Efficiently check if a string has duplicates without using any additional data structure

Implement an space efficient algorithm to determine if a string (of characters from ‘a’ to ‘z’) has all unique characters or not. Use additional data structures like count array, hash, etc is not allowed.

Expected Time Complexity : O(n)

Input  : str = "aaabbccdaa"
Output : No

Input  : str = "abcd"
Output : Yes

The idea is to use an integer variable and use bits in its binary representation to store whether a character is present or not. Typically an integer has at-least 32 bits and we need to store presence/absence of only 26 characters.

Below is C++ implementation of the idea.

// A space efficient C++ program to check if
// all characters of string are unique.
using namespace std;

// Returns true if all characters of str are
// unique.
// Assumptions : (1) str contains only characters
//                   from 'a' to 'z'
//               (2) integers are stored using 32
//                   bits
bool areChractersUnique(string str)
    // An integer to store presence/absence
    // of 26 characters using its 32 bits.
    int checker = 0;

    for (int i = 0; i < str.length(); ++i)
        int val = (str[i]-'a');

        // If bit corresponding to current
        // character is already set
        if ((checker & (1 << val)) > 0)
            return false;

        // set bit in checker
        checker |=  (1 << val);

    return true;

// Driver code
int main()
    string s = "aaabbccdaa";
    if (areChractersUnique(s))
        cout << "Yes";
        cout << "No";
    return 0;



Time Complexity: O(n)
Auxiliary Space : O(1)

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