2.0 KiB
2.0 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3b91000cf542c50fecc | Problem 77: Prime summations | 5 | 302190 | problem-77-prime-summations |
--description--
It is possible to write ten as the sum of primes in exactly five different ways:
7 + 3
5 + 5
5 + 3 + 2
3 + 3 + 2 + 2
2 + 2 + 2 + 2 + 2
5 + 5
5 + 3 + 2
3 + 3 + 2 + 2
2 + 2 + 2 + 2 + 2
What is the first value which can be written as the sum of primes in over n
ways?
--hints--
primeSummations(5)
should return a number.
assert(typeof primeSummations(5) === 'number');
primeSummations(5)
should return 11
.
assert.strictEqual(primeSummations(5), 11);
primeSummations(100)
should return 31
.
assert.strictEqual(primeSummations(100), 31);
primeSummations(1000)
should return 53
.
assert.strictEqual(primeSummations(1000), 53);
primeSummations(5000)
should return 71
.
assert.strictEqual(primeSummations(5000), 71);
--seed--
--seed-contents--
function primeSummations(n) {
return true;
}
primeSummations(5);
--solutions--
function primeSummations(n) {
function getSievePrimes(max) {
const primesMap = new Array(max).fill(true);
primesMap[0] = false;
primesMap[1] = false;
const primes = [];
for (let i = 2; i < max; i += 2) {
if (primesMap[i]) {
primes.push(i);
for (let j = i * i; j < max; j += i) {
primesMap[j] = false;
}
}
if (i === 2) {
i = 1;
}
}
return primes;
}
const MAX_NUMBER = 100;
const primes = getSievePrimes(MAX_NUMBER);
for (let curNumber = 2; curNumber < MAX_NUMBER; curNumber++) {
const combinations = new Array(curNumber + 1).fill(0);
combinations[0] = 1;
for (let i = 0; i < primes.length; i++) {
for (let j = primes[i]; j <= curNumber; j++) {
combinations[j] += combinations[j - primes[i]];
}
}
if (combinations[curNumber] > n) {
return curNumber;
}
}
return false;
}