ImageColor WaterShedDecomposer::filterGaussSinglePass(ImageColor const & image, int r) const {
r = std::max(1, r);
int n = (r<<1) + 1;
// create kernel
unsigned long long * kernel = new unsigned long long[n];
for (int i=0; i<r; ++i) {
kernel[i] = kernel[n-i-1] = nCr(n-1, i);
}
kernel[r] = nCr(n-1, r);
ImageColor filtered(image.height(), image.width());
for (int y=0; y<image.height(); ++y) {
for (int x=0; x<image.width(); ++x) {
Color color;
unsigned long long weights = 0;
for (int i=0; i<n; ++i) {
if (x-r+i >= 0 && x-r+i < image.width()) {
color += image.at(x-r+i, y) * kernel[i];
weights += kernel[i];
}
}
filtered.at(y, x) = color / double(weights);
}
}
delete[] kernel;
return filtered;
}
int nCr(int n, int r){
if(r==0){
return 1;
}
else if(r==n){
return 1;
}
else{
nCr(n-1, r-1) + nCr(n-1,r);
}
}
int nCr(int n, int r)
{
if(r==0 || r==n)
return 1;
if(r==1 || r==n-1)
return n;
if(ara[n][r]!=-1)
return ara[n][r];
else
{
ara[n][r]=nCr(n-1,r)+nCr(n-1,r-1);
return ara[n][r];
}
}
float /* RET - time (seconds) */
old_probs_estimate(
TREE *tree, /* IN - tree */
int max_order, /* IN - number of cut sets */
int min_term, /* IN - min number of terms to evaluate */
int max_term) /* IN - max number of terms to evaluate */
{
int num_mcs; /* number of cut sets used */
float t = 0;
int i;
/* TimeEstimate Base; */
/* find out how many cut sets are actually used */
num_mcs = ExprCountOrder(tree->mcs_expr, max_order);
for (i = min_term; i <= max_term; i++) {
/* t += (CONST_A + CONST_B * i) * nCr(num_mcs, i); */
t += nCr(num_mcs, i);
}
/* return t * tree->num_bas; */
/* return t * tree->num_bas * ( BaseTimeEstimate() / 2500.0 ); */
/* return t * tree->num_bas * ( Base.ReferenceEstimate() / 2500.0 ); */
return t * tree->num_bas * ( ReferenceEstimate() / 2500.0 );
} /* probs_estimate */
double PostCal::totalLikelihood(double * stat, double NCP) {
int num = 0;
double sumLikelihood = 0;
double tmp_likelihood = 0;
long int total_iteration = 0 ;
int * configure = (int *) malloc (snpCount * sizeof(int *)); // original data
for(long int i = 0; i <= maxCausalSNP; i++)
total_iteration = total_iteration + nCr(snpCount, i);
for(long int i = 0; i < snpCount; i++)
configure[i] = 0;
for(long int i = 0; i < total_iteration; i++) {
tmp_likelihood = likelihood(configure, stat, NCP) * (pow(SMALL, num))*(pow(1-SMALL, snpCount-num));
sumLikelihood += tmp_likelihood;
for(int j = 0; j < snpCount; j++) {
postValues[j] = postValues[j] + tmp_likelihood * configure[j];
}
histValues[num] = histValues[num] + tmp_likelihood;
num = nextBinary(configure, snpCount);
if(i % 1000 == 0)
cout << i << " " << sumLikelihood << endl;
}
for(int i = 0; i <= maxCausalSNP; i++)
histValues[i] = histValues[i]/sumLikelihood;
free(configure);
return(sumLikelihood);
}
main()
{
int N = 50;
int R = 5;
int *x, *z;
int n;
int i;
n = nCr(N, R);
printf("%dC%d = %d\n", N, R, n);
/*
n = nPr(N, R);
printf("%dP%d = %d\n", N, R, n);
*/
if ( (x = (int *)malloc( N * sizeof(int) )) == NULL ) {
printf("*** malloc failed for x\n");
exit(1);
}
for(i=0; i<N; i++) {
x[i] = i+1;
}
if ( (z = (int *)malloc( N * sizeof(int) )) == NULL ) {
printf("*** malloc failed for z\n");
exit(1);
}
combs(x, N, R, z, 0, comb_count, &n);
/* perms(x, N, R, z, 0, vec_print, NULL); */
}
/*---------------------------------------------------------------
Routine : nKr
Purpose : Calculate sum of nCi, for i = 0 to r.
Direct sum
---------------------------------------------------------------*/
float
nKr( int n, int r)
{
float result = 0;
while( r >= 0 ) {
result += nCr(n, r--);
}
return result;
} /* nKr */
void gvp_space::get_score(float* &dataset_score)
{
// For each dataset
for (space_freq_iter space_freq_it = space_freq.begin(); space_freq_it != space_freq.end(); space_freq_it++)
{
size_t dataset_id = space_freq_it->first;
float score = 0.0f;
// Prepare score space and initialize
float* score_list = new float[total_space];
for (int score_id = 0; score_id < total_space; score_id++)
score_list[score_id] = 0.0f;
/// Accumulate score from each space
for (int space_id = 0; space_id < total_space; space_id++)
{
ncr_score space_bin_score = space_freq[dataset_id][space_id];
if (space_bin_score >= (ncr_score)_gvp_length)
{
//cout << "space[space_id]:" << space[space_id] << " space_id:" << space_id << " _gvp_length:" << _gvp_length << endl;
///-- tf for frequency is necessary for too big value, wtf = 1 + log10(freq)
///-- idf is necessary for emphasizing the important word
//score_list[space_id] = (1 + log10(nCr(space_bin_score - 1, _gvp_length - 1))) * space_idf[dataset_id][space_id]; // tf-idf with ncr minus 1
//score_list[space_id] = (1 + log10(nCr(space_b in_score - 1, _gvp_length - 1))) * space_idf[dataset_id][space_id]; // tf-idf
//score_list[space_id] = nCr(space_bin_score, _gvp_length) * space_idf[dataset_id][space_id]; // idf
//score_list[space_id] = 1 + log10(nCr(space_bin_score, _gvp_length)); // tf
score_list[space_id] = log10(nCr(space_bin_score, _gvp_length) * space_idf[dataset_id][space_id]); // tf-idf
//score_list[space_id] = log10(nCr(space_bin_score, _gvp_length)); // tf
}
}
/// Normalization
// Unit length
float sum_of_square = 0.0f;
float unit_length = 0.0f;
for (int score_id = 0; score_id < total_space; score_id++)
sum_of_square += score_list[score_id] * score_list[score_id];
unit_length = sqrt(sum_of_square);
// Normalizing
for (int score_id = 0; score_id < total_space; score_id++)
score_list[score_id] = score_list[score_id] / unit_length;
/// Calculate total score
for (int score_id = 0; score_id < total_space; score_id++)
score += score_list[score_id];
// Release memory
delete[] score_list;
//cout << "score:" << score << endl;
dataset_score[dataset_id] = score;
}
}
int main() {
ullong total = 0;
for(long long x = 0; x <= 5; ++x) {
for(long long y = 0; y <= 5; ++y) {
if((isPerfectSquare(y)) && (isPerfectSquare(x)) && (isPerfectSquare(x+y))) {
++total;
std::cout << '(' << x << ", " << y << ")\n";
}
}
}
std::cout << total << "\nnCr: " << nCr(10, 5);
}
int main()
{
int t;
i64 n, r;
scanf("%d", &t);
while(t--)
{
scanf("%llu %llu", &n, &r);
printf("%llu\n", nCr(n-1, r-1));
}
return 0;
}
int main()
{
int c,n,t,p;
scanf("%d",&c);
nCr(141,71);
while(c--)
{
scanf("%d %d %d",&n,&t,&p);
printf("%llu\n",comb[t-n*p+n-1][n-1]);
}
return 0;
}
unsigned long long WaterShedDecomposer::nCr(int n, int r) const {
if (r<<1 > n) {
return nCr(n, n-r);
}
else {
unsigned long long result = 1;
for (int i=1; i<=r; ++i) {
result *= n - r + i;
result /= i;
}
return result;
}
}
int main(int argc, char* argv[]){
int n,r;
int count = 0;
int check = 0;
for(n=1;n <= 100;n++){
for(r=n;r >0;r--){
if(nCr(n,r) > 1000000){
count++;
}
}
}
printf("count = %d\n",count);
return 0;
}
int _Problem053() {
int n, r;
int count = 0;
int val;
for(n=1;n<100;n++) {
for(r=1;r<n;r++) {
val = nCr(n,r);
if(val>1000000) {
count++;
} } }
printf("%30d", count);
return 0;
}
int nCr(int n, int r, int start, int prev_val)
{
static int count =0;
int j;
if(start ==r)
{
count++;
return count;
}
for(j= prev_val;j<=(n-(r-start));j++)
{
nCr(n,r,start+1,j+1);
}
return count;
}
int main()
{
int i,j,n,r;
memset(ara,-1,sizeof(ara));
while(scanf("%d%d",&n,&r)==2)
{
if(n==0 || r==0)break;
printf("%d\n",nCr(n,r));
}
return 0;
}
double molecule_t::calculateAbundance(composition_t composition)
{
double totalAbundance = 1;
for (composition_t::iterator it = composition.begin(); it != composition.end(); it++)
{
if (it.key()->isotopeOf() != NULL && it.key()->isotopeOf() > 0) // If an isotope of an element is present, calculate its count and abundance
{
int countThisIsotope = it.value();
int countParentElement = composition.find(it.key()->isotopeOf()).value();
double abundance = it.key()->abundance();
totalAbundance = (totalAbundance * pow(abundance,countThisIsotope) * nCr(countParentElement+countThisIsotope,countThisIsotope));
}
}
return totalAbundance;
}
int main(int argc, char *argv[])
{
int n;
printf("Enter the number of rows\n");
scanf("%d", &n);
int i, j, k;
for (i=0;i<n;i++){
for(j=n-i;j>0;j--){ // Insert white space total number of rows - row that is currently printed
printf(" ");
}
for(k=0;k<=i;k++){
printf("%d ", nCr(i,k));
}
printf("\n");
}
}
/* A sample main function */
int main()
{
LLI n,m,l;
while(scanf("%lld%lld%lld",&l,&n,&m)!=EOF)
{
l=l*l;
LLI sum=0;
for( LLI i=n; i<=m; i++ )
{
//printf("35 %lld\n",nCr(l,i));
for( int j=l; j>=i; j-- )
sum=((sum%mod)+nCr(j,1)%mod)%mod;
printf("38 %lld\n",sum);
}
}
return 0;
}
int main(int argc, char** argv) {
struct timeval start, end;
gettimeofday(&start, NULL);
if (argc < 2) {
fprintf(stderr,"Not enough arguments\n");
return 0;
}
else if (argc > 2) {
fprintf(stderr,"Too many arguments\n");
return 0;
}
if (strcmp(argv[1],"-h") == 0) {
printf("Usage: formula <positive integer>\n");
return 0;
}
curr_state = mightBeDecFirstNum;
if (checkInt(argv[1]) == 1) {
fprintf(stderr,"Input not in positive integer form\n");
return 0;
}
int n = atoi(argv[1]);
if (factorial(n) == 0) {
fprintf(stderr,"Overflow detected\n");
return 0;
}
printf("(1 + x)^%d = 1",n);
int i = 1, fact;
for (i; i <= n; i++) {
fact = nCr(n,i);
printf(" + %d*x^%d",fact,i);
}
printf("\n");
gettimeofday(&end, NULL);
printf("%ld microseconds\n", ((end.tv_sec * 1000000 + end.tv_usec) - (start.tv_sec * 1000000 + start.tv_usec)));
return 0;
}
int main()
{
init();
unsigned long int n;
int ans;
scanf("%ld",&n);
if(n<13)
ans=0;
else
{
n-=13;
if (n&1)
n-=1;
n=n>>1;
ans=nCr(n+7-1,n);
}
printf("%d\n",ans);
return 0;
}
int main()
{
int t, r, n;
int N, T, P;
//freopen( "in.in", "r", stdin );
scanf( "%d", &t );
while ( t-- )
{
scanf( "%d %d %d", &N, &T, &P );
r = T - N * P;
n = N;
printf( "%lld\n", nCr( n + r - 1, r ) );
}
return 0;
}
int Account1(long double &a,long double b,char c)//双目算术运算
{
switch(c)
{
case'+':
a+=b;
break;
case'-':
a-=b;
break;
case'*':
a*=b;
break;
case'/':
{
if(b==0)
return 0;
a/=b;
break;
}
case'%':
{
if(b==0)
return 0;
a=fmod(a,b);
break;
}
case'^':
a=pow(a,b);
break;
case'A':
return nAr(a,a,b);
case'C':
return nCr(a,a,b);
default:
return 0;
}
return 1;
}
int main(){
int n,m;
scanf("%d %d", &n, &m);
int index;
permutations[0] = 1;
for(index = 0; index <= m; index ++){
calpermutations(index, m);
}
permutations2[0][0] = 1;
permutations2[1][0] = 1;
int i,j;
for(i = 2; i <= 4000; i++){
permutations2[i][0] = 1;
for(j = 1; j <= i; j ++){
permutations2[i][j] = nCr(i, j);
}
}
printf("\n%lld\n",permutations[8]);
printf("\n%lld\n",permutations2[57][8]);
return 0;
}
float /* RET - time (seconds) */
probs_estimate(
TREE *tree, /* IN - tree */
int max_order, /* IN - number of cut sets */
int min_term, /* IN - min number of terms to evaluate */
int max_term) /* IN - max number of terms to evaluate */
{
int num_mcs; /* number of cut sets used */
float t = 0;
int i,j;
Group **index; /* index to the groups */
int *z;
Group *p; /* pointer */
clock_t time1, time2;
BitArray *stop = BitCreate(1); /* 1-bit zero */
float *probs;
/* TimeEstimate Base; */
/* find out how many cut sets are actually used */
num_mcs = ExprCountOrder(tree->mcs_expr, max_order);
/* make sure that max_term does not exceed number of mcs */
/* if number of mcs is zero then return 0 */
if(num_mcs == 0) {
return 0.0f;
} else if (max_term > num_mcs) {
max_term = num_mcs;
}
/* allocate memory required for testing */
if ( !fNewMemory( (void *)&probs, ( tree->num_bas * sizeof(float) ) ) )
{
exit(1);
}
if ( !fNewMemory( (void *)&index, ( num_mcs * sizeof(Group *) ) ) )
{
exit( 1 );
}
if ( !fNewMemory( (void *)&z, ( num_mcs * sizeof(int) ) ) )
{
exit( 1 );
}
/* populate the arrays with default data */
for(i=0, p=tree->mcs_expr; i<num_mcs; i++, p=p->next) {
index[i] = p;
z[i] = i;
}
/* fill the probs array */
get_probs( probs );
/* set the static variables to sensible values */
set_basic_n(tree->num_bas);
set_prob_term(0.0);
set_basic_prob(probs);
/* The function that takes most of the time is calc_sub_term().
Run this function for each number of terms required. Run it
enough times for the CPU clock to change. */
for (i = min_term; i <= max_term; i++) {
time1 = clock();
j = 0;
do {
calc_sub_term(z, i, index);
j++;
time2 = clock();
} while(time1 == time2);
t += nCr(num_mcs, i) * (time2 - time1) / j;
}
FreeMemory(index);
FreeMemory(z);
FreeMemory(probs);
return t/CLOCKS_PER_SEC;
} /* probs_estimate */
int main(int argc, char ** argv){
//check for extra arguements
if(argc != 2){
fprintf(stderr, "Incorrect number of arguements\n");
return -1;
}
char *input = argv[1];
int j ;
//check for usage flag
if(strlen(input) > 1){
if(input[0] == '-' && input[1] == 'h'){
fprintf(stderr, "Usage: formula <positive integer>\n\n");
return -1;
}
}
//check for error
for(j = 0; j < strlen(input); j++){
if(isdigit(input[j]) == 0){
fprintf(stderr, "Incorrect input\n\n");
return -1;
}
}
struct timeval start, end;
int val = atoi(argv[1]);
if(val < 0){
fprintf(stderr, "Incorrect input \n\n");
return -1;
}
if(val > 20){
fprintf(stderr, "Overflow\n\n");
return 0;
}
//check for overflow
printf("(1 + x)^%d = 1", val);
gettimeofday(&start, NULL);
//calculates coeffecient and prints it
if(val == 0){
printf("\n");
gettimeofday(&end, NULL);
printf("%ld Milliseconds \n", ((end.tv_sec * 1000000 + end.tv_usec) - (start.tv_sec * 1000000 + start.tv_usec)));
return 0;
}
else{
int i;
int coeff;
for(i = 1; i <= val; i++){
coeff = nCr(val, i);
printf(" + %d*x^%d", coeff, i);
}
printf("\n");
}
gettimeofday(&end, NULL);
//prints time
printf("%ld Milliseconds \n", ((end.tv_sec * 1000000 + end.tv_usec) - (start.tv_sec * 1000000 + start.tv_usec)));
return 0;
}
int main () {
int i;
printf("gi");
printf("%d\n", Factorial(5));
printf("%d\n", nCr(5, 2));
}
/*---------------------------------------------------------------
Routine : calculate_probs
Purpose : Calculate the probabilities for the tree, based upon
the minimal cut sets.
---------------------------------------------------------------*/
BOOL
calculate_probs(
char *filename, /* IN - filename to write report to */
TREE *tree, /* IN - tree */
int max_order, /* IN - max order of cut sets to use */
int prob_n_terms, /* IN - number of terms in expansion */
float unit_time ) /* IN - unit time factor to be applied */
{
BitArray *stop = BitCreate(1); /* 1-bit zero */
FILE *file;
Expr e;
Group *g;
float *probs, *cp, *imp;
float p;
int num_bas, num_mcs, i, j;
/* char *mcs_file; */
/* int order; */
clock_t time1, time2;
time_t tp;
BOOL success = TRUE;
float one_increment /* value for one increment of the progress bar */;
/* start clock */
time1 = clock();
if ( (file = fopen(filename, "w")) == NULL) {
printf("*** calculate_probs : error opening file\n");
return FALSE;
}
/* printf("calculate_probs()\n"); */
/* include transfered-in trees and build the primary event list
*
* We need to do something different to deal with Common Cause Analysis
* We don't need the tree, but we do need the primary event list.
* Need to add the common cause events into the primary event list.
*/
/* if necessary, expand tree */
expand_tree(tree);
/* set probs in BASLIST from the events database */
set_bas_prob( unit_time );
/* get number of primary events */
if ((num_bas = tree->num_bas) == 0) {
fclose( file );
return FALSE;
}
if (GenerateNumericalProbabilityCheckForInterrupt()) {
success = FALSE;
fclose( file );
return success;
}
/* create array of probabilities of primary events */
if ( !fNewMemory( (void *)&probs, ( num_bas * sizeof(float) ) ) )
{
printf("\n*** calculate_probs 1 : malloc failed ***\n");
exit(1);
}
if ( !fNewMemory( (void *)&imp, ( num_bas * sizeof(float) ) ) )
{
printf("\n*** calculate_probs : malloc failed ***\n");
exit(1);
}
/* fill array */
get_probs( probs );
/* get mcs list */
e = tree->mcs_expr;
/* num_mcs = ExprCount(e); */
/* how many mcs are actually used? */
num_mcs = ExprCountOrder(tree->mcs_expr, max_order);
/* make sure that max_term does not exceed number of mcs */
/* if number of mcs is zero then return FALSE */
if(num_mcs == 0) {
return FALSE;
} else if (prob_n_terms > num_mcs) {
prob_n_terms = num_mcs;
}
/* initialise Working dialog */
/* most of the cpu time is taken up in the ExprProb() function */
/* the working dialog is incremented in the combs() function */
one_increment = 0.0;
for(i = 1; i <= prob_n_terms; i++) {
one_increment += nCr(num_mcs, i);
}
/* set up progress bar */
one_increment /= 100.0;
set_one_increment(one_increment);
GenerateNumericalProbabilitySetProgressBarMax(100);
/* ExprPrint(e); */
/* print header */
fprintf(file,
"Probabilities Analysis\n"
"======================\n\n");
fprintf(file, "Tree : %s\n", tree->name);
time(&tp);
fprintf(file, "Time : %s\n", ctime(&tp));
fprintf(file, "Number of primary events = %d\n", num_bas);
fprintf(file, "Number of minimal cut sets = %d\n", num_mcs);
fprintf(file, "Order of minimal cut sets = %d\n", tree->max_order);
if (max_order < tree->max_order) {
fprintf(file, " (order <= %d used)\n\n", max_order);
} else {
fprintf(file, "\n");
}
fprintf(file, "Unit time span = %f\n\n", unit_time);
/* calculate cut set probabilities - use ALL the cut sets */
cp = ExprCutsetProbs(e, probs);
fprintf(file, "Minimal cut set probabilities :\n\n");
i = 0;
for(g=e; !BitEquals(g->b, stop); g=g->next) {
char **fp = BitPara( g->b, 30 );
/* printf("(%3d) %s %-20s - %E\n", */
/* i+1, */
/* BitString(g->b), */
/* fp[0], */
/* cp[i]); */
/* */
/* for (j = 1; fp[j] != NULL; j++) { */
/* printf(" %-20s\n", fp[j]); */
/* } */
if (GenerateNumericalProbabilityCheckForInterrupt()) {
success = FALSE;
CleanUpOperations(
file,
probs,
cp,
imp,
stop);
ParaDestroy(fp);
return success;
}
fprintf(file,
"%3d %-30s %E\n",
i+1,
fp[0],
cp[i]);
for (j = 1; fp[j] != NULL; j++) {
fprintf(file,
" %-20s\n", fp[j]);
}
ParaDestroy(fp);
i++;
}
/* calculate top level probability - use only up to max_order cut sets */
fprintf(file, "\n\n"
"Probability of top level event "
"(minimal cut sets up to order %d used):\n\n", max_order);
p = 0;
for (i = 1; i <= prob_n_terms && i <= num_mcs && !GenerateNumericalProbabilityCheckForInterrupt(); i++) {
float term;
char *sign, *s, *bound;
p += (term = ExprProb(e, probs, max_order, i));
sign = ((i % 2) ? "+" : "-" );
s = ((i > 1) ? "s" : " " );
bound = ((i % 2) ? "upper" : "lower" );
fprintf(file, "%2d term%s %s%E = %E (%s bound)\n",
i, s, sign, fabs(term), p, bound);
}
if (prob_n_terms >= num_mcs) {
fprintf(file, "\nExact value : %E\n", p);
}
if (GenerateNumericalProbabilityCheckForInterrupt()) {
success = FALSE;
CleanUpOperations(
file,
probs,
cp,
imp,
stop);
return success;
}
/* calculate importances of individual events */
for (j = 0; j < num_bas; j++) {
imp[j] = 0;
}
i = 0;
for(g=e; !BitEquals(g->b, stop); g=g->next) {
for (j = 0; j < g->b->n; j++) {
if ( BitGet(g->b, (g->b->n-1) - j) ) {
imp[j] += cp[i];
}
}
i++;
}
if (GenerateNumericalProbabilityCheckForInterrupt()) {
success = FALSE;
CleanUpOperations(
file,
probs,
cp,
imp,
stop);
return success;
}
fprintf(file, "\n\nPrimary Event Analysis:\n\n");
fprintf(file, " Event "
"Failure contrib. "
"Importance\n\n");
for (i = 0; i < num_bas; i++) {
char *fs = BasicString(num_bas, i);
fprintf(file, "%-15s %E %5.2f%%\n",
fs, imp[i], 100 * imp[i] / p);
strfree(fs);
}
time2 = clock();
/* printf("calculate_probs : num_terms = %d : time = %f\n", */
/* prob_n_terms, (time2-time1)/(float)CLOCKS_PER_SEC); */
CleanUpOperations(
file,
probs,
cp,
imp,
stop);
/* fclose(file); */
/* FreeMemory(probs); */
/* free(cp); */
/* FreeMemory(imp); */
return ( TRUE );
} /* calculate_probs */
