Codeforces #806 Problem D: Double Strings

Question

I tried solving the following problem by following the suggested approach to solving the problem in the problem tutorial. However, the online judge still says my solution exceeds the time limit. Is there a way to optimize the program to perform faster?

The Problem:

You are given \$n\$ strings \$s_1, s_2, \dots, s_n\$ of length at most 8.

For each string \$s_i\$, determine if there exist two strings \$s_j\$ and \$s_k\$ such that \$s_i = s_j + s_k\$. That is, \$s_i\$ is the concatenation of \$s_j\$ and \$s_k\$. Note that \$j\$ can be equal to \$k\$.

Recall that the concatenation of strings \$s\$ and \$t\$ is \$s + t = s_1 s_2 \dots s_p t_1 t_2 \dots p_q\$, where \$p\$ and \$q\$ are the lengths of strings \$s\$ and \$t\$ respectively. For example, concatenation of "code" and "forces" is "codeforces".

Input

The first line contains a single integer \$t\$ (\1ドル \leq t \leq 10^4\$) — the number of test cases.

The first line of each test case contains a single integer \$n\$ (\1ドル \leq n \leq 10^5\$) — the number of strings.

Then \$n\$ lines follow, the \$i\$-th of which contains non-empty string \$s_i\$ of length at most 8, consisting of lowercase English letters. Among the given \$n\$ strings, there may be duplicates.

The sum of \$n\$ over all test cases doesn't exceed \10ドル^5\$.

Output

For each test case, output a binary string of length \$n\$. The \$i\$-th bit should be 1 if there exist two strings \$s_j\$ and \$s_k\$ where \$s_i = s_j + s_k\$, and 0 otherwise. Note that \$j\$ can be equal to \$k\$.

Example

Input:

3
5
abab
ab
abc
abacb
c
3
x
xx
xxx
8
codeforc
es
codes
cod
forc
forces
e
code

Output:

10100
011
10100101

The Problem Tutorial (Hint):

Use some data structure that allows you to answer queries of the form: "does the string \$t\$ appear in the array \$s_1, \dots, s_n\$?" For example, in C++ you can use a map<string, bool>, while in Python you can use a dictionary.

Afterwards, for each string \$s\$, brute force all strings \$x\$ and \$y\$ such that \$s=x+y\$. There are at most 7 such strings, because \$s\$ has length at most 8. Then check if both \$x\$ and \$y\$ appear in the array using your data structure.

The time complexity is \$O(l n \log n)\$ per test case, where \$l\$ is the maximum length of an input string.

My Solution

#include <iostream>
#include <string>
#include <unordered_map>
using namespace std;
int main()
{
 int tests;
 cin >> tests;
 for (int i = 0; i < tests; i++) { //one loop per each test case
 int NumOfStrings;
 cin >> NumOfStrings;
 unordered_map<string, bool> phrases;
 string words[100000];
 for (int j = 0; j < NumOfStrings; j++) { // adds all input strings for each test case into words and phrases
 string temp;
 cin >> temp;
 phrases.insert({ temp, false });
 words[j] = temp;
 }
 for (int k = 0; k < NumOfStrings; k++) { // loop for each string in the test case
 int len = words[k].length(); // len is length of current word
 for (int o = 0; o < len; o++) { // loops through current word
 string partition1 = "";
 string partition2 = "";
 for (int m = 0; m <= o; m++) {
 partition1 += words[k][m];
 }
 for (int n = o+1; n < len; n++) {
 partition2 += words[k][n];
 }
 if (phrases.find(partition1) != phrases.end() && phrases.find(partition2) != phrases.end()) { //if both substrings exist in the map, then value for word is 1.
 phrases[words[k]] = true;
 }
 }
 }
 for (int j = 0; j < NumOfStrings; j++) {
 int value = 0;
 if (phrases[words[j]] == true) value = 1;
 cout << value;
 }
 cout << endl;
 }
 return 0;
}

• qwr: I thought code review SE was for code that already works as intended. if it doesn't it probably belongs on SO
• Deduplicator: @qwr Too inefficient (time or space) is the one failure we accept here.

Answer 1

You are failing with the datastructures.

What you need is:

1. A string to mark your answers.
   Start with all no.

2. A std::vector to collect your strings.

3. A way to identify all candidates for the prefix fast.
   A sorted std::vector will do.

   • You might want to get fancy when iterating it to identify candidates even faster.
   • Don't forget to include the id to mark your answers.

4. A way to test existence of a matching suffix.
   A hashset will do fabulously.

And for the love of all, don't duplicate strings for the two datastructures, use std::string_view.

As you only use it once it's not that bad, but you really don't need the manual flush in std::endl. And if you did need it, you should still be explicit and use std::flush.

• panik: Now I'm questioning my beliefs whether unordered_set is almost always faster than set. I had a solution using unordered_set rejected with "time limit exceeded" verdict, but the one using set was accepted. I packed strings into unsigned long long integers and used bit operations.

Answer 2

Move solution into a separate function

Doing this greatly improves code readability.

void solve() {
 int NumOfStrings;
 /* ... */ 
}
int main() {
 int t;
 cin >> t;
 while (t--)
 solve();
 return 0;
}

Be careful about using resources

On each iteration, we do a lot of redundant work by creating and destroying 100k strings.

for (int i = 0; i < tests; i++) { //one loop per each test case
 string words[100000];
}

Presumably, heap allocation is not involved due to the small string optimization.

To optimize memory usage, make the array static.

for (int i = 0; i < tests; i++) { //one loop per each test case
 static string words[100000];
}

Misleading hint

Before checking the author's solution, I didn't quite understand the purpose of using map. Let's find it out.

void solve() {
 /* ... */
 map<string, bool> mp;
 for (int i = 0; i < n; i++) {
 cin >> s[i];
 mp[s[i]] = true; // map input string to true
 }
 for (int i = 0; i < n; i++) {
 /* ... */
 /* mp[pref] adds pair {pref, false} to mp
 if pref is not presented and returns false;
 otherwise, returns true if pref is an input string */ 
 if (mp[pref] && mp[suff]) { ok = true; } 
 /* ... */
}

The author's map gradually growths, but only input strings are mapped to true.

Looks like the hint was misinterpreted, which is not surprising because it had been taken out of the context.

for (int k = 0; k < NumOfStrings; k++) { // loop for each string in the test case
 /* ... */
 if (phrases.find(partition1) != phrases.end() && phrases.find(partition2) != phrases.end()) { //if both substrings exist in the map, then value for word is 1.
 phrases[words[k]] = true;
 }
 }
}
for (int j = 0; j < NumOfStrings; j++) {
 int value = 0;
 if (phrases[words[j]] == true) value = 1;
 cout << value;
}

Needlessly changing mapped values to check them later in the separate loop, is a lot of redundant work. Searching for partitions is the only crucial part here, which may be performed with a set instead of map.

In conclusion

It suffices to apply the proposed improvements to make your solution accepted.

#include <iostream>
#include <string>
#include <unordered_set>
using namespace std;
void solve()
{
 int NumOfStrings;
 cin >> NumOfStrings;
 unordered_set<string> phrases;
 static string words[100000];
 for (int j = 0; j < NumOfStrings; j++) { // adds all input strings for each test case into words and phrases
 string temp;
 cin >> temp;
 phrases.insert(temp);
 words[j] = temp;
 }
 for (int k = 0; k < NumOfStrings; k++) { // loop for each string in the test case
 int len = words[k].length(); // len is length of current word
 bool ok = false;
 for (int o = 0; o < len; o++) { // loops through current word
 string partition1 = "";
 string partition2 = "";
 for (int m = 0; m <= o; m++) {
 partition1 += words[k][m];
 }
 for (int n = o+1; n < len; n++) {
 partition2 += words[k][n];
 }
 if (phrases.find(partition1) != phrases.end() && phrases.find(partition2) != phrases.end()) { //if both substrings exist in the map, then value for word is 1.
 ok = true;
 break;
 }
 }
 cout << ok;
 }
 cout << endl;
}
int main()
{
 int tests;
 cin >> tests;
 while (tests--)
 solve();
 return 0;
}