In this problem, one positive integer string is given, we have to find the permutation whose value is maximum by swapping digits’ k times, into different places.
We will solve this problem by choosing a digit and swap it with digits following it one at a time to find a maximum number. We repeat the process k times. The backtracking strategy is working here because when we find a number which is not greater than the previous value, we backtrack to old value and check again.
Input and Output
Input: A number of multiple digits. The input is: 129814999 Output: The maximum value from these digits by swapping them. The output is: 999984211
Algorithm
maxNum(number, swaps, maxNumber)
Input − The number as a string, the number of swaps and the maxNumber string.
Output − Update the maxNumber to get the largest value.
Begin if swaps = 0, then return n := number of digits in the number for i := 0 to n-2, do for j := i+1 to n-1, do if number[i] < number[j], then exchange number[i] and number[j] if number is greater than maxNumber, then maxNumber := number maxNum(number, swaps-1, maxNumber) exchange number[i] and number[j] again for backtrack done done End
Example
#include <iostream>
using namespace std;
void maxNum(string str, int swaps, string &max) {
if(swaps == 0) //when no swaps are left
return;
int n = str.length();
for (int i = 0; i < n - 1; i++) { //for every digits og given number
for (int j = i + 1; j < n; j++) {
if (str[i] < str[j]) { //when ith number smaller than jth number
swap(str[i], str[j]);
if (str.compare(max) > 0) //when current number is greater, make it maximum
max = str;
maxNum(str, swaps - 1, max); //go for next swaps
swap(str[i], str[j]); //when it fails, reverse the swapping
}
}
}
}
int main() {
string str = "129814999";
int swapNumber = 4;
string max = str;
maxNum(str, swapNumber, max);
cout <<"The given number is: " <<str << endl;
cout <<"The maximum number is: "<< max << endl;
}Output
The given number is: 129814999 The maximum number is: 999984211