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Use interval tree and square root of n amortized approach. Wrong answer and same timeout though

main
Titouan Rigoudy 11 years ago
parent
70697e7afc
commit
626654ae69
5 changed files with 774 additions and 63 deletions
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  1. +2
    -2
      arithmetic_progressions/Makefile
  2. +522
    -0
      arithmetic_progressions/ap_all.c
  3. +60
    -61
      arithmetic_progressions/arithmetic_progressions.c
  4. +155
    -0
      arithmetic_progressions/itree.c
  5. +35
    -0
      arithmetic_progressions/itree.h

+ 2
- 2
arithmetic_progressions/Makefile View File

@ -7,8 +7,8 @@ all: ap
%.o: %.c
$(CC) -o $@ -c $^ $(CFLAGS)
ap: arithmetic_progressions.c segtree.o
ap: arithmetic_progressions.c itree.o
$(CC) -o $@ $^ $(CFLAGS)
clean:
rm -f segtree.o ap
rm -f segtree.o itree.o ap

+ 522
- 0
arithmetic_progressions/ap_all.c View File

@ -0,0 +1,522 @@
#ifndef ITREE_H
#define ITREE_H
/*
* Simple integer interval tree implementation
* Author: Titouan Rigoudy
*/
struct itree {
int i;
int j;
long v;
struct itree *left;
struct itree *right;
};
// Describes the start or end of an interval
struct ievent {
int i;
long v; // i.v for interval start, -i.v for interval end
};
struct itree *itree_new(int i, int j, long v);
void itree_free(struct itree *it);
void itree_print(struct itree *it);
void itree_add(struct itree *it, int i, int j, long v);
// Flatten the tree into a list of events representing
// interval start and end points
int itree_flatten(struct itree *it, struct ievent **events);
#endif
/*
* Simple integer interval tree implementation
* Kept sorted by interval starting point
* Not balanced
* Author: Titouan Rigoudy
*/
#include <stdlib.h>
#include <stdio.h>
#define EVENTS_MIN_SIZE 1024
struct itree *itree_new(int i, int j, long v) {
struct itree *it = malloc(sizeof *it);
if (!it) {
return NULL;
}
it->i = i;
it->j = j;
it->v = v;
it->left = NULL;
it->right = NULL;
return it;
}
void itree_free(struct itree *it) {
if (!it) {
return;
}
itree_free(it->left);
itree_free(it->right);
free(it);
}
void itree_print(struct itree *it) {
if (!it) {
puts("NULL itree");
}
printf("itree{i: %d, j:%d, v:%ld}\n", it->i, it->j, it->v);
puts("Left:");
if (it->left) {
itree_print(it->left);
}
puts("Right:");
if (it->right) {
itree_print(it->right);
}
}
void itree_add(struct itree *it, int i, int j, long v) {
if (!it) {
fputs("Adding to null interval tree", stderr);
return;
}
if (it->i == i && it->j == j) {
it->v += v;
return;
}
if (i < it->i || (i == it->i && j <= it->j)) {
if (it->left) {
itree_add(it->left, i, j, v);
} else {
it->left = itree_new(i, j, v);
}
return;
}
if (it->right) {
itree_add(it->right, i, j, v);
} else {
it->right = itree_new(i, j, v);
}
}
// For use in qsort
int ieventcmp(const void *event1, const void *event2) {
const struct ievent *ev1 = event1;
const struct ievent *ev2 = event2;
return ev1->i - ev2->i;
}
// For debugging purposes
void ievent_print(const struct ievent ev) {
printf("ievent{i:%d, v:%ld}\n", ev.i, ev.v);
}
// Recursively add events from it to *events
// *events is of size *n, *i is the current number of events in *events
// Returns 0 on success, 1 on error
int itree_flatten_aux(
struct itree *it, struct ievent **events, int *n, int *i) {
if (!it) {
return 0;
}
int err = itree_flatten_aux(it->left, events, n, i);
if (err) {
return err;
}
free(it->left);
it->left = NULL;
if (*i == *n) {
// grow events
*n = *n * 2 + 2; // just in case n was 0
*events = realloc(*events, *n);
if (*events == NULL) {
return 1; // signal error
}
}
if (it->v != 0) {
// Add interval start event
(*events)[*i].i = it->i;
(*events)[*i].v = it->v;
(*i)++;
// Add interval end event
(*events)[*i].i = it->j;
(*events)[*i].v = -it->v;
(*i)++;
}
err = itree_flatten_aux(it->right, events, n, i);
if (err) {
return err;
}
free(it->right);
it->right = NULL;
it->v = 0;
return 0;
}
// Flatten the tree into a list of events representing
// interval start and end points
int itree_flatten(struct itree *it, struct ievent **events) {
int n = EVENTS_MIN_SIZE;
*events = malloc(n * sizeof(**events));
if (*events == NULL) {
return 0;
}
int i = 0;
int err = itree_flatten_aux(it, events, &n, &i);
if (err) {
*events = NULL;
return 0;
}
qsort(*events, i, sizeof(**events), ieventcmp);
return i;
}
// https://www.hackerrank.com/challenges/arithmetic-progressions
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <stdbool.h>
#include <assert.h>
#define INTS_START_SIZE 8
#define INTS_DELIM " \t\n"
#define BUF_SIZE 10000000
#define LINE_SIZE 16
#define BIG_MOD 1000003
/* Arithmetic modulo BIG_MOD */
long INVERSES[BIG_MOD];
void calc_inverses() {
long tmp[BIG_MOD - 2];
long acc = 2; // powers of 2 will run the full range of the set
int i;
for (i = 0; i < BIG_MOD - 2; i++) {
tmp[i] = acc;
acc = (acc * 2) % BIG_MOD;
}
INVERSES[0] = 0;
INVERSES[1] = 1;
for (i = 0; i < BIG_MOD - 2; i++) {
INVERSES[tmp[i]] = tmp[BIG_MOD - 3 - i];
}
}
long pow_mod(long a, long b, long mod, long acc) {
long powa = a % mod;
while (b > 0) {
if (b & 1) {
acc = (acc * powa) % mod;
}
powa = (powa * powa) % mod;
b >>= 1;
}
return acc;
}
long factorial_mod(long n, long mod, long acc) {
int i;
for (i = 2; i <= n; i++) {
acc = (acc * i) % mod;
}
return acc;
}
/* The actual logic */
struct adp {
long a;
long d;
long p;
long psum; // Cumulative sum of p values
long dpowp; // d ^ p
long dprod; // Cumulative product of d values
long dpowprod; // Cumulative product of d ^ p values
};
/* Read space-separated integers */
size_t read_ints(char *line, int **ints) {
if (line == NULL) {
return 0;
}
size_t size = INTS_START_SIZE;
*ints = malloc(INTS_START_SIZE * sizeof *ints);
if (*ints == NULL) {
return 0;
}
char *tok = line;
char *numend;
size_t i = 0;
long tmp;
while (*tok != '\n' && *tok != '\0') {
if (isspace(*tok)) {
tok++;
} else if (isdigit(*tok)) {
tmp = strtol(tok, &numend, 10);
if (i == size) {
// If we have filled array, double its size
size *= 2;
*ints = realloc(*ints, size * sizeof *ints);
if (*ints == NULL) {
return 0;
}
}
// store in array
(*ints)[i] = tmp;
i++;
tok = numend;
} else {
free(*ints);
*ints = NULL;
return 0;
}
}
return i;
}
int read_adp(char *buf, int n, struct adp *adp) {
int *ints;
size_t ints_len;
int i;
char *line;
long dpowp;
long psum = 0;
long dprod = 1;
long dpowprod = 1;
for (i = 0; i < n; i++) {
line = strtok(NULL, "\n");
ints_len = read_ints(line, &ints);
if (ints_len != 3) {
return 1;
}
adp[i].a = ints[0];
adp[i].d = ints[1];
adp[i].p = ints[2];
psum += adp[i].p;
adp[i].psum = psum;
dpowp = pow_mod(adp[i].d, adp[i].p, BIG_MOD, 1);
adp[i].dpowp = dpowp;
dprod = (dprod * adp[i].d) % BIG_MOD;
adp[i].dprod = dprod;
dpowprod = (dpowprod * dpowp) % BIG_MOD;
adp[i].dpowprod = dpowprod;
free(ints);
}
return 0;
}
// Calculate sum of p and product of d^p for [i, j[
void itree_mcd(
struct adp *adp,
struct itree *ptree,
int i,
int j,
long *k,
long *dprod)
{
if (!ptree) {
return;
}
bool intersects = (i < j) && (i < ptree->j) && (ptree->i < j);
if (intersects && ptree->v > 0) {
// We need to calculate the sum of the p values
// and the product of the d^p at the same time
int start = i > ptree->i ? i : ptree->i;
int end = j < ptree->j ? j : ptree->j;
*k += ptree->v * (end-start);
// calculate the product of all d values in [start, end[
long dtmp = adp[end-1].dprod;
if (i > 0) {
dtmp = (dtmp * INVERSES[adp[start-1].dprod]) % BIG_MOD;
}
*dprod = pow_mod(dtmp, ptree->v, BIG_MOD, *dprod);
}
if (j > ptree->i) {
// [i,j[ may intersect with children intervals to the right
itree_mcd(adp, ptree->right, i, j, k, dprod);
}
// [i,j[ can always intersect with children intervals to the left
itree_mcd(adp, ptree->left, i, j, k, dprod);
}
// Calculate and print for [i-1, j-1]
int min_const_diff(
int n,
struct adp *adp,
struct itree *ptree,
int i,
int j)
{
if (i < 1 || j > n) {
return 1;
}
// k is initialized to the sum of initial p values in [i-1, j-1]
long k = adp[j-1].psum;
// dprod is initializaed to the product of d^p values in [i-1, j-1]
long dprod = adp[j-1].dpowprod;
if (i >= 2) {
k -= adp[i-2].psum;
dprod = (dprod * INVERSES[adp[i-2].dpowprod]) % BIG_MOD;
}
itree_mcd(adp, ptree, i-1, j, &k, &dprod);
long v = factorial_mod(k, BIG_MOD, dprod);
printf("%ld %ld\n", k, v);
return 0;
}
void update_adp(struct adp *adp, struct ievent *events, int n) {
if (!events || n <= 0) {
return;
}
int i = 0;
int p = 0;
int psum = 0;
int dpowprod = 1;
while (true) {
// Compress all events at the same index into one
int start = events[i].i;
while (i < n && events[i].i == start) {
p += events[i].v;
i++;
}
if (i == n) {
// The last event should close the last remaining interval
assert(p == 0);
break;
}
int end = events[i].i; // next event
// p is now constant on [start, end[
for (int j = start; j < end; j++) {
adp[j].p += p;
psum += p;
adp[j].psum += psum;
adp[j].dpowp = pow_mod(adp[j].d, adp[j].p, BIG_MOD, 1);
dpowprod = (dpowprod * adp[j].dpowp) % BIG_MOD;
adp[j].dpowprod = dpowprod;
}
}
}
int ptree_size = 0;
int add_powers(int n, struct adp *adp, struct itree *ptree, int i, int j, int v) {
if (i < 1 || j > n) {
return 1;
}
itree_add(ptree, i-1, j, v);
ptree_size++;
if (ptree_size * ptree_size >= n) {
struct ievent *events = NULL;
int n_events = itree_flatten(ptree, &events);
update_adp(adp, events, n_events);
free(events);
ptree_size = 0;
}
return 0;
}
int handle_query(char *str, int n, struct adp *adp, struct itree *ptree) {
int *ints;
int ints_len = read_ints(str, &ints);
if (ints_len < 1) {
return 1;
}
int query_type = ints[0];
if (query_type == 0) {
if (ints_len != 3) {
return 1;
}
return min_const_diff(n, adp, ptree, ints[1], ints[2]);
}
if (query_type == 1) {
if (ints_len != 4) {
return 1;
}
return add_powers(n, adp, ptree, ints[1], ints[2], ints[3]);
}
return 1;
}
int main(int argc, char **argv) {
// Prep work
calc_inverses();
char *buf = malloc(BUF_SIZE * sizeof *buf);
if (buf == NULL) {
return 0;
}
fread(buf, BUF_SIZE, 1, stdin);
char *line = strtok(buf, "\n");
char *end;
int n = strtol(line, &end, 10);
if ((!isspace(*end) && *end != '\0') || n < 1) {
return 0;
}
struct adp *adp = malloc(n * sizeof *adp);
struct itree *ptree = itree_new(0, n, 0);
if (adp == NULL || ptree == NULL) {
return 0;
}
int err = read_adp(buf, n, adp);
if (err) {
return 0;
}
line = strtok(NULL, "\n");
int q = strtol(line, &end, 10);
if ((!isspace(*end) && *end != '\0') || q < 1) {
return 0;
}
int i;
for (i = 0; i < q; i++) {
line = strtok(NULL, "\n");
err = handle_query(line, n, adp, ptree);
if (err) {
return 0;
}
}
return 0;
}

+ 60
- 61
arithmetic_progressions/arithmetic_progressions.c View File

@ -4,8 +4,10 @@
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <stdbool.h>
#include <assert.h>
#include "segtree.h"
#include "itree.h"
#define INTS_START_SIZE 8
#define INTS_DELIM " \t\n"
@ -143,9 +145,9 @@ int read_adp(char *buf, int n, struct adp *adp) {
}
// Calculate sum of p and product of d^p for [i, j[
void segtree_mcd(
void itree_mcd(
struct adp *adp,
struct segtree *ptree,
struct itree *ptree,
int i,
int j,
long *k,
@ -155,42 +157,39 @@ void segtree_mcd(
return;
}
// We need to calculate the sum of the p values
// and the product of the d^p at the same time
bool intersects = (i < j) && (i < ptree->j) && (ptree->i < j);
*k += ptree->v * (j-i);
if (intersects && ptree->v > 0) {
// We need to calculate the sum of the p values
// and the product of the d^p at the same time
int start = i > ptree->i ? i : ptree->i;
int end = j < ptree->j ? j : ptree->j;
*k += ptree->v * (end-start);
// dtmp is the product of all d values in [i, j[
if (ptree->v > 0) {
long dtmp = adp[j-1].dprod;
// calculate the product of all d values in [start, end[
long dtmp = adp[end-1].dprod;
if (i > 0) {
dtmp = (dtmp * INVERSES[adp[i-1].dprod]) % BIG_MOD;
dtmp = (dtmp * INVERSES[adp[start-1].dprod]) % BIG_MOD;
}
*dprod = pow_mod(dtmp, ptree->v, BIG_MOD, *dprod);
}
int mid = (ptree->i + ptree->j) / 2;
if (j <= mid) {
segtree_mcd(adp, ptree->left, i, j, k, dprod);
return;
}
if (i >= mid) {
segtree_mcd(adp, ptree->right, i, j, k, dprod);
return;
if (j > ptree->i) {
// [i,j[ may intersect with children intervals to the right
itree_mcd(adp, ptree->right, i, j, k, dprod);
}
// i < mid && j > mid
segtree_mcd(adp, ptree->left, i, mid, k, dprod);
segtree_mcd(adp, ptree->right, mid, j, k, dprod);
// [i,j[ can always intersect with children intervals to the left
itree_mcd(adp, ptree->left, i, j, k, dprod);
}
// Calculate and print for [i-1, j-1]
int min_const_diff(
int n,
struct adp *adp,
struct segtree *ptree,
struct itree *ptree,
int i,
int j)
{
@ -205,70 +204,70 @@ int min_const_diff(
k -= adp[i-2].psum;
dprod = (dprod * INVERSES[adp[i-2].dpowprod]) % BIG_MOD;
}
segtree_mcd(adp, ptree, i-1, j, &k, &dprod);
itree_mcd(adp, ptree, i-1, j, &k, &dprod);
long v = factorial_mod(k, BIG_MOD, dprod);
printf("%ld %ld\n", k, v);
return 0;
}
// Flatten tree and add it to the adp array
void segtree_flatten(struct segtree *ptree, struct adp *adp, int n) {
if (!adp || !ptree) {
void update_adp(struct adp *adp, struct ievent *events, int n) {
if (!events || n <= 0) {
return;
}
int i = 0;
int p = 0;
int psum = 0;
int dpowprod = 1;
while (true) {
// Compress all events at the same index into one
int start = events[i].i;
while (i < n && events[i].i == start) {
p += events[i].v;
i++;
}
segtree_flatten(ptree->left, adp, n);
segtree_free(ptree->left);
ptree->left = NULL;
segtree_flatten(ptree->right, adp, n);
segtree_free(ptree->right);
ptree->right = NULL;
if (ptree->v != 0) {
for (int k = ptree->i; k < ptree->j && k < n; k++) {
adp[k].p += ptree->v;
if (i == n) {
// The last event should close the last remaining interval
assert(p == 0);
break;
}
}
int end = events[i].i; // next event
ptree->v = 0;
}
// p is now constant on [start, end[
for (int j = start; j < end; j++) {
adp[j].p += p;
void update_adp(struct adp *adp, int n) {
int psum = 0;
int dpowprod = 1;
for (int i = 0; i < n; i++) {
psum += adp[i].p;
adp[i].psum = psum;
psum += p;
adp[j].psum += psum;
adp[i].dpowp = pow_mod(adp[i].d, adp[i].p, BIG_MOD, 1);
adp[j].dpowp = pow_mod(adp[j].d, adp[j].p, BIG_MOD, 1);
dpowprod = (dpowprod * adp[i].dpowp) % BIG_MOD;
adp[i].dpowprod = dpowprod;
dpowprod = (dpowprod * adp[j].dpowp) % BIG_MOD;
adp[j].dpowprod = dpowprod;
}
}
}
int ptree_size = 0;
int add_powers(int n, struct adp *adp, struct segtree *ptree, int i, int j, int v) {
int add_powers(int n, struct adp *adp, struct itree *ptree, int i, int j, int v) {
if (i < 1 || j > n) {
return 1;
}
//segtree_print(ptree);
//printf("Adding %ld to [%d,%d]\n", v, i, j);
segtree_add(ptree, i-1, j, v);
itree_add(ptree, i-1, j, v);
ptree_size++;
if (ptree_size * ptree_size >= n) {
//puts("Flattening the tree");
segtree_flatten(ptree, adp, n);
update_adp(adp, n);
struct ievent *events = NULL;
int n_events = itree_flatten(ptree, &events);
update_adp(adp, events, n_events);
free(events);
ptree_size = 0;
}
//segtree_print(ptree);
return 0;
}
int handle_query(char *str, int n, struct adp *adp, struct segtree *ptree) {
int handle_query(char *str, int n, struct adp *adp, struct itree *ptree) {
int *ints;
int ints_len = read_ints(str, &ints);
if (ints_len < 1) {
@ -309,7 +308,7 @@ int main(int argc, char **argv) {
}
struct adp *adp = malloc(n * sizeof *adp);
struct segtree *ptree = segtree_new_simple(n);
struct itree *ptree = itree_new(0, n, 0);
if (adp == NULL || ptree == NULL) {
return 0;
}


+ 155
- 0
arithmetic_progressions/itree.c View File

@ -0,0 +1,155 @@
/*
* Simple integer interval tree implementation
* Kept sorted by interval starting point
* Not balanced
* Author: Titouan Rigoudy
*/
#include <stdlib.h>
#include <stdio.h>
#include "itree.h"
#define EVENTS_MIN_SIZE 1024
struct itree *itree_new(int i, int j, long v) {
struct itree *it = malloc(sizeof *it);
if (!it) {
return NULL;
}
it->i = i;
it->j = j;
it->v = v;
it->left = NULL;
it->right = NULL;
return it;
}
void itree_free(struct itree *it) {
if (!it) {
return;
}
itree_free(it->left);
itree_free(it->right);
free(it);
}
void itree_print(struct itree *it) {
if (!it) {
puts("NULL itree");
}
printf("itree{i: %d, j:%d, v:%ld}\n", it->i, it->j, it->v);
puts("Left:");
if (it->left) {
itree_print(it->left);
}
puts("Right:");
if (it->right) {
itree_print(it->right);
}
}
void itree_add(struct itree *it, int i, int j, long v) {
if (!it) {
fputs("Adding to null interval tree", stderr);
return;
}
if (it->i == i && it->j == j) {
it->v += v;
return;
}
if (i < it->i || (i == it->i && j <= it->j)) {
if (it->left) {
itree_add(it->left, i, j, v);
} else {
it->left = itree_new(i, j, v);
}
return;
}
if (it->right) {
itree_add(it->right, i, j, v);
} else {
it->right = itree_new(i, j, v);
}
}
// For use in qsort
int ieventcmp(const void *event1, const void *event2) {
const struct ievent *ev1 = event1;
const struct ievent *ev2 = event2;
return ev1->i - ev2->i;
}
// For debugging purposes
void ievent_print(const struct ievent ev) {
printf("ievent{i:%d, v:%ld}\n", ev.i, ev.v);
}
// Recursively add events from it to *events
// *events is of size *n, *i is the current number of events in *events
// Returns 0 on success, 1 on error
int itree_flatten_aux(
struct itree *it, struct ievent **events, int *n, int *i) {
if (!it) {
return 0;
}
int err = itree_flatten_aux(it->left, events, n, i);
if (err) {
return err;
}
free(it->left);
it->left = NULL;
if (*i == *n) {
// grow events
*n = *n * 2 + 2; // just in case n was 0
*events = realloc(*events, *n);
if (*events == NULL) {
return 1; // signal error
}
}
if (it->v != 0) {
// Add interval start event
(*events)[*i].i = it->i;
(*events)[*i].v = it->v;
(*i)++;
// Add interval end event
(*events)[*i].i = it->j;
(*events)[*i].v = -it->v;
(*i)++;
}
err = itree_flatten_aux(it->right, events, n, i);
if (err) {
return err;
}
free(it->right);
it->right = NULL;
it->v = 0;
return 0;
}
// Flatten the tree into a list of events representing
// interval start and end points
int itree_flatten(struct itree *it, struct ievent **events) {
int n = EVENTS_MIN_SIZE;
*events = malloc(n * sizeof(**events));
if (*events == NULL) {
return 0;
}
int i = 0;
int err = itree_flatten_aux(it, events, &n, &i);
if (err) {
*events = NULL;
return 0;
}
qsort(*events, i, sizeof(**events), ieventcmp);
return i;
}

+ 35
- 0
arithmetic_progressions/itree.h View File

@ -0,0 +1,35 @@
#ifndef ITREE_H
#define ITREE_H
/*
* Simple integer interval tree implementation
* Author: Titouan Rigoudy
*/
struct itree {
int i;
int j;
long v;
struct itree *left;
struct itree *right;
};
// Describes the start or end of an interval
struct ievent {
int i;
long v; // i.v for interval start, -i.v for interval end
};
struct itree *itree_new(int i, int j, long v);
void itree_free(struct itree *it);
void itree_print(struct itree *it);
void itree_add(struct itree *it, int i, int j, long v);
// Flatten the tree into a list of events representing
// interval start and end points
int itree_flatten(struct itree *it, struct ievent **events);
#endif

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