1. Boggle Game: Backtracking Algorithm Implementation
CS 1501

2. Recursive Implementation
Things to implementation for a recursive algorithm:
Find the common behavior in the algorithm, and implement that as a function.
Action: what to do for the current situation
Recursive call: how to trigger next step
Stop criteria: when to stop further recursion
function Test (data) {
if data satisfies stop criteria (1)
return;
do sometime for data (2)
for all new_data from data
Test (new_data); (3) }
2017/4/12

3. Recursive Boggle Each move on the board can be a recursive call
They accomplish similar tasks based on the string we have so far.
function AdvanceStep (pos, string) {
new_string = string + letter[pos];
if new_string is not prefix, not word (1)
return; }
2017/4/12

4. Recursive Boggle Each move on the board can be a recursive call
They accomplish similar tasks based on the string we have so far.
function AdvanceStep (pos, string) {
new_string = string + letter[pos];
if new_string is not prefix, not word (1)
return;
if new_string is a word (2)
output string }
2017/4/12

5. Recursive Boggle Each move on the board can be a recursive call
They accomplish similar tasks based on the string we have so far.
function AdvanceStep (pos, string) {
new_string = string + letter[pos];
if new_string is not prefix, not word (1)
return;
if new_string is a word (2)
output string
if new_string is a prefix (3)
for all possible next step new_pos
AdvanceStep (new_pos, new_string);
return }
2017/4/12

6. de la Briandias Tree: Dealing with string prefix
CS 1501

7. Note Structure DLB tree is used to organize key set (dictionary).
A path from root to leaf represents a word. a
Child
Pointer
Char
Sibling b c d e $ f $ $
abe ac
adf
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8. Node Structure Determine prefix? Determine word? a Char b c d e $ f $
The node has at least one child that is not a “end-of-string” sign.
Determine word?
Node has a child with “end-of-string” sign. a
Child
Pointer
Char
Sibling b c d e $ f $ $
abe ac
adf
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9. An Example Construct a DLB tree for the following words:
abc, abe, abet, abx, ace, acid
hives, iodin, inval, zoo, zool, zurich
2017/4/12

10. Insert Operation INSERTION (tree pointer TREE, word WORD) { out = 0;
letter = word [at position i];
current = TREE;
DO WHILE (( i <= length of WORD) and (out=0)) {
IF (letter equals (current->key)) { //if we have a match
i = i +1;
letter = word[ at position i];
current = current->child_pointer; //follow the child
} ELSE { //we have to check siblings
IF (current->sibling_pointer does not equal Null)
current = current->sibling;
ELSE
out=1; //no sibling, we add new node }
} (end of DO WHILE)
…… // insertion
2017/4/12

11. Insert Operation INSERTION (tree pointer TREE, word WORD) {
…….. // search
// we're at the point of insertion of new node,
// unless the word is already there:
IF (out = 0) EXIT //if the word was already there, exit
// otherwise add a new node with the current letter
current->sibling_pointer = CREATE new NODE (letter);
i = i + 1; // and move on to append the rest of the letters
FOR (m=i ; m<= length of WORD; m++) {
current.child_pointer = CREATE new NODE ( WORD[at position m]);
current = current->child_pointer; }
// now we just add the $ marker for end of word
current.child_pointer = CREATE new TERMINAL $ MARKER NODE;
2017/4/12

12. Delete Operation DELETE (tree pointer TREE, word WORD) {
current = TREE; // we start with the first node again
out=0;
i=0;
letter = WORD [at position i];
DO WHILE (( i <= length of WORD) and (out=0)) {
IF (letter is equal to current->key)
current = current->child_pointer; //we move down one level
i = i + 1;
letter = WORD [at position i]; // we move onto next letter
ELSE
IF (there is a sibling node) {
last_sibling = current; //store the last sibling
current = current->sibling // move to the sibling node }
IF (there is no sibling node)
out =1; // EXIT with ERROR
} DO WHILE
…… // deleteion
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13. Delete Operation DELETE (tree pointer TREE, word WORD) { ……. // search
PUSH last_sibling->sibling_pointer onto STACK
PUSH all the children of last_sibling->sibling_pointer onto STACK one by one,
until the $ marker
Set all of the pointers on STACK to Null. as you're POPPING them off the STACK }
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14. Corner cases The tree is empty when insert a word
The word is the last one in the tree …
2017/4/12