Recently, I began to peruse the CLRS (Introduction to Algorithms).
Now I would like to scan all basic algorithms, especially sorting and searching.
Let me first present a classic sorting algorithm - merge sort. Here is my code. Before I reach here, some mistakes are made, thus I note these "pitfalls" in the code
#include <stdlib.h>
#include <stdio.h>
#define MAX 1e9 // the biggest possible value of a int number is 2^31 - 1 which is approximately 10^9
#define SIZE 10
int *a;
int *b;
int *c;
// merge [p, q] and [q+1, r], where within each range number are sorted
void merge(int p, int q, int r)
{
int k;
int length = r - p +1; // the length the range to be merge
for (k = 0; k < q - p + 1; k++) {
b[k] = a[p + k]; // copy number in a[p, q] to b
}
b[k] = MAX; // b[k] = MAX, not b[k+1]=MAX
for (k = 0; k < r - q; k++) {
c[k] = a[q + 1 + k]; // copy number in a[q+1, r] to c
}
c[k] = MAX; // c[k] = MAX, not c[k+1]=MAX
/* BEGIN merging */
int i = 0;
int j = 0;
for (k=0;k<length;k++) { // do exactly length times of copy
if (b[i] < c[j]) {
a[p + k] = b[i++]; // be careful! a[p, r] is a whole range now, and watch out the base "p"
} else {
a[p + k] = c[j++];
}
}
}
void merge_sort(int l, int u)
{
if (l == u) return; // when to stop recursion? only one number needs no sorting
int m = (l + u)/2;
merge_sort(l, m);
merge_sort(m + 1, u);
merge(l, m, u);
}
int main()
{
a = (int*)malloc(SIZE * sizeof(int));
b = (int*)malloc(SIZE * sizeof(int)); // cache, avoid many "malloc" in the merge function
c = (int*)malloc(SIZE * sizeof(int)); // this trick is from "Programming Pearls"
int i;
for (i = 0; i < SIZE; i++) {
a[i] = SIZE - i;
}
merge_sort(0, SIZE - 1); // watch out the range
for (i = 0; i < SIZE; i++) {
printf("%d\n", a[i]);
}
return 1;
}
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