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Programming Articles
Page 142 of 2547
Program to find hoe many children will get candies while distributing them maintaining the rules in Python
Suppose we have k number of candies to distribute among children following specific rules. This problem requires finding the maximum number of children who can receive candies while maintaining distribution constraints. Distribution Rules The ith child will get i² number of candies Children must be served in order − child at index i cannot get candies until all children from index 1 to i−1 are served If the ith child cannot get exactly i² candies, the distribution stops Example Walkthrough If k = 20, the distribution works as follows ? 1st child ...
Read MoreProgram to find remainder after dividing n number of 1s by m in Python
Suppose we have two numbers n and m. We have to find the remainder after dividing n number of 1s by m. So, if the input is like n = 4 and m = 27, then the output will be 4, because 1111 mod 27 = 4. Understanding the Problem When we have n number of 1s, we create a number like: n = 1: Number is 1 n = 2: Number is 11 n = 3: Number is 111 ...
Read MoreProgram to find number of pairs from N natural numbers whose sum values are divisible by k in Python
Suppose we have a number n and another value k. We need to find the total number of pairs from the first N natural numbers whose sum is divisible by k. Given an array A with first N natural numbers [1, 2, 3, ..., n], we have to find pairs A[i] and A[j] where i < j and (A[i] + A[j]) % k == 0. Example If n = 10 and k = 4, the output will be 10 because there are 10 pairs whose sum is divisible by 4: [(1, 3), (1, 7), (2, 6), ...
Read MoreProgram to find common fraction between min and max using given constraint in Python
Finding the best rational approximation to π (pi) within given constraints is a classic problem in number theory. We need to find a fraction n/d where the denominator d falls between minimum and maximum values, and the fraction is as close to π as possible. Problem Statement Given two integers minimum and maximum, find a common fraction n/d such that: min ≤ d ≤ max |n/d - π| is minimized If multiple fractions satisfy this condition, return the one with the smallest denominator Algorithm Overview The solution uses the Farey sequence approach to ...
Read MoreProgram to find probability that any proper divisor of n would be an even perfect square number in Python
Given a number n, we need to find the probability that any proper divisor of n would be an even perfect square number. A proper divisor is any positive divisor of n except n itself. So, if the input is like n = 36, then the output will be 1/8 because there are eight proper divisors of 36, these are {1, 2, 3, 4, 6, 9, 12, 18} and among them only one number (4) is both a perfect square and even. Algorithm To solve this, we will follow these steps − If n mod ...
Read MoreProgram to find value of find(x, y) is even or odd in Python
Given an array nums and a pair (x, y), we need to determine whether the value of find(x, y) is odd or even. The find() function is defined recursively: find(x, y) = 1 if x > y find(x, y) = nums[x] ^ find(x+1, y) otherwise Where ^ represents the XOR (exclusive OR) operation. Understanding the Problem Let's trace through an example with nums = [3, 2, 7] and (x, y) = (1, 2): find(1, 2) = nums[1] ^ find(2, 2) ...
Read MoreProgram find number of subsets of colorful vertices that meets given conditions in Python
Given an array colors representing colors for vertices of a regular n-gon polygon, we need to find the number of special subsets that meet specific conditions. Each vertex is randomly colored with one of n different colors. Problem Conditions A special subset must satisfy these requirements: The subset size must be at least two When we remove vertices in the subset (and their adjacent edges), the remaining vertices form continuous paths None of these paths should contain two vertices of the same color If the answer is large, return the result modulo 10^9 + ...
Read MoreProgram to find number of expected moves required to win Lotus and Caterpillar game in Python
Suppose we have a grid with n rows and m columns. Amal and Bimal are playing a strategic game on this grid with specific movement rules. Game Rules The game follows these rules: Amal places a white lotus tile somewhere in the top row Bimal places a caterpillar tile somewhere in the bottom row Amal starts first, and they play alternately Amal can move to any of the 8 adjacent cells (including diagonals) Bimal's caterpillar can only move left, right, or stay in the same position Amal's goal is to catch Bimal using minimum moves Bimal's ...
Read MoreProgram to find expected growth of virus after time t in Python
Suppose there is a dangerous virus that grows rapidly. The probability of virus cells growing by a factor x is 0.5, and the probability of growing by a factor y is also 0.5. Starting with a single virus cell, we need to calculate the expected number of virus cells after time t. If the result is large, we return it modulo 10^9+7. The expected growth factor at each time step is (x + y) / 2, since each factor has probability 0.5. Problem Analysis At each time step, the virus can grow by factor x or y ...
Read MoreProgram to find number of solutions for given equations with four parameters in Python
Suppose we have four numbers a, b, c and d. We need to find the number of pairs (x, y) that satisfy the equation: x² + y² = (x*a) + (y*b) where x is in range [1, c] and y is in range [1, d]. For example, if a = 2, b = 3, c = 2, d = 4, then the output will be 1 because one valid pair is (1, 1). Mathematical Approach We can rearrange the equation x² + y² = x*a + y*b as a quadratic in y: y² - b*y + ...
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