int main(int argc, char** argv) {
int ans = 0;
int chainLength = 1;
//78498 = pi^-1(1000000)
int* primes = (int*)malloc(78498 * sizeof(int));
int i = 2;
int c = 0;
//make list of primes
for (i = 0; i < 1000000; ++i) {
if (isPrime(i)) {
primes[c] = i;
++c;
}
}
int j;
for (i = 0; i < 78498; ++i) {
for (j = i+chainLength; j < 78498; ++j) {
int temp = partialSum(primes,i,j);
if (temp > 1000000) {
break;
}
if (isPrime(temp)) {
ans = temp > ans ? temp : ans;
chainLength = j - i;
}
}
}
printf("%d\n",ans);
return 0;
}
/**
* @param nums: A list of integers
* @return: A list of integers includes the index of the first number
* and the index of the last number
*/
vector<int> subarraySum(vector<int> nums){
vector<int> result;
if (nums.empty()) return result;
vector<pair<int, int>> partialSum(nums.size() + 1);
partialSum[0].first = 0;
partialSum[0].second = -1;
for(int i = 0; i < nums.size(); i++) {
partialSum[i+1].first = partialSum[i].first + nums[i];
partialSum[i+1].second = i;
if (partialSum[i+1].first == 0) {
result.push_back(0);
result.push_back(i);
return result;
}
}
sort(partialSum.begin(), partialSum.end());
for (int j = 1; j < partialSum.size()-1; j++) {
if (partialSum[j].first == partialSum[j+1].first) {
result.push_back(partialSum[j].second+1);
result.push_back(partialSum[j+1].second);
break; // only one solution is needed
}
}
return result;
}
UInt QuadratureRule::checkExactnessTriangle() const
{
// Degre 0: f=1 => exact value : 1/2
Real partialSum(0.0);
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += weight(iterQ);
}
if ( std::fabs(partialSum - 0.5) > S_exactnessTol)
{
return 0;
}
// Degre 1: f=x+y => exact value : 1/3
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0) + quadPointCoor(iterQ,1))
* weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/3.0) > S_exactnessTol)
{
return 0;
}
// Degre 2: f=x*x+3*x*y => exact value : 5/24
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)
+ 3*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,1))
* weight(iterQ);
}
if ( std::fabs(partialSum - 5.0/24.0) > S_exactnessTol)
{
return 1;
}
// Degre 3: f=x*x*y-5*x*y => exact value :-23/120
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,1)
- 5*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,1))
* weight(iterQ);
}
if ( std::fabs(partialSum + 23.0/120.0) > S_exactnessTol)
{
return 2;
}
// Degre 4: f=x*x*x*y - x*y*y + y*y*y*y => exact value : 1/40
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,1)
- quadPointCoor(iterQ,0)*quadPointCoor(iterQ,1)*quadPointCoor(iterQ,1)
+ quadPointCoor(iterQ,1)*quadPointCoor(iterQ,1)*quadPointCoor(iterQ,1)*quadPointCoor(iterQ,1) )
* weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/40.0) > S_exactnessTol)
{
return 3;
}
// Degre 5: f= x^4*y - x*y^2 + y^5 => exact value : 1/84
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += ( std::pow(quadPointCoor(iterQ,0),4.0)*quadPointCoor(iterQ,1)
-quadPointCoor(iterQ,0)*quadPointCoor(iterQ,1)*quadPointCoor(iterQ,1)
+ std::pow(quadPointCoor(iterQ,1),5.0)
) * weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/84.0) > S_exactnessTol)
{
return 4;
}
return 5;
}
UInt QuadratureRule::checkExactnessSegment() const
{
// Degre 0: f=1 => exact value : 1
Real partialSum(0.0);
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += weight(iterQ);
}
if ( std::fabs(partialSum - 1.0) > S_exactnessTol)
{
return 0;
}
// Degre 1: f=x => exact value: 1/2
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0))*weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/2.0) > S_exactnessTol)
{
return 0;
}
// Degre 2: f=x*x => exact value: 1/3
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0) )*weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/3.0) > S_exactnessTol)
{
return 1;
}
// Degre 3: f=x*x*x => exact value: 1/4
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0) )*weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/4.0) > S_exactnessTol)
{
return 2;
}
// Degre 4: f=x*x*x*x => exact value: 1/5
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)
)*weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/5.0) > S_exactnessTol)
{
return 3;
}
// Degre 5: f=x*x*x*x*x => exact value: 1/6
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)
*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)
*quadPointCoor(iterQ,0)
)*weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/6.0) > S_exactnessTol)
{
return 4;
}
return 5;
}
UInt QuadratureRule::checkExactnessTetra() const
{
// Degre 0: f=1 => exact value : 1/6
Real partialSum(0.0);
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/6.0) > S_exactnessTol)
{
return 0;
}
// Degre 1: f=x+y+2z => exact value: 1/6
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0) + quadPointCoor(iterQ,1) + 2*quadPointCoor(iterQ,2) )*weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/6.0) > S_exactnessTol)
{
return 0;
}
// Degre 2: f=x*x + y*z + y*y => exact value: 1/24
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)
+ quadPointCoor(iterQ,1)*quadPointCoor(iterQ,2)
+ quadPointCoor(iterQ,1)*quadPointCoor(iterQ,1)
)*weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/24.0) > S_exactnessTol)
{
return 1;
}
// Degre 3: f=x*x*x + y*y + y*y*z + x => exact value: 5/72
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)
+ quadPointCoor(iterQ,1)*quadPointCoor(iterQ,1)
+ quadPointCoor(iterQ,1)*quadPointCoor(iterQ,1)*quadPointCoor(iterQ,2)
+ quadPointCoor(iterQ,0)
)*weight(iterQ);
}
if ( std::fabs(partialSum - 5.0/72.0) > S_exactnessTol)
{
return 2;
}
// Degre 4: f=x*x*x*x +y*y*z*z + z*z*z => exact value: 1/72
partialSum=0.0;
for (UInt iterQ(0); iterQ<M_nbQuadPt; ++iterQ)
{
partialSum += (quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)*quadPointCoor(iterQ,0)
+ quadPointCoor(iterQ,1)*quadPointCoor(iterQ,1)*quadPointCoor(iterQ,2)*quadPointCoor(iterQ,2)
+ quadPointCoor(iterQ,2)*quadPointCoor(iterQ,2)*quadPointCoor(iterQ,2)
)*weight(iterQ);
}
if ( std::fabs(partialSum - 1.0/72.0) > S_exactnessTol)
{
return 3;
}
return 4;
}
