vmorph
Reputation: 709
Optimized Selection Sort Algorithm (OSSA) - how to fix it?
I found this paper, that describes an optimized version of selection sort, that is supposed to outperform the classic selection sort in general. On page 4, the pseudo code for this particular variant is described as follows:
k = 0
for i = n–1 to k
IndexOfLarge = IndexOfSmall = k
for j = k+1 to i
if (X[j] > X[IndexOfLarge])
IndexOfLarge = j
if (X[j] < X[IndexOfSmall])
IndexOfSmall = j
Large = X[IndexOfLarge]
Small = X[IndexOfSmall]
X[IndexOfLarge] = X[i]
X[IndexOfSmall] = X[k]
if (IndexOfLarge == k)
Temp = X[i]
X[i] = Large
X[IndexOfSmall] = Temp
Else
X[i] = Large
if (IndexOfSmall == i)
Temp = X[k]
X[k] = Small
X[IndexOfLarge] = Temp
Else
X[k] = Small
k = k+1
It's fairly easy to translate that into C:
#include "selectionsort.h"
void selectionsort(int *array, size_t num) {
int *x = array;
for(int i = num-1, k = 0; i > k; --i, ++k) {
int i_small = k;
int i_large = k;
for(int j = k+1; j <= i; ++j) {
if(x[j] > x[i_large]) {
i_large = j;
}
if(x[j] < x[i_small]) {
i_small = j;
}
}
int large = x[i_large];
int small = x[i_small];
x[i_large] = x[i];
x[i_small] = x[k];
int tmp;
if(i_large == k) {
tmp = x[i];
x[i] = large;
x[i_small] = tmp;
} else {
x[i] = large;
}
if(i_small == i) {
tmp = x[k];
x[k] = small;
x[i_large] = tmp;
} else {
x[k] = small;
}
}
Now it turns out, this particular implementation doesn't always sort all inputs fully. For example, below is an array of 100 random integers, ranging from 0 to 100. If laid out for each iteration, then in the last two lines, right in the middle of the array, you will see the number 52 simply being overwritten.
0 86 85 24 38 64 29 8 50 38 64 1 71 71 93 1 35 18 52 31 10 88 21 64 61 85 39 71 26 98 94 1 83 78 25 20 7 55 96 57 59 59 59 29 96 17 30 93 35 49 90 11 36 10 76 97 95 14 33 88 78 93 89 60 36 80 46 44 8 41 0 59 66 25 89 61 42 85 20 44 33 76 55 36 87 97 32 47 10 32 0 88 24 55 13 61 35 60 71 98
0 0 85 24 38 64 29 8 50 38 64 1 71 71 93 1 35 18 52 31 10 88 21 64 61 85 39 71 26 71 94 1 83 78 25 20 7 55 96 57 59 59 59 29 96 17 30 93 35 49 90 11 36 10 76 97 95 14 33 88 78 93 89 60 36 80 46 44 8 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 97 32 47 10 32 0 88 24 55 13 61 35 60 98 98
0 0 0 24 38 64 29 8 50 38 64 1 71 71 93 1 35 18 52 31 10 88 21 64 61 85 39 71 26 71 94 1 83 78 25 20 7 55 96 57 59 59 59 29 96 17 30 93 35 49 90 11 36 10 76 60 95 14 33 88 78 93 89 60 36 80 46 44 8 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 97 32 47 10 32 85 88 24 55 13 61 35 97 98 98
0 0 0 1 38 64 29 8 50 38 64 24 71 71 93 1 35 18 52 31 10 88 21 64 61 85 39 71 26 71 94 1 83 78 25 20 7 55 96 57 59 59 59 29 96 17 30 93 35 49 90 11 36 10 76 60 95 14 33 88 78 93 89 60 36 80 46 44 8 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 47 10 32 85 88 24 55 13 61 97 97 98 98
0 0 0 1 1 64 29 8 50 38 64 24 71 71 93 38 35 18 52 31 10 88 21 64 61 85 39 71 26 71 94 1 83 78 25 20 7 55 61 57 59 59 59 29 96 17 30 93 35 49 90 11 36 10 76 60 95 14 33 88 78 93 89 60 36 80 46 44 8 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 47 10 32 85 88 24 55 13 96 97 97 98 98
0 0 0 1 1 1 29 8 50 38 64 24 71 71 93 38 35 18 52 31 10 88 21 64 61 85 39 71 26 71 94 64 83 78 25 20 7 55 61 57 59 59 59 29 13 17 30 93 35 49 90 11 36 10 76 60 95 14 33 88 78 93 89 60 36 80 46 44 8 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 47 10 32 85 88 24 55 96 96 97 97 98 98
0 0 0 1 1 1 7 8 50 38 64 24 71 71 93 38 35 18 52 31 10 88 21 64 61 85 39 71 26 71 94 64 83 78 25 20 29 55 61 57 59 59 59 29 13 17 30 93 35 49 90 11 36 10 76 60 55 14 33 88 78 93 89 60 36 80 46 44 8 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 47 10 32 85 88 24 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 50 38 64 24 71 71 93 38 35 18 52 31 10 88 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 13 17 30 93 35 49 90 11 36 10 76 60 55 14 33 88 78 93 89 60 36 80 46 44 8 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 47 10 32 85 88 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 38 64 24 71 71 88 38 35 18 52 31 10 88 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 13 17 30 93 35 49 90 11 36 10 76 60 55 14 33 88 78 93 89 60 36 80 46 44 50 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 47 10 32 85 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 64 24 71 71 88 38 35 18 52 31 38 88 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 13 17 30 85 35 49 90 11 36 10 76 60 55 14 33 88 78 93 89 60 36 80 46 44 50 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 47 10 32 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 24 71 71 88 38 35 18 52 31 38 88 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 13 17 30 85 35 49 90 11 36 64 76 60 55 14 33 88 78 32 89 60 36 80 46 44 50 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 47 10 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 71 71 88 38 35 18 52 31 38 88 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 13 17 30 85 35 49 24 11 36 64 76 60 55 14 33 88 78 32 89 60 36 80 46 44 50 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 47 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 71 88 38 35 18 52 31 38 88 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 13 17 30 85 35 49 24 71 36 64 76 60 55 14 33 88 78 32 47 60 36 80 46 44 50 41 86 59 66 25 89 61 42 85 20 44 33 76 55 36 87 35 32 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 88 38 35 18 52 31 38 88 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 71 17 30 85 35 49 24 71 36 64 76 60 55 14 33 88 78 32 47 60 36 80 46 44 50 41 86 59 66 25 32 61 42 85 20 44 33 76 55 36 87 35 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 38 35 18 52 31 38 88 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 71 17 30 85 35 49 24 71 36 64 76 60 55 35 33 88 78 32 47 60 36 80 46 44 50 41 86 59 66 25 32 61 42 85 20 44 33 76 55 36 87 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 35 18 52 31 38 87 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 71 38 30 85 35 49 24 71 36 64 76 60 55 35 33 88 78 32 47 60 36 80 46 44 50 41 86 59 66 25 32 61 42 85 20 44 33 76 55 36 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 35 52 31 38 87 21 64 61 85 39 71 26 71 24 64 83 78 25 20 29 55 61 57 59 59 59 29 71 38 30 85 35 49 24 71 36 64 76 60 55 35 33 36 78 32 47 60 36 80 46 44 50 41 86 59 66 25 32 61 42 85 20 44 33 76 55 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 52 31 38 55 21 64 61 85 39 71 26 71 24 64 83 78 25 35 29 55 61 57 59 59 59 29 71 38 30 85 35 49 24 71 36 64 76 60 55 35 33 36 78 32 47 60 36 80 46 44 50 41 86 59 66 25 32 61 42 85 20 44 33 76 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 31 38 55 21 64 61 85 39 71 26 71 24 64 83 78 25 35 29 55 61 57 59 59 59 29 71 38 30 85 35 49 24 71 36 64 76 60 55 35 33 36 78 32 47 60 36 80 46 44 50 41 76 59 66 25 32 61 42 85 52 44 33 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 38 55 31 64 61 33 39 71 26 71 24 64 83 78 25 35 29 55 61 57 59 59 59 29 71 38 30 85 35 49 24 71 36 64 76 60 55 35 33 36 78 32 47 60 36 80 46 44 50 41 76 59 66 25 32 61 42 85 52 44 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 55 31 64 61 33 39 71 26 71 38 64 83 78 25 35 29 55 61 57 59 59 59 29 71 38 30 44 35 49 24 71 36 64 76 60 55 35 33 36 78 32 47 60 36 80 46 44 50 41 76 59 66 25 32 61 42 85 52 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 31 64 61 33 39 71 26 71 38 64 83 78 25 35 29 55 61 57 59 59 59 29 71 38 30 44 35 49 55 71 36 64 76 60 55 35 33 36 78 32 47 60 36 80 46 44 50 41 76 59 66 25 32 61 42 52 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 64 61 33 39 71 26 71 38 64 52 78 31 35 29 55 61 57 59 59 59 29 71 38 30 44 35 49 55 71 36 64 76 60 55 35 33 36 78 32 47 60 36 80 46 44 50 41 76 59 66 25 32 61 42 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 61 33 39 71 26 71 38 64 52 78 31 35 29 55 61 57 59 59 59 29 71 38 30 44 35 49 55 71 36 64 76 60 55 35 33 36 78 32 47 60 36 42 46 44 50 41 76 59 66 64 32 61 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 33 39 71 61 71 38 64 52 61 31 35 29 55 61 57 59 59 59 29 71 38 30 44 35 49 55 71 36 64 76 60 55 35 33 36 78 32 47 60 36 42 46 44 50 41 76 59 66 64 32 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 39 71 61 71 38 64 52 61 31 35 33 55 61 57 59 59 59 29 71 38 30 44 35 49 55 71 36 64 76 60 55 35 33 36 32 32 47 60 36 42 46 44 50 41 76 59 66 64 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 71 61 71 38 64 52 61 31 35 33 55 61 57 59 59 59 39 71 38 30 44 35 49 55 71 36 64 64 60 55 35 33 36 32 32 47 60 36 42 46 44 50 41 76 59 66 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 61 71 38 64 52 61 31 35 33 55 61 57 59 59 59 39 71 38 71 44 35 49 55 71 36 64 64 60 55 35 33 36 32 32 47 60 36 42 46 44 50 41 66 59 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 59 38 64 52 61 61 35 33 55 61 57 59 59 59 39 71 38 71 44 35 49 55 71 36 64 64 60 55 35 33 36 32 32 47 60 36 42 46 44 50 41 66 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 38 64 52 61 61 35 33 55 61 57 59 59 59 39 66 38 71 44 35 49 55 71 36 64 64 60 55 35 33 36 59 32 47 60 36 42 46 44 50 41 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 64 52 61 61 35 33 55 61 57 59 59 59 39 66 38 41 44 35 49 55 71 36 64 64 60 55 35 33 36 59 38 47 60 36 42 46 44 50 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 52 61 61 35 64 55 61 57 59 59 59 39 66 38 41 44 35 49 55 50 36 64 64 60 55 35 33 36 59 38 47 60 36 42 46 44 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 61 61 35 64 55 61 57 59 59 59 39 44 38 41 44 35 49 55 50 36 64 64 60 55 35 52 36 59 38 47 60 36 42 46 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 61 61 46 55 61 57 59 59 59 39 44 38 41 44 35 49 55 50 36 64 64 60 55 35 52 36 59 38 47 60 36 42 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 61 46 55 61 57 59 59 59 39 44 38 41 44 61 49 55 50 36 42 64 60 55 35 52 36 59 38 47 60 36 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 46 55 61 57 59 59 59 39 44 38 41 44 61 49 55 50 36 42 36 60 55 61 52 36 59 38 47 60 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 55 60 57 59 59 59 39 44 38 41 44 61 49 55 50 46 42 36 60 55 61 52 36 59 38 47 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 60 57 59 59 59 39 44 38 41 44 47 49 55 50 46 42 55 60 55 61 52 36 59 38 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 57 59 59 59 39 44 38 41 44 47 49 55 50 46 42 55 60 55 38 52 60 59 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 59 59 59 39 44 57 41 44 47 49 55 50 46 42 55 59 55 38 52 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 59 59 39 44 57 41 44 47 49 55 50 46 42 55 59 55 59 52 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 39 59 52 44 57 41 44 47 49 55 50 46 42 55 59 55 59 59 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 39 41 52 44 57 59 44 47 49 55 50 46 42 55 59 55 59 59 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 39 41 42 44 57 55 44 47 49 55 50 46 52 55 59 59 59 59 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 39 41 42 44 57 55 44 47 49 55 50 46 52 55 59 59 59 59 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 39 41 42 44 44 55 55 47 49 55 50 46 52 57 59 59 59 59 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 39 41 42 44 44 46 55 47 49 55 50 52 55 57 59 59 59 59 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 39 41 42 44 44 46 47 52 49 55 50 55 55 57 59 59 59 59 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 39 41 42 44 44 46 47 49 52 50 55 55 55 57 59 59 59 59 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
0 0 0 1 1 1 7 8 8 10 10 10 11 13 14 17 18 20 20 21 24 24 25 25 26 29 29 30 31 32 32 33 33 35 35 35 36 36 36 38 38 39 41 42 44 44 46 47 49 50 50 55 55 55 57 59 59 59 59 60 60 61 61 61 64 64 64 66 71 71 71 71 76 76 78 78 80 83 85 85 85 86 87 88 88 88 89 89 90 93 93 93 94 95 96 96 97 97 98 98
For every input, there's always one value overwritten, but if I'm lucky, that value is overwritten by a duplicate, then it's sorted. But that doesn't always happen.
How do I fix this?
Upvotes: 2
Views: 367
Answers (2)
John Bollinger
Reputation: 181149
As @Bob__ points out, the program does the wrong thing when the largest element of one of the sub-arrays appears at the first position (unless the smallest element also appears at the last position). It appears that this error is faithfully copied from the referenced authors' pseudocode, which seems par for the course with that not-very-impressive paper. Inasmuch as their analysis of specific complexity is based on their pseudocode, its details are also called into question, though the fact that the algorithm is faster than simple selection sort is not in doubt.
In any event, I would write the swapping section of this code rather differently:
// swap the maximum and minimum elements into place, handling
// a bit of trickiness when one (or both) of the extreme values
// is at the far opposite end of the interval from where it belongs.
int large = x[i_large];
int small = x[i_small];
if (i_small == i) {
if (i_large != k) {
// Three-way swap: move the middle element to index i_large
x[i_large] = x[k];
} // else a straight swap of positions k and i
} else if (i_large == k) {
// Three-way swap: move the middle element to index i_small
x[i_small] = x[i];
} else {
// Two independent swaps
x[i_small] = x[k];
x[i_large] = x[i];
}
// In all cases:
x[k] = small;
x[i] = large;
That
- Produces the right result in all cases
- Performs the same number of comparisons as the analogous section of original code in the worst case, but may perform fewer
- Performs the same number of assignments as the analogous section of the original code in the worst case, but may perform fewer
Upvotes: 4
Bob__
Reputation: 12779
In your code, those lines:
int large = x[i_large];
int small = x[i_small];
x[i_large] = x[i]; // if k == i_large ==> x[k] = x[i]; or x[i_large] = x[i_small];
x[i_small] = x[k]; // and i == i_small
Generates the issue when k == i_large and i == i_small. To avoid the problem use:
int tmp = x[k];
x[i_large] = x[i];
x[i_small] = tmp;
Upvotes: 2
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