Given a binary string S, the task is to find the minimum number of Powers of 2 required to express a S.
Examples:
Input:_ S = “111”_
Output:_ 2_
Explanation:
Two possible representations of “111” (= 7) using powers of 2 are:
20 + 21 + 22 = 1 + 2 + 4 = 7
23 – 20 = 8 – 1 = 7
Therefore, the minimum powers of 2 required to represent S is 2.
Input:_ S = “1101101”_
Output:_ 4_
Explanation:
1101101 can be represented as 27 – 24 – 22 + 20.
Approach:
The key observation to solve this problem is that we can replace any consecutive sequence of 1 by using only two powers of 2.
Illustration:
S = “1001110”
The sequence of 3 consecutive 1’s, “1110” can be expressed as 24 – 21
Therefore, the given str
Follow the steps below to solve the problem:
- Reverse the string S.
- Iterate over the string S.
- Replace every substring of 1’s lying within indices [L, R] by placing 1 at R+1 and -1 at L.
- Once the entire string is traversed, count the number of non-zero values in the string as the required answer.
Below is the implementation of the above approach:
- C++
filter_none
edit
play_arrow
brightness_4
// C++ Program to implement the
// above approach
#include <bits/stdc++.h>
**using** **namespace** std;
// Function to return the minimum
// distinct powers of 2 required
// to express s
**void** findMinimum(string s)
{
**int** n = s.size();
**int** x[n + 1] = { 0 };
// Reverse the string to
// start from lower powers
reverse(s.begin(), s.end());
**for** (``**int** i = 0; i < n; i++) {
// Check if the character is 1
**if** (s[i] == '1'``) {
**if** (x[i] == 1) {
x[i + 1] = 1;
x[i] = 0;
}
// Add in range provided range
**else** **if** (i and x[i - 1] == 1) {
x[i + 1] = 1;
x[i - 1] = -1;
}
**else**
x[i] = 1;
}
}
// Initialize the counter
**int** c = 0;
**for** (``**int** i = 0; i <= n; i++) {
// Check if the character
// is not 0
**if** (x[i] != 0)
// Increment the counter
c++;
}
// Print the result
cout << c << endl;
}
// Driver Code
**int** main()
{
string str = "111"``;
findMinimum(str);
**return** 0;
}
Output:
2
#arrays #competitive programming #greedy #mathematical #strings #binary-string #substring
