1. Radix Sort CSC 172 SPRING 2004 LECTURE 25

2. Theoretical bound? A * n logn = t A* 524,288 * 19 = 111 A = 1.1*10^-5 1.1*10^-5 * 134,217,728 * 27 = 40,380 1.1*10^-5 * 524,288 * 256 * 27/19 = 40,380 But we got ~26,700 ~= 111 * 256

3. What happened?  The key word in the theoretical proof was “comparison based”  Some sorts are not comparison based

4. Radix Sort  Unlike other methods, radix sort considers the structure of the keys  Assume that the keys are represented in base M number system (M == radix)  i.e. if M == 2 we are in the binary number system  9 10 == 1001 2  Sorting is done by comparing bits in the same position  This will extend to keys that are alphanumeric strings

5. Radix Exchange Sort 1 1 0 1 0 0 0 1 1 1 Sort array with respect to the leftmost bit

6. Radix Exchange Sort 0 0 1 1 1 0 0 Partition Array 1 1 1 Recursively sort subarrays Ignoring leftmost bit

7. Time How many bits in the keys? “b” How much work per bit? “N” O(bN) Not bad for 16 bit shorts

8. Exchange  In place, like Quicksort Repeat Scan top-down to find a “1” Scan bottom-up to find a “0” Exchange keys Until scan indices cross

9. public static void mySorter(short[]B) { int mask = 0x8000; mySorter(B,0,B.length -1, mask); }

10. public static void mySorter(short[] B,int bottom,int top, int mask){ if (mask <= 0 ) return; int oldtop = top; int oldbottom = bottom; while (top > bottom) { while ((bottom < (B.length - 1)) && ((((int) B[bottom]) & mask) == 0)) bottom++; while ((top >0) && ((((int) B[top]) & mask) > 0)) top --; if (top > bottom) { short temp = B[bottom]; B[bottom] = B[top]; B[top] = temp; } mySorter(B,oldbottom,top,mask>>1); mySorter(B,top+1,oldtop,mask>>1); return; }