Radix Sort CSC 172 SPRING 2004 LECTURE 25

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, *10^-5 * 524,288 * 256 * 27/19 = 40,380 But we got ~26,700 ~= 111 * 256

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

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 ==  Sorting is done by comparing bits in the same position  This will extend to keys that are alphanumeric strings

Radix Exchange Sort Sort array with respect to the leftmost bit

Radix Exchange Sort Partition Array Recursively sort subarrays Ignoring leftmost bit

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

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

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

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; }