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Programming Articles
Page 104 of 2547
Program to find lexicographically smallest subsequence of size k in Python
Given a list of numbers and a value k, we need to find the lexicographically smallest subsequence of size k. A subsequence maintains the relative order of elements from the original list. Problem Understanding For example, if we have nums = [2, 3, 1, 10, 3, 4] and k = 3, we need to select 3 numbers that form the smallest possible sequence when compared lexicographically. The answer would be [1, 3, 4]. Algorithm Approach To solve this problem, we use a greedy approach ? For each position in our result, find the smallest ...
Read MoreProgram to get maximum profit by scheduling jobs in Python
Suppose we have a list of intervals where each interval contains three values [start, end, profit]. We can perform only one task at a time, and we have to find the maximum amount of profit we can get by scheduling non-overlapping jobs. So, if the input is like intervals = [[1, 2, 100], [3, 5, 40], [6, 19, 150], [2, 100, 250]], then the output will be 350, as we can take these two intervals [1, 2, 100] and [2, 100, 250]. Algorithm Overview To solve this problem, we will use dynamic programming with the following approach: ...
Read MoreProgram to find number of increasing subsequences of size k in Python
Given a list of numbers and a value k, we need to find the number of strictly increasing subsequences of size k. A subsequence maintains the relative order of elements but doesn't need to be contiguous. So, if the input is like nums = [2, 3, 4, 1] and k = 2, then the output will be 3, as we have the subsequences of size 2: [2, 3], [3, 4], [2, 4]. Approach Using Dynamic Programming We use dynamic programming where dp[i] represents the number of increasing subsequences of current length ending at position i ? ...
Read MoreProgram to find cost to reach final index of any of given two lists in Python
Suppose we have two lists of numbers nums0 and nums1 of the same length and two other values d as distance and c as cost. If we start from index 0 at either nums0 or nums1 and want to end up at the final index of either list. Now, in each round, we can select to switch to the other list for cost of cost. Then we can jump forward at most d distance away where the cost of landing at an index is the value at that point. So we have to find the minimum total cost possible to ...
Read MoreProgram to check we can cross river by stones or not in Python
Suppose we have a list of sorted numbers called stones representing the positions of stones on a river that we are trying to cross. To cross the river, we must finish at the last stone. In each step, we can jump (k - 1, k, or k + 1) steps ahead where k is the distance of the last jump. We have to check whether we can cross the river or not. So, if the input is like stones = [0, 1, 3, 4, 5, 6, 8, 9, 13], then the output will be True. We can start from ...
Read MoreProgram to find minimum number colors remain after merging in Python
Suppose we have a list of colors (R, G, B). When two different colors are adjacent, they can merge into a single color item of the third color. We need to find the minimum number of colors remaining after any possible sequence of such transformations. So, if the input is like colors = ["G", "R", "G", "B", "R"], then the output will be 1 as it can transform like below ? Initial: G R G ...
Read MoreProgram to find land with longest distance from water in Python
When given a binary matrix where 0 represents water and 1 represents land, we need to find the land cell with the longest Manhattan distance from any water cell. The Manhattan distance is the sum of absolute differences of coordinates. So, if the input matrix is ? 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 Then the output will be 3, as the cell at [0, 0] has a Manhattan distance of 3 from the nearest water. Algorithm ...
Read MoreProgram to count number of ways we can fill 3 x n box with 2 x 1 dominos in Python
Suppose we have a number n, we have to find the number of ways we can fill a (3 x n) block with 2 x 1 dominos. We can rotate the dominos when required. If the answer is very large then return this mod 10^9 + 7. For example, if the input is n = 4, then the output will be 11. Algorithm To solve this problem, we need to use dynamic programming. The key insight is that we can only fill a 3×n grid if n is even, because each domino covers 2 cells. We ...
Read MoreProgram to find nth term of a sequence which are divisible by a, b, c in Python
Given four numbers n, a, b, and c, we need to find the nth (0-indexed) term of the sorted sequence of numbers divisible by a, b, or c. For example, if n = 8, a = 3, b = 7, c = 9, the first 9 terms of the sequence are [3, 6, 7, 9, 12, 14, 15, 18, 21], so the 8th term (0-indexed) is 18. Approach We use binary search with the inclusion-exclusion principle to count numbers divisible by a, b, or c up to a given value ? If minimum of a, ...
Read MoreProgram to find length of the largest subset where one element in every pair is divisible by other in Python
Given a list of unique numbers, we need to find the largest subset where every pair of elements satisfies the divisibility condition: either i % j = 0 or j % i = 0. This means one element must divide the other in every pair. For example, if the input is nums = [3, 6, 12, 24, 26, 39], the output will be 4 because the largest valid subset is [3, 6, 12, 24] where 6 is divisible by 3, 12 is divisible by 6, and 24 is divisible by 12. Algorithm We use dynamic programming with ...
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