of n friends, let f(n) be the number of ways how they can be paired up or remain single. Then either the nth person remains single, or paired up. If the nth person is single, then we recur for (n - 1) friends. If ...
Read MoreWildcard Pattern Matching
For this problem, one main string and another wildcard patterns are given. In this algorithm, it will check whether the wildcard pattern is matching with the main text or not.The wildcard pattern may contain letters or ‘*’ or ‘?’ Symbols. The ‘?’ Is used to match a single character and ‘*’ is used to match the sequence of characters including empty space.When the character is ‘*’: We can ignore the star character and move to check next characters in the pattern.When the next character is ‘?’, then we can ignore only the current character in the text, and check for ...
Read MorePartition problem
For this problem, a given set can be partitioned in such a way, that sum of each subset is equal.At first, we have to find the sum of the given set. If it is even, then there is a chance to divide it into two sets. Otherwise, it cannot be divided.For even value of the sum, then we will create a table named partTable, now use the following condition to solve the problem.partTable[i, j] is true, when subset of array[0] to array[j-1] has sum equal to i, otherwise it is false.Input and OutputInput: A set of integers. {3, 1, 1, ...
Read MorePalindrome Partitioning
In this algorithm, the input is a string, a partitioning of that string is palindrome partitioning when every substring of the partition is a palindrome.In this algorithm, we have to find the minimum cuts are needed to palindrome partitioning the given string.Input and OutputInput: A string. Say “ababbbabbababa” Output: Minimum cut to partition as palindrome. Here 3 cuts are needed. The palindromes are: a | babbbab | b | ababaAlgorithmminPalPart(str)Input: The given string.Output: Minimum number of palindromic partitioning from the string.Begin n := length of str define cut matrix and pal matrix each of order n x n ...
Read MoreLongest Palindromic Subsequence
Longest Palindromic Subsequence is the subsequence of a given sequence, and the subsequence is a palindrome.In this problem, one sequence of characters is given, we have to find the longest length of a palindromic subsequence.To solve this problem, we can use the recursive formula, If L (0, n-1) is used to store a length of longest palindromic subsequence, thenL (0, n-1) := L (1, n-2) + 2 (When 0'th and (n-1)'th characters are same).Input and OutputInput: A string with different letters or symbols. Say the input is “ABCDEEAB” Output: The longest length of the largest palindromic subsequence. Here it is ...
Read MoreMaximum Length Chain of Pairs
There is a chain of pairs is given. In each pair, there are two integers and the first integer is always smaller, and the second one is greater, the same rule can also be applied for the chain construction. A pair (x, y) can be added after a pair (p, q), only if q < x.To solve this problem, at first, we have to sort given pairs in increasing order of the first element. After that, we will compare the second element of a pair, with the first element of the next pair.Input and OutputInput: A chain of number pairs. ...
Read MoreMaximum size square submatrix with all 1s
When a binary matrix is given, our task is to find a square matrix whose all elements are 1.For this problem, we will make an auxiliary size matrix, whose order is the same as the given matrix. This size matrix will help to represent, in each entry Size[i, j], is the size of a square matrix with all 1s. From that size matrix, we will get the maximum number to get the size of the biggest square matrix.Input and OutputInput: The binary matrix. 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 ...
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