This version of bubble sort stops when there are no more exchanges and it also sorts a smaller range each time.

void bubbleSort3(int x[], int n) {  bool exchanges;  do {    n--;               // make loop smaller each time.    exchanges = false; // assume this is last pass over array    for (int i=0; i x[i+1]) {        int temp = x[i];  x[i] = x[i+1];  x[i+1] = temp;        exchanges = true;  // after an exchange, must look again      }    }  } while (exchanges);}

There’s one disadvantage: after the first pass it may not be necessary to examine the entire range of the array?only from where the lowest exchange occurred to where the highest exchange occurred.