# Find The Shortest Superstring Problem

## Description

LeetCode Problem 943.

Given an array of strings words, return the smallest string that contains each string in words as a substring. If there are multiple valid strings of the smallest length, return any of them.

You may assume that no string in words is a substring of another string in words.

Example 1:

``````1
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Input: words = ["alex","loves","leetcode"]
Output: "alexlovesleetcode"
Explanation: All permutations of "alex","loves","leetcode" would also be accepted.
``````

Example 2:

``````1
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Input: words = ["catg","ctaagt","gcta","ttca","atgcatc"]
Output: "gctaagttcatgcatc"
``````

Constraints:

• 1 <= words.length <= 12
• 1 <= words[i].length <= 20
• words[i] consists of lowercase English letters.
• All the strings of words are unique.

## Sample C++ Code

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class Solution {
public:
string shortestSuperstring(vector<string>& A) {
const int n = A.size();
vector<vector<int> > g(n, vector<int>(n));
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
g[i][j] = A[j].length();
for (int k = 1; k <= min(A[i].length(), A[j].length()); k++) {
if (A[i].substr(A[i].length()- k) == A[j].substr(0, k)) {
g[i][j] = A[j].length() - k;
}
}
}

vector<vector<int> > dp(1<<n, vector<int>(n, INT_MAX/2));
vector<vector<int> > parent(1<<n, vector<int>(n, -1));
for (int i = 0; i < n; i++)
dp[1<<i][i] = A[i].length();

for (int s = 1; s < (1<<n); s++) {
for (int j = 0; j < n; j++) {
if (!s & (1 << j))
continue;
int ps = s & ~(1 << j);
for (int i = 0; i < n; i++) {
if (dp[s][j] > dp[ps][i] + g[i][j]) {
dp[s][j] = dp[ps][i] + g[i][j];
parent[s][j] = i;
}
}
}
}

string res;
auto it = min_element(begin(dp.back()), end(dp.back()));
int j = it - begin(dp.back());
int s = (1 << n) - 1;
while (s) {
int i = parent[s][j];
if (i < 0)
res = A[j] + res;
else
res = A[j].substr(A[j].length() - g[i][j]) + res;
s &= ~(1 << j);
j = i;
}
return res;
}
};
``````