C语言、数据结构、算法

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:1, 3, 6, 10, 15, 21, 2...

A Pythagorean triplet is a set of three natural numbers, a  b  c, for which,a2 + b2 = c2For example, 32 + 42 = 9 + 16 = 25 = 52.There exists exactly one Pythagorean triplet for which a + b +...

You are given the following information, but you may prefer to do some research for yourself.1 Jan 1900 was a Monday.Thirty days has September,April, June and November.All the rest have thirty-...

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:21 22 23 24 2520  7   8   9  1019  6   1   2  1118  5   4   3  1217 16 15 14 13It...

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.Find the sum of all numbers which are equal to the sum of the factorial of their digits.Note: as 1! = 1 and 2! = 2 are not sums they...

Consider all integer combinations of ab for 2  a  5 and 2  b  5:22=4, 23=8, 24=16, 25=3232=9, 33=27, 34=81, 35=24342=16, 43=64, 44=256, 45=102452=25, 53=125, 54=625, 55=3125If they are then plac...

The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that49/98 = 4/8, which is correct, is obtained by cancelling the 9s....

The sum of the squares of the first ten natural numbers is,12 + 22 + ... + 102 = 385The square of the sum of the first ten natural numbers is,(1 + 2 + ... + 10)2 = 552 = 3025Hence the differ...

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.What is the 10 001st prime number? 题目大意：前六个质数是2,3,5,7,11和13，其中第6个是13.第10001个质数是多少？#inc...

The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 7...

A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.For example,44  32  13  10  1  185  89  145  42  20  4  1...

Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).If d(a) = b and d(b) = a, where a  b, then a and b are an amicable pair and each of a and b ar...

The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...By converting each letter in a word to a...

The decimal number, 585 = 10010010012 (binary), is palindromic in both bases.Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.(Please note that the ...

The following iterative sequence is defined for the set of positive integers:n  n/2 (n is even)n  3n + 1 (n is odd)Using the rule above and starting with 13, we generate the following sequence:...

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.9 = 7 + 21215 = 7 + 22221 = 3 + 23225 = 7 + 23227 = 19 + 22233 = 31 + 2...

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.What is the largest n-digit pand...

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.Find the sum of all the multiples of 3 or 5 below 1000.#include &...

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...By considering t...

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.What is the smallest positive number that is evenly divisible by all of the numbers from 1...

215 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.What is the sum of the digits of the number 21000? 题目大意：215 = 32768 并且其各位之和为 is 3 + 2 + 7 + 6 + 8 = 26.21000 的各位数之和是多少？ ...

If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.If all the numbers from 1 to 1000 (one thousand) inclusive ...

Using names.txt (right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical ...

The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we c...