This is more of a refresher for people that learned combinations and permutations but then later forgot the formula [like me]. How many combinations of wins are there in 12 football games? If so, could you do another explanation in that field, I have been reading your posts and this one and the ones on e and ln are terribly interesting.
It turns out to be quite easy about one page of code for the main idea and two pages for embellishments using two ideas: Sudoku Notation and Preliminary Notions First we have to agree on some notation.
A Sudoku puzzle is a grid of 81 squares; the majority of enthusiasts label the columnsthe rows A-I, and call a collection of nine squares column, row, or box a unit and the squares that share a unit the peers. A puzzle leaves some squares blank and fills others with digits, and the whole idea is: A puzzle is solved if the squares in each unit are filled with a permutation of the digits 1 to 9.
That is, no digit can appear twice in a unit, and every digit must appear once. This implies that each square must have a different value from any of its peers. Here are the names of the squares, a typical puzzle, and the solution to the puzzle: For example, here are the units and peers for the square C2: So read this assignment statement as "units is a dictionary where each square maps to the list of units that contain the square".
Similarly, read the next assignment statement as "peers is a dictionary where each square s maps to the set of squares formed by the union of the squares in the units of s, but not s itself".
It can't hurt to throw in some tests they all pass: Actually we need two representations: First, a textual format used to specify the initial state of a puzzle; we will reserve the name grid for this. Second, an internal representation of any state of a puzzle, partially solved or complete; this we will call a values collection because it will give all the remaining possible values for each square.
For the textual format grid we'll allow a string of characters with indicating a digit, and a 0 or period specifying an empty square. All other characters are ignored including spaces, newlines, dashes, and bars.
So each of the following three grid strings represent the same puzzle: One might think that a 9 x 9 array would be the obvious data structure. But squares have names like 'A1', not 0,0. Therefore, values will be a dict with squares as keys. The value of each key will be the possible digits for that square: This collection of digits could be represented by a Python set or list, but I chose instead to use a string of digits we'll see why later.
Here is the code to parse a grid into a values dict: Those with experience solving Sudoku puzzles know that there are two important strategies that we can use to make progress towards filling in all the squares: These updates to A2 may in turn cause further updates to its peers, and the peers of those peers, and so on.
This process is called constraint propagation. The function assign values, s, d will return the updated values including the updates from constraint propagationbut if there is a contradiction--if the assignment cannot be made consistently--then assign returns False.
For example, if a grid starts with the digits ' It turns out that the fundamental operation is not assigning a value, but rather eliminating one of the possible values for a square, which we implement with eliminate values, s, d.
Once we have eliminate, then assign values, s, d can be defined as "eliminate all the values from s except d". Return values, except return False if a contradiction is detected.SBI PO Exam SBI PO NOTIFICATION OUT!!!!
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"My fruit salad is a combination of apples, When the order does matter it is a Permutation. So, we should really call this a "Permutation Lock"! In other words: A Permutation is an ordered Combination. Combinations and Permutations Calculator Pascal's Triangle Lotteries.
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Permutations and Combinations: An Easy Method. by Ron Corcillo on October 12th, 81 comments. It's a combination question, not permutation, because the order in which the members are chosen or placed does not matter (questions about forming teams or committees are usually combination questions.) Here's how to do each scenario.
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