How Would You Move Mount Fuji ? Andrzej Hoppe. Goals Algorithms and Puzzles are fun Give a chance to win coffee What does the title mean ?

How Would You Move Mount Fuji ?

Andrzej Hoppe

Goals

• Algorithms and Puzzles are fun

• Give a chance to win coffee• What does the title mean ?

Why should we like algorithms ?

• 6111 - A+ • Free pizza• Internship• 50,000 $

Problem definition

Input:Array(t) of length n, contains entries from the set { 1, 2, …, n-1 }

Output:One of duplicated numbers

Criterions

• Time complexity - Ot

• Memory complexity - Om

• Destructive

An algorithm is destructive if and only if it destroy a input.

6 solutions

Time complexity Memory Complexity Destructive

n2 1 no

nlgn n yes

nlgn n no

n n no

n 1 yes

n 1 no

Ot(n2) , Om(1) , no

For each number check if number doesn’t occur twice

for (int i=1; i<=n; i++) // for each number int occurrence = 0;

for (int j=0; j<n;j++) // for each cell if (t[j]==i)

occurrence++;if (occurance==2)

return i;

Ot(nlgn) , Om(1) , yes

Sort and check if two values in sibling cells are not equal.

sort(t);for (int i=0;i<n-1;i++)

if (t[i]==t[i+1])return t[i];

Ot(n) , Om(n) , no

Remember numbers which occur and return number if occursrs second time.

bool tB[n+1]; //all false at the begging for (int i=0;i<n;i++)

if (tB[t[i]]==true)return t[i];

tB[t[i]]=true;

Ot(n) , Om(1) , yes

Traverse a table and mark a cell as visited by writing 0. If a cell has value zero then return the index of the cell.

int i=0;while (t[i]!=0)

j=t[i];t[i]=0;i=j;

return i;

Ot(n) , Om(1) , no

int a = t[ t[0] ];int b = t[0];do

a = t[ t[a] ]; b = t[b];

while ( a != b )

b = 0;do

a = t[a];b = t[b];

while ( a != b )return a;

Different abstract level

• Input 0 1 2 3 4 5

1

2

3

4

50

1 34 5 2 4

Animal code

a = turtle;b = greyhound; do

run ;while not meat togetherb = second turtle b - start from beggingdo

run ;while not meat togetherreturn place of meeting

Race

A

B

C

DAB = L/2BC = L/2CD = LDC = M-LEC = L

E

Puzzle to solve

How many points are there on the globe where, by walking one mile south, one mile east, and one mile north, you reach the place where you started?

Future reading

• HOW WOULD YOU MOVE MOUNT FUJI? Microsoft’s Cult of Puzzle , William Poundstone

• http://www.research.ibm.com/ponder/ -

IBM Research – monthly puzzles