Record Keys: 27, 18, 29, 28, 39, 13, 16

Table Size = 11; Hash Function = hash(key) = key mod 11

Incrementing Function = i(key) = Quotient (Key / 11) mod 11 (computed on incoming key)

	Key
0
1
2
3
4
5	27	1. 27 mod 11 = 5
6
7	18	2. 18 mod 11 = 7; 3. 29 mod 11 = 7; i(29) = 2 so try 9
8
9
10

Should we move 18 to reduce the total # of probes? 18 has 1; 29 has 2; Is there any combination of i + j < 2? No, so don't move anything. Only if s (# of probes required to retrieve the item if nothing is moved) is 3 or more do we try to move.

	Key
0
1
2
3
4
5	27
6	28	4. 28 mod 11 = 6; 5. 39 mod 11 = 6; collision
7	18
8
9	29
10

s value of 39 is 3 (i(39) = 3; try loc9; then loc1 so we need 3 probes to find 39) - try to reduce this; start with i = 1 and j = 1 ; try moving what is at the home address one offset along its chain i.e. move 28 to (i(28) = 2; so offset is 2) loc8. This works, so move 28 to loc8 and put 39 in loc6

	Key
0
1
2	13	6. 13 mod 11 = 2
3
4
5	27	7. 16 mod 11 = 5; i(16) = 1; its s value is 6
6	39
7	18
8	28
9	29
10

try i=1; j=1; moving 27 i(27) = 2; but loc7 is filled so try another.

try i=1; j=2; moving 27 to the next location 9; but it's filled too

try i=2; j=1; moving 39 i(39) = 3; but it's filled too

try i=1;j=3; moving 27 to the next location 0 - this works so move 27 to loc0 and put 16 in loc5

Is this better? Total probes for 27 and 16 without moves is 7; but with moves is 5 so we're ahead.

	Key
0	27
1
2	13
3
4
5	16
6	39
7	18
8	28
9	29
10