## Wednesday, June 2, 2010

### Merge sort

How it Works;
1) divide the list in half
2) perform mergesort on the left and right parts
3) merge the left and right parts back in order

Properties;
Best, Average and Worst case speed is O(nlog(n)).
Memory is n
It is Stable

//compile with g++
#include <iostream>
#include <iomanip>
using namespace std;

void mergeSort(int* data, int* buffer, int size)
{
if(size < 2)
return;

int mid       = size/2;

mergeSort(data,       buffer, mid);
mergeSort(&data[mid], buffer, size - mid);

int left      = 0;
int right     = mid;
int out       = 0;
while(
(left  != mid ) &&
(right != size)
)
{
if(data[right] < data[left]) { buffer[out++] = data[right++]; }
else                         { buffer[out++] = data[left++];  }
}

while(left  != mid  ) { buffer[out++] = data[left++];  }
while(right != size ) { buffer[out++] = data[right++]; }

//transfer the buffer back to the main... small size sort so its better then doing mallocs all over the place
out = 0;
while(out != size ) { data[out] = buffer[out]; out++; }
}

//test
#define SIZE 20
#define SCRAMBLE(x, y) ((0xa57b & ~y) + ((0x3829 & x) << 1))

bool check(int data[], int size)
{
for(int i = 1; i < size; i++)
if(data[i] < data[i-1])
{
cout << "FAIL!" << endl;
return false;
}
cout << "PASS" << endl;
return true;
}

void print(int data[], int size)
{
for(int i = 0; i < size; i++)
cout << setw(5) << data[i] << " ";
cout << endl;
}

bool test(int* data, int* buffer, int size)
{
print(data, SIZE);
mergeSort(data, buffer, SIZE);
print(data, SIZE);
return check(data, SIZE);
}

int main()
{
int data[SIZE];
int buffer[SIZE];
bool pass = true;

//easy data
data[0] = 1;
for(int i = 0; i < SIZE; i++)
data[i] = SIZE - i;
pass &= test(data, buffer, SIZE);

//semi repeated data
data[0] = 1;
for(int i = 1; i < SIZE; i++)
data[i] = SCRAMBLE(i, data[i-1]);
pass &= test(data, buffer, SIZE);

//the sort killer!
for(int i = 0; i < SIZE; i++)
data[i] = 5;
pass &= test(data, buffer, SIZE);

//and some randoms to catch anything i missed
srand ( time(NULL) );

for(int j = 0; j < 100; j++)
{
for(int i = 0; i < SIZE; i++)
data[i] = (int)((float)(j+1)*((float)rand()/(float)RAND_MAX));
pass &= test(data, buffer, SIZE);
}

if(pass)
cout << "ALL PASSED" << endl;
else
cout << "FAILED" << endl;
}