You are given a matrix grid of size m x n filled with positive integers. Starting from any cell in the first column, you can move to any of the cells on the next column (right) that are strictly greater than the value of the current cell. The possible directions you can move to are: the cell directly to the right, the cell diagonally to the top-right, or the cell diagonally to the bottom-right. Your task is to return the maximum number of moves that you can perform by starting at any cell in the first column.
You are given a string and a list of words. Your task is to break the string into one or more non-overlapping substrings such that each substring is a word from the given list. However, some characters of the string may not be used in any substring. Your goal is to minimize the number of unused characters.
You are given an integer array representing the scores of students in an exam. Your task is to form a non-empty group of students such that the group’s strength, defined as the product of their scores, is maximized. The goal is to return the maximum possible strength that can be achieved by choosing an optimal group of students.
You are given a binary string s of length n. You can perform two types of operations: (1) Flip all characters from index 0 to i (inclusive), with a cost of i + 1. (2) Flip all characters from index i to n - 1 (inclusive), with a cost of n - i. The goal is to return the minimum cost required to make all the characters in the string equal (either all 0s or all 1s).
You are given a list of distinct positive integers nums. A permutation of nums is considered special if, for every pair of consecutive numbers in the permutation, one number is divisible by the other. Your task is to return the total number of special permutations of nums, modulo 10^9 + 7.