Two Two
Problem Statement :
Prof. Twotwo as the name suggests is very fond powers of 2. Moreover he also has special affinity to number 800. He is known for carrying quirky experiments on powers of 2.
One day he played a game in his class. He brought some number plates on each of which a digit from 0 to 9 is written. He made students stand in a row and gave a number plate to each of the student. Now turn by turn, he called for some students who are standing continuously in the row say from index i to index j (i<=j) and asked them to find their strength.
The strength of the group of students from i to j is defined as:
strength(i , j)
{
if a[i] = 0
return 0; //If first child has value 0 in the group, strength of group is zero
value = 0;
for k from i to j
value = value*10 + a[k]
return value;
}
Prof called for all possible combinations of i and j and noted down the strength of each group. Now being interested in powers of 2, he wants to find out how many strengths are powers of two. Now its your responsibility to get the answer for prof.
Input Format
First line contains number of test cases T
Next T line contains the numbers of number plates the students were having when standing in the row in the form of a string A.
Constraints
1 ≤ T ≤ 100
1 ≤ len(A) ≤ 105
0 ≤ A[i] ≤ 9
Output Format
Output the total number of strengths of the form 2x such that 0 ≤ x ≤ 800.
Solution :
Solution in C :
In C++ :
#include <iostream>
#include <cstdio>
#include <ctime>
using namespace std;
struct node
{
int e;
struct node *path[10];
};
int prodf[400],prodlen;
char bstr[123456];
struct node *posStack[300];
int stackSize=0;
struct node* addEdge(struct node *start, int edge)
{
if (start->path[edge]==NULL)
{
struct node *tempNode = new node;
tempNode->e=0;
for(int i=0;i<10;++i)
tempNode->path[i]=NULL;
start->path[edge]=tempNode;
}
return (start->path[edge]);
}
void markEnd(struct node *vnode)
{
vnode->e=1;
}
int main()
{
clock_t t_start =clock();
prodlen=1;
prodf[0]=1;
struct node *automaton = new struct node;
automaton->e=0;
for(int i=0;i<10;++i)
automaton->path[i]=NULL;
struct node *ppos=automaton;
ppos=addEdge(ppos,1);
markEnd(ppos);
for(int n=1;n<=800;++n)
{
int rem=0;
for(int i=0;i<prodlen;++i)
{
rem=(2*prodf[i]+rem);
prodf[i]=rem%10;
rem/=10;
}
if(rem!=0)
prodf[prodlen++]=rem;
ppos=automaton;
for(int i=prodlen-1;i>=0;--i)
{
ppos = addEdge(ppos,prodf[i]);
}
markEnd(ppos);
}
clock_t t_end=clock();
// cout<<(t_end+0.0-t_start)/CLOCKS_PER_SEC<<endl;
int T,k;
cin>>T;
while(T--)
{
long long ans=0;
stackSize=0;
scanf("%s",bstr);
for(int i=0,j;bstr[i]!='\0';++i)
{
k=bstr[i]-'0';
for(j=0;j<stackSize;)
{
if(posStack[j]->path[k]!=NULL)
{
posStack[j]=posStack[j]->path[k];
if(posStack[j]->e==1)
ans++;
++j;
}
else
posStack[j]=posStack[--stackSize];
}
if(automaton->path[k]!=NULL)
{
posStack[stackSize]=automaton->path[k];
if(posStack[stackSize]->e==1)
ans++;
++stackSize;
}
}
cout<<ans<<endl;
}
return 0;
}
In Java :
import java.io.*;
import java.math.BigInteger;
import java.util.ArrayList;
public class Solution {
static class Node {
Node[] edges = new Node[10];
Node slink;
int weight;
}
public static void solve(Input in, PrintWriter out) throws IOException {
Node root = new Node();
for (int pow = 0; pow <= 800; ++pow) {
String s = BigInteger.ONE.shiftLeft(pow).toString();
Node cur = root;
for (char c : s.toCharArray()) {
if (cur.edges[c - '0'] == null) {
cur.edges[c - '0'] = new Node();
}
cur = cur.edges[c - '0'];
}
cur.weight++;
}
ArrayList<Node> q = new ArrayList<Node>();
q.add(root);
for (int it = 0; it < q.size(); ++it) {
Node n = q.get(it);
for (int i = 0; i < 10; ++i) {
Node n1 = n.edges[i];
if (n1 == null) {
continue;
}
q.add(n1);
n1.slink = n.slink;
while (n1.slink != null && n1.slink.edges[i] == null) {
n1.slink = n1.slink.slink;
}
if (n1.slink == null) {
n1.slink = root;
} else {
n1.slink = n1.slink.edges[i];
}
}
}
for (Node n : q) {
if (n.slink != null) {
n.weight += n.slink.weight;
}
}
for (Node n : q) {
for (int i = 0; i < 10; ++i) {
if (n.edges[i] == null) {
if (n.slink == null) {
n.edges[i] = root;
} else {
n.edges[i] = n.slink.edges[i];
}
}
}
}
int tests = in.nextInt();
for (int test = 0; test < tests; ++test) {
String s = in.next();
int ans = 0;
Node cur = root;
for (char c : s.toCharArray()) {
cur = cur.edges[c - '0'];
ans += cur.weight;
}
out.println(ans);
}
}
public static void main(String[] args) throws IOException {
PrintWriter out = new PrintWriter(System.out);
solve(new Input(new BufferedReader(new InputStreamReader(System.in))), out);
out.close();
}
static class Input {
BufferedReader in;
StringBuilder sb = new StringBuilder();
public Input(BufferedReader in) {
this.in = in;
}
public Input(String s) {
this.in = new BufferedReader(new StringReader(s));
}
public String next() throws IOException {
sb.setLength(0);
while (true) {
int c = in.read();
if (c == -1) {
return null;
}
if (" \n\r\t".indexOf(c) == -1) {
sb.append((char)c);
break;
}
}
while (true) {
int c = in.read();
if (c == -1 || " \n\r\t".indexOf(c) != -1) {
break;
}
sb.append((char)c);
}
return sb.toString();
}
public int nextInt() throws IOException {
return Integer.parseInt(next());
}
public long nextLong() throws IOException {
return Long.parseLong(next());
}
public double nextDouble() throws IOException {
return Double.parseDouble(next());
}
}
}
In C :
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
static int read_int() {
int ret;
scanf("%d", &ret);
return ret;
}
static int *read_int_array(int n) {
int *ret = malloc(n * sizeof(int));
for (int i = 0; i < n; ++i) {
scanf("%d", ret + i);
}
return ret;
}
static int intcomp(const void *v1, const void *v2) {
return *(const int *)v1 - *(const int *)v2;
}
#define BASE 801
static char powers[BASE][250];
static int power_nums[801];
static void build_powers() {
powers[0][0] = '1';
powers[0][1] = '\0';
power_nums[0] = 1;
for (int i = 1; i <= 800; ++i) {
int previous = power_nums[i - 1];
char *ppower = powers[i - 1];
int start_pos = previous;
if (ppower[0] >= '5') {
start_pos ++;
}
power_nums[i] = start_pos;
char *current = powers[i];
current[start_pos] = '\0';
int rem = 0;
for (int j = previous - 1; j >= 0; --j) {
int val = (ppower[j] - '0') * 2 + rem;
rem = val / 10;
current[start_pos - 1] = '0' + (val % 10);
start_pos --;
}
if (rem != 0) {
current[0] = '0' + rem;
}
}
}
struct node {
struct node *childs;
char child_count;
char c;
char end;
};
static void init_node(struct node *n, char c, char end) {
n->c = c;
n->end = end;
}
static struct node *build_node() {
struct node * root = malloc(sizeof(struct node));
init_node(root, 0, -1);
for (int i = 0; i < BASE; ++i) {
struct node *n = root;
for (const char *iter = powers[i]; *iter; iter++) {
if (!n->childs) {
n->childs = malloc(10 * sizeof(struct node));
n->child_count = 10;
for (int i = 0; i < 10; ++i) {
n->childs[i].c = '0' + i;
}
}
n = n->childs + (*iter - '0');
}
n->end = 1;
}
return root;
}
static long long int count_appearance(const char *haystack, const char *needle) {
long long int result = 0;
while (1) {
if ((haystack = strstr(haystack, needle))) {
result ++;
haystack++;
} else {
return result;
}
}
}
static long long int solve(const char *buffer, struct node *root) {
long long result = 0;
for (const char *iter = buffer; *iter; ++iter) {
struct node *n = root;
for (const char *iter2 = iter; *iter2; ++iter2) {
if (!n->childs) {
break;
} else {
n = &n->childs[*iter2 - '0'];
if (n->end) {
result++;
}
}
}
}
return result;
}
int main(int argc, char *argv[]) {
build_powers();
struct node *root = build_node();
int t = read_int();
char buffer[100001];
for (int i = 0; i < t; ++i) {
scanf(" %s", buffer);
printf("%lld\n", solve(buffer, root));
}
return 0;
}
In Python3 :
tree = [False, {}]
def add(word) :
current = tree
for c in word :
try :
current = current[1][c]
except KeyError :
current[1][c] = [False, {}]
current = current[1][c]
current[0] = True
def count(word) :
count = 0
for start in range(len(word)) :
current, index = tree, start
while True :
if current[0] :
count += 1
try :
current = current[1][word[index]]
index += 1
except (KeyError, IndexError) :
break
return count
v = 1
for x in range(801) :
add(str(v)[::-1])
v <<= 1
Done = {}
T = int(input())
for t in range(T) :
A = input()
if not A in Done :
Done[A] = count(A[::-1])
print(Done[A])
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