I need to create N nested loops to print all combinations of a binary sequence of length N. Im not sure how to do this.
Any help would be greatly appreciated. Thanks.
Use recursion. e.g., in Java
public class Foo {
public static void main(String[] args) {
new Foo().printCombo("", 5);
}
void printCombo(String soFar, int len) {
if (len == 1) {
System.out.println(soFar+"0");
System.out.println(soFar+"1");
}
else {
printCombo(soFar+"0", len-1);
printCombo(soFar+"1", len-1);
}
}
}
will print
00000
00001
00010
...
11101
11110
11111
You have two options here:
Use backtracking instead.
Write a program that generates a dynamic program with N loops and then executes it.
You don't need any nested loops for this. You need one recursive function to print a binary value of length N and a for loop to iterate over all numbers [0 .. (2^N)-1].
user949300's solution is also very good, but it might not work in all languages.
Here's my solution(s), the recursive one is approximately twice as slow as the iterative one:
#include <stdio.h>
#ifdef RECURSIVE
void print_bin(int num, int len)
{
if(len == 0)
{
printf("\n");
return;
}
print_bin(num >> 1, len -1);
putchar((num & 1) + '0');
}
#else
void print_bin(int num, int len)
{
char str[len+1];
int i;
str[len] = '\0';
for (i = 0; i < len; i++)
{
str[len-1-i] = !!(num & (1 << i)) + '0';
}
printf("%s\n", str);
}
#endif
int main()
{
int len = 24;
int i;
int end = 1 << len;
for (i = 0; i < end ; i++)
{
print_bin(i, len);
}
return 0;
}
(I tried this myself on a Mac printing all binary numbers of length 24 and the terminal froze. But that is probably a poor terminal implementation. :-)
$ gcc -O3 binary.c ; time ./a.out > /dev/null ; gcc -O3 -DRECURSIVE binary.c ; time ./a.out > /dev/null
real 0m1.875s
user 0m1.859s
sys 0m0.008s
real 0m3.327s
user 0m3.310s
sys 0m0.010s
I don't think we need recursion or n nested for-loops to solve this problem. It would be easy to handle this using bit manipulation.
In C++, as an example:
for(int i=0;i<(1<<n);i++)
{
for(int j=0;j<n;j++)
if(i&(1<<j))
printf("1");
else
printf("0");
printf("\n");
}
Related
I am trying to write a simple nonogram solver, in a kind of bruteforce way, but I am stuck on a relatively easy task. Let's say I have a row with clues [2,3] that has a length of 10
so the solutions are:
$$-$$$----
$$--$$$---
$$---$$$--
$$----$$$-
$$-----$$$
-$$----$$$
--$$---$$$
---$$--$$$
----$$-$$$
-$$---$$$-
--$$-$$$--
I want to find all the possible solutions for a row
I know that I have to consider each block separately, and each block will have an availible space of n-(sum of remaining blocks length + number of remaining blocks) but I do not know how to progress from here
Well, this question already have a good answer, so think of this one more as an advertisement of python's prowess.
def place(blocks,total):
if not blocks: return ["-"*total]
if blocks[0]>total: return []
starts = total-blocks[0] #starts = 2 means possible starting indexes are [0,1,2]
if len(blocks)==1: #this is special case
return [("-"*i+"$"*blocks[0]+"-"*(starts-i)) for i in range(starts+1)]
ans = []
for i in range(total-blocks[0]): #append current solutions
for sol in place(blocks[1:],starts-i-1): #with all possible other solutiona
ans.append("-"*i+"$"*blocks[0]+"-"+sol)
return ans
To test it:
for i in place([2,3,2],12):
print(i)
Which produces output like:
$$-$$$-$$---
$$-$$$--$$--
$$-$$$---$$-
$$-$$$----$$
$$--$$$-$$--
$$--$$$--$$-
$$--$$$---$$
$$---$$$-$$-
$$---$$$--$$
$$----$$$-$$
-$$-$$$-$$--
-$$-$$$--$$-
-$$-$$$---$$
-$$--$$$-$$-
-$$--$$$--$$
-$$---$$$-$$
--$$-$$$-$$-
--$$-$$$--$$
--$$--$$$-$$
---$$-$$$-$$
This is what i got:
#include <iostream>
#include <vector>
#include <string>
using namespace std;
typedef std::vector<bool> tRow;
void printRow(tRow row){
for (bool i : row){
std::cout << ((i) ? '$' : '-');
}
std::cout << std::endl;
}
int requiredCells(const std::vector<int> nums){
int sum = 0;
for (int i : nums){
sum += (i + 1); // The number + the at-least-one-cell gap at is right
}
return (sum == 0) ? 0 : sum - 1; // The right-most number don't need any gap
}
bool appendRow(tRow init, const std::vector<int> pendingNums, unsigned int rowSize, std::vector<tRow> &comb){
if (pendingNums.size() <= 0){
comb.push_back(init);
return false;
}
int cellsRequired = requiredCells(pendingNums);
if (cellsRequired > rowSize){
return false; // There are no combinations
}
tRow prefix;
int gapSize = 0;
std::vector<int> pNumsAux = pendingNums;
pNumsAux.erase(pNumsAux.begin());
unsigned int space = rowSize;
while ((gapSize + cellsRequired) <= rowSize){
space = rowSize;
space -= gapSize;
prefix.clear();
prefix = init;
for (int i = 0; i < gapSize; ++i){
prefix.push_back(false);
}
for (int i = 0; i < pendingNums[0]; ++i){
prefix.push_back(true);
space--;
}
if (space > 0){
prefix.push_back(false);
space--;
}
appendRow(prefix, pNumsAux, space, comb);
++gapSize;
}
return true;
}
std::vector<tRow> getCombinations(const std::vector<int> row, unsigned int rowSize) {
std::vector<tRow> comb;
tRow init;
appendRow(init, row, rowSize, comb);
return comb;
}
int main(){
std::vector<int> row = { 2, 3 };
auto ret = getCombinations(row, 10);
for (tRow r : ret){
while (r.size() < 10)
r.push_back(false);
printRow(r);
}
return 0;
}
And my output is:
$$-$$$----
$$--$$$---
$$---$$$--
$$----$$$--
$$-----$$$
-$$-$$$----
-$$--$$$--
-$$---$$$-
-$$----$$$-
--$$-$$$--
--$$--$$$-
--$$---$$$
---$$-$$$-
---$$--$$$
----$$-$$$
For sure, this must be absolutely improvable.
Note: i did't test it more than already written case
Hope it works for you
I am working on simple naive string search in CUDA.
I am new in CUDA. It works fine fol smaller files ( aprox. ~1MB ). After I make these files bigger ( ctrl+a ctrl+c several times in notepad++ ), my program's results are higher ( about +1% ) than a
grep -o text file_name | wc -l
It is very simple function, so I don't know what could cause this. I need it to work with larger files ( ~500MB ).
Kernel code ( gpuCount is a __device__ int global variable ):
__global__ void stringSearchGpu(char *data, int dataLength, char *input, int inputLength){
int id = blockDim.x*blockIdx.x + threadIdx.x;
if (id < dataLength)
{
int fMatch = 1;
for (int j = 0; j < inputLength; j++)
{
if (data[id + j] != input[j]) fMatch = 0;
}
if (fMatch)
{
atomicAdd(&gpuCount, 1);
}
}
}
This is calling the kernel in main function:
int blocks = 1, threads = fileSize;
if (fileSize > 1024)
{
blocks = (fileSize / 1024) + 1;
threads = 1024;
}
clock_t cpu_start = clock();
// kernel call
stringSearchGpu<<<blocks, threads>>>(cudaBuffer, strlen(buffer), cudaInput, strlen(input));
cudaDeviceSynchronize();
After this I just copy the result to Host and print it.
Can anyone please help me with this?
First of all, you should always check return values of CUDA functions to check for errors. Best way to do so would be the following:
#define gpuErrchk(ans) { gpuAssert((ans), __FILE__, __LINE__); }
inline void gpuAssert(cudaError_t code, const char *file, int line, bool abort=true)
{
if (code != cudaSuccess)
{
fprintf(stderr,"GPUassert: %s %s %d\n", cudaGetErrorString(code), file, line);
if (abort) exit(code);
}
}
Wrap your CUDA calls, such as:
gpuErrchk(cudaDeviceSynchronize());
Second, your kernel accesses out of bounds memory. Suppose, dataLength=100, inputLength=7 and id=98. In your kernel code:
if (id < dataLength) // 98 is less than 100, so condition true
{
int fMatch = 1;
for (int j = 0; j < inputLength; j++) // j runs from [0 - 6]
{
// if j>1 then id+j>=100, which is out of bounds, illegal operation
if (data[id + j] != input[j]) fMatch = 0;
}
Change the condition to something like:
if (id < dataLength - inputLength)
I am trying to implement a method to get all subset of a set. I understand the logic of doing that. i.e. Subset(n) = n + Subset(n-1), but the code I wrote keep printing out the wrong answers. Here is my code:
void subset(vector<int> &input, vector<int> output, int current) {
if (current == input.size()-1) {
output.push_back(input[current]);
print(output);
}
else {
for (int i = current; i < input.size();i++) {
output.push_back(input[i]);
print(output);
subset(input, output, i+1);
}
}
}
Here is the output I got (input is {1,2,3}):
1
1 2
1 2 3
1 2 3
1 2
1 2 3
1 2 3
Any idea where I went wrong? Any help will be appreciated!
I think this can help you:
void subset(vector<int> &input, vector<int> output, int current) {
static int n=0;
if (current == input.size()) {
cout<<n++<<":\t {";
for(int i=0;i<output.size();i++) cout<<output[i]<<", ";
cout<<"\b\b}\n";
}
else {
subset(input, output, current+1); //exclude current'th item
output.push_back(input[current]);
subset(input, output, current+1); //include current'th item
}
}
and first time you may call it like this:
int main()
{
std::vector<int> inp, out;
for(int i=0; i<5; i++) // for example {1,2,3,4,5}
inp.push_back(i);
subset(inp, out, 0);
return 0;
}
You always print the output from its beginning: therefore you would never see [2,3], or [2] or [3] in the output
You have print statements in two places - thus the duplication of outputs
You are developing a smartphone app. You have a list of potential
customers for your app. Each customer has a budget and will buy the app at
your declared price if and only if the price is less than or equal to the
customer's budget.
You want to fix a price so that the revenue you earn from the app is
maximized. Find this maximum possible revenue.
For instance, suppose you have 4 potential customers and their budgets are
30, 20, 53 and 14. In this case, the maximum revenue you can get is 60.
**Input format**
Line 1 : N, the total number of potential customers.
Lines 2 to N+1: Each line has the budget of a potential customer.
**Output format**
The output consists of a single integer, the maximum possible revenue you
can earn from selling your app.
Also, upper bound on N is 5*(10^5) and upper bound on each customer's budget is 10^8.
This is a problem I'm trying to solve . My strategy was to sort the list of budgets and then multiply each of those with its position-index in the sequence - and then print the max of the resulting sequence. However this seems to be quite time-inefficient (at least in the way I'm implementing it - I've attached the code for reference). My upper bound on time is 2 seconds. Can anyone help me find a
more time-efficient algorithm (or possibly a more efficient way to implement my algorithm) ?
Here is my solution :
#include <iostream>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
using namespace std;
long long max(long long[],long long);
void quickSortIterative(long long[],long long,long long);
long long partition(long long[],long long,long long);
void swap(long long*,long long*);
int main(){
long long n,k=1;
scanf("%lld",&n);
if(n<1 || n > 5*((long long)pow(10,5))){
exit(0);
}
long long budget[n],aux[n];
for(long long i=0;i<n;i++){
scanf("%lld",&budget[i]);
if(budget[i]<1 || budget[i] > (long long)pow(10,8)){
exit(0);
}
}
quickSortIterative(budget,0,n-1);
for(long long j=n-1;j>=0;j--){
aux[j] = budget[j]*k;
k++;
}
cout<<max(aux,n);
return 0;
}
long long partition (long long arr[], long long l, long long h){
long long x = arr[h];
long long i = (l - 1);
for (long long j = l; j <= h- 1; j++)
{
if (arr[j] <= x)
{
i++;
swap (&arr[i], &arr[j]);
}
}
swap (&arr[i + 1], &arr[h]);
return (i + 1);
}
void swap ( long long* a, long long* b ){
long long t = *a;
*a = *b;
*b = t;
}
void quickSortIterative(long long arr[], long long l, long long h){
long long stack[ h - l + 1 ];
long long top = -1;
stack[ ++top ] = l;
stack[ ++top ] = h;
while ( top >= 0 ){
h = stack[ top-- ];
l = stack[ top-- ];
long long p = partition( arr, l, h );
if ( p-1 > l ){
stack[ ++top ] = l;
stack[ ++top ] = p - 1;
}
if ( p+1 < h ){
stack[ ++top ] = p + 1;
stack[ ++top ] = h;
}
}
}
long long max(long long arr[],long long length){
long long max = arr[0];
for(long long i=1;i<length;i++){
if(arr[i]>max){
max=arr[i];
}
}
return max;
}
Quicksort can take O(n^2) time for certain sequences (often already sorted sequences are bad).
I would recommend you try using a sorting approach with guaranteed O(nlogn) performance (e.g. heapsort or mergesort). Alternatively, you may well find that using the sort routines in the standard library will give better performance than your version.
You might use qsort in C or std::sort in C++, which is most likely faster than your own code.
Also, your "stack" array will cause you trouble if the difference h - l is large.
I have used STL library function sort() of C++. It's time complexity is O(nlogn). Here, you just need to sort the given array and check from maximum value to minimum value for given solution. It is O(n) after sorting.
My code which cleared all the test cases :
#include <algorithm>
#include <stdio.h>
#include <cmath>
#include <iostream>
using namespace std;
int main(){
long long n, a[1000000], max;
int i, j;
cin>>n;
for(i = 0; i < n; i++){
cin>>a[i];
}
sort(a, a + n);
max = a[n - 1];
for(i = n - 2; i >= 0; i--){
//printf("%lld ", a[i]);
if(max < (a[i] * (n - i)))
max = a[i] * (n - i);
}
cout<<max<<endl;
return 0;
}
I dont know if my answer is right or wrong please point out mistakes if there is any
#include<stdio.h>
void main()
{
register int i,j;
long long int n,revenue;
scanf("%Ld",&n);
long long int a[n];
for(i=0;i<n;i++)
scanf("%Ld",&a[i]);
for (i=0;i<n;i++)
{
for(j=i+1;j<n;j++)
{
if(a[i]>a[j])
{
a[i]=a[i]+a[j];
a[j]=a[i]-a[j];
a[i]=a[i]-a[j];
}
}
}
for(i=0;i<n;i++)
a[i]=(n-i)*a[i];
revenue=0;
for(i=0;i<n;i++)
{
if(revenue<a[i])
revenue=a[i];
}
printf("%Ld\n",revenue);
}
passed all the test cases
n=int(input())
r=[]
for _ in range(n):
m=int(input())
r.append(m)
m=[]
r.sort()
l=len(r)
for i in range(l):
m.append((l-i)*r[i])
print(max(m))
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
int main() {
// your code goes here
long long n;
std::cin >> n;
long long a[n];
for(long long i=0;i<n;i++)
{
std::cin >> a[i];
}
sort(a,a+n);
long long max=LONG_MIN,count;
for(long long i=0;i<n;i++)
{
if(a[i]*(n-i)>max)
{
max=a[i]*(n-i);
}
}
std::cout << max << std::endl;
return 0;
}
The following solution is in C programming Language.
The Approach is:
Input the number of customers.
Input the budgets of customers.
Sort the budget.
Assign revenue=0
Iterate through the budget and Multiply the particular budget with the remaining budget values.
If the previous-revenue < new-revenue. assign the new-revenue to revenue variable.
The code is as follows:
#include <stdio.h>
int main(void) {
int i,j,noOfCustomer;
scanf("%d",&noOfCustomer);
long long int budgetOfCustomer[noOfCustomer],maximumRevenue=0;
for(i=0;i<noOfCustomer;i++)
{
scanf("%Ld",&budgetOfCustomer[i]);
}
for(i=0;i<noOfCustomer;i++)
{
for(j=i+1;j<noOfCustomer;j++)
{
if(budgetOfCustomer[i]>budgetOfCustomer[j])
{
budgetOfCustomer[i]=budgetOfCustomer[i] + budgetOfCustomer[j];
budgetOfCustomer[j]=budgetOfCustomer[i] - budgetOfCustomer[j];
budgetOfCustomer[i]=budgetOfCustomer[i] - budgetOfCustomer[j];
}
}
}
for(i=0;i<noOfCustomer;i++)
{
budgetOfCustomer[i]=budgetOfCustomer[i]*(noOfCustomer-i);
}
for(i=0;i<noOfCustomer;i++)
{
if(maximumRevenue<budgetOfCustomer[i])
maximumRevenue=budgetOfCustomer[i];
}
printf("%Ld\n",maximumRevenue);
return 0;
}
I am trying to solve this problem.
The goal is to determine the number of ways a morse string can be interpreted, given a dictionary of word.
What I did is that I first "translated" words from my dictionary into morse. Then, I used a naive algorithm, searching for all the ways it can be interpreted recursively.
#include <iostream>
#include <vector>
#include <map>
#include <string>
#include <iterator>
using namespace std;
string morse_string;
int morse_string_size;
map<char, string> morse_table;
unsigned int sol;
void matches(int i, int factor, vector<string> &dictionary) {
int suffix_length = morse_string_size-i;
if (suffix_length <= 0) {
sol += factor;
return;
}
map<int, int> c;
for (vector<string>::iterator it = dictionary.begin() ; it != dictionary.end() ; it++) {
if (((*it).size() <= suffix_length) && (morse_string.substr(i, (*it).size()) == *it)) {
if (c.find((*it).size()) == c.end())
c[(*it).size()] = 0;
else
c[(*it).size()]++;
}
}
for (map<int, int>::iterator it = c.begin() ; it != c.end() ; it++) {
matches(i+it->first, factor*(it->second), dictionary);
}
}
string encode_morse(string s) {
string ret = "";
for (unsigned int i = 0 ; i < s.length() ; ++i) {
ret += morse_table[s[i]];
}
return ret;
}
int main() {
morse_table['A'] = ".-"; morse_table['B'] = "-..."; morse_table['C'] = "-.-."; morse_table['D'] = "-.."; morse_table['E'] = "."; morse_table['F'] = "..-."; morse_table['G'] = "--."; morse_table['H'] = "...."; morse_table['I'] = ".."; morse_table['J'] = ".---"; morse_table['K'] = "-.-"; morse_table['L'] = ".-.."; morse_table['M'] = "--"; morse_table['N'] = "-."; morse_table['O'] = "---"; morse_table['P'] = ".--."; morse_table['Q'] = "--.-"; morse_table['R'] = ".-."; morse_table['S'] = "..."; morse_table['T'] = "-"; morse_table['U'] = "..-"; morse_table['V'] = "...-"; morse_table['W'] = ".--"; morse_table['X'] = "-..-"; morse_table['Y'] = "-.--"; morse_table['Z'] = "--..";
int T, N;
string tmp;
vector<string> dictionary;
cin >> T;
while (T--) {
morse_string = "";
cin >> morse_string;
morse_string_size = morse_string.size();
cin >> N;
for (int j = 0 ; j < N ; j++) {
cin >> tmp;
dictionary.push_back(encode_morse(tmp));
}
sol = 0;
matches(0, 1, dictionary);
cout << sol;
if (T)
cout << endl << endl;
}
return 0;
}
Now the thing is that I only have 3 seconds of execution time allowed, and my algorithm won't work under this limit of time.
Is this the good way to do this and if so, what am I missing ? Otherwise, can you give some hints about what is a good strategy ?
EDIT :
There can be at most 10 000 words in the dictionary and at most 1000 characters in the morse string.
A solution that combines dynamic programming with a rolling hash should work for this problem.
Let's start with a simple dynamic programming solution. We allocate an vector which we will use to store known counts for prefixes of morse_string. We then iterate through morse_string and at each position we iterate through all words and we look back to see if they can fit into morse_string. If they can fit then we use the dynamic programming vector to determine how many ways we could have build the prefix of morse_string up to i-dictionaryWord.size()
vector<long>dp;
dp.push_back(1);
for (int i=0;i<morse_string.size();i++) {
long count = 0;
for (int j=1;j<dictionary.size();j++) {
if (dictionary[j].size() > i) continue;
if (dictionary[j] == morse_string.substring(i-dictionary[j].size(),i)) {
count += dp[i-dictionary[j].size()];
}
}
dp.push_back(count);
}
result = dp[morse_code.size()]
The problem with this solution is that it is too slow. Let's say that N is the length of morse_string and M is the size of the dictionary and K is the size of the largest word in the dictionary. It will do O(N*M*K) operations. If we assume K=1000 this is about 10^10 operations which is too slow on most machines.
The K cost came from the line dictionary[j] == morse_string.substring(i-dictionary[j].size(),i)
If we could speed up this string matching to constant or log complexity we would be okay. This is where rolling hashing comes in. If you build a rolling hash array of morse_string then the idea is that you can compute the hash of any substring of morse_string in O(1). So you could then do hash(dictionary[j]) == hash(morse_string.substring(i-dictionary[j].size(),i))
This is good but in the presence of imperfect hashing you could have multiple words from the dictionary with the same hash. That would mean that after getting a hash match you would still need to match the strings as well as the hashes. In programming contests, people often assume perfect hashing and skip the string matching. This is often a safe bet especially on a small dictionary. In case it doesn't produce a perfect hashing (which you can check in code) you can always adjust your hash function slightly and maybe the adjusted hash function will produce a perfect hashing.