Prepared for New Acmerhttp: // acm.hdu.edu.cn/showproblem.php? Pid = 1420 Montgomery power mode idea:
In power modulo operations, a power modulo operation is usually used to convert a power modulo operation to a Multiplication Modulo operation.
NYOJ modulo of the power of 102
Power modulus time limit: 1000 MS | memory limit: 65535 KB difficulty: 3
Description
Evaluate the remainder of a's power B on c
Input
Enter an integer n in the first line to
For an integer, a, or a method to find the remainder of the operation is divided into the following two steps:
1. Seeking integer quotient: c=a/b
2. Calculating the modulus or remainder: r=a-(c*b)
Modulo operation and redundancy operation are
I. Problem description:
Calculate (a ^ power) % m, where power is a non-negative big integer, A, M is an integer greater than 1.
Ii. Problem Analysis:
Obviously, power is a big integer, so the overflow of Power computing must be considered. How can
I think a lot of people do not know the difference between these two concepts, just in the translation of the LUA manual with the math.fmod of the two operations, by the way to explain it.
The difference between the modulus and the remainder is
Transmission DoorLarge number of 1116 K-Input systemBase time limit: 1 seconds space limit: 131072 KB score: 20 Difficulty: 3-Level algorithm topic collection concernThere is a string s, record a large number, but do not know how much this large
Power modulus time limit: 1000 MS | memory limit: 65535 kb difficulty: 3
Description
Evaluate the remainder of A's power B on C
Input
Enter an integer N in the first line to indicate the number of groups of
Topic linksJzzhu have invented a kind of sequences, they meet the following property: You is given x and y, please calculate fn modulo 1000000007 (Ten9?+?7). InputThe first line contains integers x and y (| X|,?| y|? ≤?109). The
[ACM] hdu 3037 Saving Beans (Lucas theorem, modulo of composite number)
Saving Beans
Problem DescriptionAlthough winter is far away, squirrels have to work day and night to save beans. they need plenty of food to get through those long cold days.
See the definition of the ACM-ICPC series of number theory, the modulo operation is such a son.Given a positive integer p, any integer n, there must be an equation: n = kp + R, where K, R is an integer, and 0≤r 0 so unhappy, wrote a program test
A very interesting phenomenon has been found today.As a division, Python2 and C + + have different divisible results in the case of negative numbers:When I was 5/3,Results for C + +: 1Results for Python2:2(Note that 5/-3 is still available in C + +-1
Proof and use of Barrett reduction algorithm.
The author has just finished the course design work, free to write an article.
Exponential operations in large numbers require a number to be modeled, because the maximum possible binary is 2048 bits
When B is large, use thisAlgorithmIs the best choice. It is often used in cryptography:
Code:
/* File: ABN. cdescription: Generic algorithm for finding a's B power modulo n Author: hanxi */ # Include # Include Int F ( Int A, Int B, Int N ){
Question: Give You A sequence for you to find out how many combinations can get 2048. The result is to get more than 998244353.
Solution: Find the number of solutions that cannot meet the conditions, and then subtract the total number from the
Whether it is good to take the model or not, it frees the majority of oier from the abyss of high precision.
However, the modulo operation is not always so convenient.
For example, division is inevitable in our operations.
Most of the time, the
Saving beans
Problem descriptionalthough winter is far away, squirrels have to work day and night to save beans. they need plenty of food to get through those long cold days. after some time the squirrel family thinks that they have to solve a
You have to colorM X N(1M,N108) Two dimen1_grid. You will be providedK(2K108) different colors to do so. You will also be provided a listB(0B500) List of blocked cells of this grid. You cannot color those blocked cells. A cell can be described (X,Y),
When it comes to calculating the parity of numbers, it is common to use "and" and "modulo", so which of these two operations are implemented in PHP language, which is faster? Before the comparison, I was inclined to the former. But it turned out to
1. Negative Division:>>> Print 45/76>>> PRINT-45/7-7>>> Print 45/-7-7>>> print-45/-76For the first example: the first number contains the number of the second number 45 contains how many 7 its result is 6For the second example: what is the distance
For the 2004^x factor and modulo 29, sum (2004^X) represents the 2004^x factor and sum (2004^x) =sum (4^x*3^x*167^x), sum () is a integrable function,
Then there is sum (2004^x)%29=sum (4^x) *sum (3^x) *sum (167^x)%29
=sum (2^ (2*x)) *sum (3^x) *sum
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