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Longest Duplicate Substring in C++
Suppose we have a string S, consider all duplicated contiguous substrings that occur 2 or more times. (The occurrences may overlap.), We have to find the duplicated substring that has the longest possible length. If there is no such substrings, then return a blank string. As the answer may very large, so return in mod 10^9 + 7.
So, if the input is like "ababbaba", then the output will be "bab"
To solve this, we will follow these steps −
m := 1e9 + 7
Define a function add(), this will take a, b,
return ((a mod m) + (b mod m)) mod m
Define a function sub(), this will take a, b,
return ((a mod m) - (b mod m) + m) mod m
Define a function mul(), this will take a, b,
return ((a mod m) * (b mod m)) mod m
Define an array power
Define a function ok(), this will take x, s,
if x is same as 0, then −
return empty string
Define one map called hash
current := 0
for initialize i := 0, when i < x, update (increase i by 1), do −
current := add(mul(current, 26), s[i] - 'a')
hash[current] := Define an array (1, 0)
n := size of s
for initialize i := x, when i < n, update (increase i by 1), do −
current := sub(current, mul(power[x - 1], s[i - x] - 'a'))
current := add(mul(current, 26), s[i] - 'a')
if count is member of hash, then −
for all it in hash[current] −
if substring of s from it to x - 1 is same as substring of s from i - x + 1 to x - 1, then −
return substring of s from it to x - 1
Otherwise
insert i - x + 1 at the end of hash[current]
return empty string
From the main method, do the following −
ret := empty string
n := size of S
power := Define an array of size n and fill this with 1
for initialize i := 1, when i < n, update (increase i by 1), do −
power[i] := mul(power[i - 1], 26)
low := 0, high := n - 1
while low <= high, do −
mid := low + (high - low) /2
temp := ok(mid, S)
if size of temp is same as 0, then −
high := mid - 1
Otherwise
if size of temp > size of ret, then −
ret := temp
low := mid + 1
return ret
Let us see the following implementation to get better understanding −
Example
#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
class Solution {
public:
int m = 1e9 + 7;
int add(lli a, lli b){
return ((a % m) + (b % m)) % m;
}
int sub(lli a, lli b){
return ((a % m) - (b % m) + m) % m;
}
int mul(lli a, lli b){
return ((a % m) * (b % m)) % m;
}
vector<int> power;
string ok(int x, string s){
if (x == 0)
return "";
unordered_map<int, vector<int> > hash;
lli current = 0;
for (int i = 0; i < x; i++) {
current = add(mul(current, 26), s[i] - 'a');
}
hash[current] = vector<int>(1, 0);
int n = s.size();
for (int i = x; i < n; i++) {
current = sub(current, mul(power[x - 1], s[i - x] -
'a'));
current = add(mul(current, 26), s[i] - 'a');
if (hash.count(current)) {
for (auto& it : hash[current]) {
if (s.substr(it, x) == s.substr(i - x + 1, x)) {
return s.substr(it, x);
}
}
} else {
hash[current].push_back(i - x + 1);
}
}
return "";
}
string longestDupSubstring(string S){
string ret = "";
int n = S.size();
power = vector<int>(n, 1);
for (int i = 1; i < n; i++) {
power[i] = mul(power[i - 1], 26);
}
int low = 0;
int high = n - 1;
while (low <= high) {
int mid = low + (high - low) / 2;
string temp = ok(mid, S);
if (temp.size() == 0) {
high = mid - 1;
} else {
if (temp.size() > ret.size())
ret = temp;
low = mid + 1;
}
}
return ret;
}
};
main(){
Solution ob;
cout << (ob.longestDupSubstring("ababbaba"));
}Input
"ababbaba"
Output
bab
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