Given a String S of length N, two integers B and C, the task is to traverse characters starting from the beginning, swapping a character with the character after C places from it, i.e. swap characters at position i and (i + C)%N. Repeat this process B times, advancing one position at a time. Your task is to find the final String after B swaps.
Examples:
Input : S = "ABCDEFGH", B = 4, C = 3;
Output: DEFGBCAH
Explanation:
after 1st swap: DBCAEFGH
after 2nd swap: DECABFGH
after 3rd swap: DEFABCGH
after 4th swap: DEFGBCAH
Input : S = "ABCDE", B = 10, C = 6;
Output : ADEBC
Explanation:
after 1st swap: BACDE
after 2nd swap: BCADE
after 3rd swap: BCDAE
after 4th swap: BCDEA
after 5th swap: ACDEB
after 6th swap: CADEB
after 7th swap: CDAEB
after 8th swap: CDEAB
after 9th swap: CDEBA
after 10th swap: ADEBC
Naive Approach:
- For large values of B, the naive approach of looping B times, each time swapping ith character with (i + C)%N-th character will result in high CPU time.
- The trick to solving this problem is to observe the resultant string after every N iterations, where N is the length of the string S.
- Again, if C is greater than or equal to the N, it is effectively equal to the remainder of C divided by N.
- Hereon, let’s consider C to be less than N.
Below is the implementation of the approach:
C++
// C++ Program to Swap characters in a String #include <iostream> #include <string> using namespace std; string swapCharacters(string s, int B, int C) { int N = s.size(); // If c is greater than n C = C % N; // loop to swap ith element with (i + C) % n th element for (int i = 0; i < B; i++) { swap(s[i % N], s[(i + C) % N]); } return s; } int main() { string s = "ABCDEFGH"; int B = 4; int C = 3; s = swapCharacters(s, B, C); cout << s << endl; return 0; } // This code is contributed by Susobhan Akhuli |
Output
DEFGBCAH
Time Complexity: O(B), to iterate B times.
Space Complexity: O(1)
Efficient Approach:
- If we observe the string that is formed after every N successive iterations and swaps (let’s call it one full iteration), we can start to get a pattern.
- We can find that the string is divided into two parts: the first part of length C comprising of the first C characters of S, and the second part comprising of the rest of the characters.
- The two parts are rotated by some places. The first part is rotated right by (N % C) places every full iteration.
- The second part is rotated left by C places every full iteration.
- We can calculate the number of full iterations f by dividing B by N.
- So, the first part will be rotated left by ( N % C ) * f . This value can go beyond C and so, it is effectively ( ( N % C ) * f ) % C, i.e. the first part will be rotated by ( ( N % C ) * f ) % C places left.
- The second part will be rotated left by C * f places. Since, this value can go beyond the length of the second part which is ( N – C ), it is effectively ( ( C * f ) % ( N – C ) ), i.e. the second part will be rotated by ( ( C * f ) % ( N – C ) ) places left.
- After f full iterations, there may still be some iterations remaining to complete B iterations. This value is B % N which is less than N. We can follow the naive approach on these remaining iterations after f full iterations to get the resultant string.
Example:
s = ABCDEFGHIJK; c = 4;
parts: ABCD EFGHIJK
after 1 full iteration: DABC IJKEFGH
after 2 full iteration: CDAB FGHIJKE
after 3 full iteration: BCDA JKEFGHI
after 4 full iteration: ABCD GHIJKEF
after 5 full iteration: DABC KEFGHIJ
after 6 full iteration: CDAB HIJKEFG
after 7 full iteration: BCDA EFGHIJK
after 8 full iteration: ABCD IJKEFGH
Below is the implementation of the approach:
C++
// C++ program to find new after swapping // characters at position i and i + c // b times, each time advancing one // position ahead #include <bits/stdc++.h> using namespace std; string rotateLeft(string s, int p) { // Rotating a string p times left is // effectively cutting the first p // characters and placing them at the end return s.substr(p) + s.substr(0, p); } // Method to find the required string string swapChars(string s, int c, int b) { // Get string length int n = s.size(); // If c is larger or equal to the length of // the string is effectively the remainder of // c divided by the length of the string c = c % n; if (c == 0) { // No change will happen return s; } int f = b / n; int r = b % n; // Rotate first c characters by (n % c) // places f times string p1 = rotateLeft(s.substr(0, c), ((n % c) * f) % c); // Rotate remaining character by // (n * f) places string p2 = rotateLeft(s.substr(c), ((c * f) % (n - c))); // Concatenate the two parts and convert the // resultant string formed after f full // iterations to a string array // (for final swaps) string a = p1 + p2; // Remaining swaps for(int i = 0; i < r; i++) { // Swap ith character with // (i + c)th character char temp = a[i]; a[i] = a[(i + c) % n]; a[(i + c) % n] = temp; } // Return final string return a; } // Driver code int main() { // Given values string s1 = "ABCDEFGHIJK"; int b = 1000; int c = 3; // Get final string print final string cout << swapChars(s1, c, b) << endl; } // This code is contributed by rag2127 |
Output:
CADEFGHIJKB
Time Complexity: O(n)
Space Complexity: O(n)
Please refer complete article on Swap characters in a String for more details!
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