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LeongHW, SoC, NUS(UIT2201: Algorithms) Page 1© Leong Hon Wai, 2003-2008
Animation of Algorithm
Goal: To understand an algorithm by animating its execution,
step-by-step.
Algorithm: Sum 1-to-5 (find sum from 1 to 5)
(Note: Similar to Sum 1-to-100, but shorter!!)
Observe carefully: sequential operations/statements conditional statements, iterative statements,
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 2© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
Let’s animate the execution of this simple algorithm.
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 3© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k ???Step 0.
CPU
sum ???
Our abstract model of the computer
Initial state of the algorithm
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 4© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k ??? Step 1.Sum 0;
CPU
sum 0
Start of execution, at Step 1.
Assignment statement;The value of 0 is stored in thestorage box called sum.
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 5© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 1 Step 2.k 1;
CPU
sum 0
Assignment statement;The value of 1 is stored in thestorage box called k.
Executing Step 2.
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 6© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 1 Step 3.sum + k = 0 + 1
CPU
sum 1
Assignment statement;The new value of sum is stored; the old value is gone.
Executing Step 3. start of “body-of-loop”
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 7© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 2 Step 4.k + 1
= 1 + 1
CPU
sum 1
Assignment statement;The new value of k is stored; the old value is gone.
Executing Step 4. inside “body-of-loop”
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 8© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 2Step 5.
(k <= 5)?(2 <= 5)?= TRUE
CPU
sum 1
Condition check: evaluate (k <= 5)? TRUE execute Step 6 next.
Executing Step 5. loop-test
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 9© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 2 Step 6.Goto Repeat
(Step 3)
CPU
sum 1
goto “Repeat” means to get algorithm to continue at the step labelled “repeat”.
Executing Step 6.
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 10© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 2 Step 3.sum + k = 1 + 2
CPU
sum 3
Add 2 to sum;The new value of sum is stored; the old value is gone.
Executing Step 3. 2nd round of loop-body
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 11© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 3 Step 4.k + 1
= 2 + 1
CPU
sum 3
Increment k;The new value of k is stored; the old value is gone.
Executing Step 4. 2nd round of loop-body
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 12© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 3Step 5.
(k <= 5)?(3 <= 5)? = TRUE
CPU
sum 3
Condition check: evaluate (k <= 5)? TRUE execute Step 6 next.
Executing Step 5. 2nd loop-test
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 13© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 3 Step 6.Goto Repeat
(Step 3)
CPU
sum 3
Goto Step 3 and Execute the loop-body again.
Executing Step 6. 2nd round
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 14© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 3 Step 3.sum + k = 3 + 3
CPU
sum 6
Add 3 to sum;The new value of sum is stored; the old value is gone.
Executing Step 3. 3rd round of loop-body
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 15© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 4 Step 4.k + 1
= 3 + 1
CPU
sum 6
Increment k;The new value of k is stored; the old value is gone.
Executing Step 4. 3rd round of loop-body
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 16© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 4Step 5.
(k <= 5)?(4 <= 5)? = TRUE
CPU
sum 6
Condition check: evaluate (k <= 5)? TRUE execute Step 6 next.
Executing Step 5. 3rd loop-test
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 17© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 4 Step 6.Goto Repeat
(Step 3)
CPU
sum 6
Goto Step 3 and Execute the loop-body again.
Executing Step 6. 3rd round
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 18© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 4 Step 3.sum + k = 6 + 4
CPU
sum 10
Add 4 to sum;The new value of sum is stored; the old value is gone.
Executing Step 3. 4th round of loop-body
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 19© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 5 Step 4.k + 1
= 4 + 1
CPU
sum 10
Increment k;The new value of k is stored; the old value is gone.
Executing Step 4. 4th round of loop-body
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 20© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 5Step 5.
(k <= 5)?(5 <= 5)? = TRUE
CPU
sum 10
Condition check: evaluate (k <= 5)? TRUE execute Step 6 next.
Executing Step 5. 4th loop-test
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 21© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 5 Step 6.goto repeat
(Step 3)
CPU
sum 10
Goto Step 3 and Execute the loop-body again.
Executing Step 6. 4th round
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 22© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 5Step 3.
sum + k = 10 + 5
CPU
sum 15
Add 5 to sum;The new value of sum is stored; the old value is gone.
Executing Step 3. 5th round of loop-body
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 23© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 6 Step 4.k + 1
= 5 + 1
CPU
sum 15
Increment k;The new value of k is stored; the old value is gone.
Executing Step 4. 5th round of loop-body
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 24© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 6Step 5.
(k <= 5)?(6 <= 5)? = FALSE
CPU
sum 15
Condition check: evaluate (k <= 5)? FALSE execute Step 7 next.
Executing Step 5. 5th loop-test
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 25© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
finish: print out the value of sum
k 6 Step 7.goto finish(Step 8)
CPU
sum 15
Goto finish (Step 8) (exit the iterative loop!)
Executing Step 7. & exit the iterative loop
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 26© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 5) (* means < or = *)
6. then Goto Step 3. Repeat
7. else Goto Finish
finish: print out the value of sum
k 6 Step 8.Print to output
CPU
sum 15
Print statement; print to output the value of sum
Executing Step 8. print output and END
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
Output of Algorithm:
15
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 27© Leong Hon Wai, 2003-2008
Summary
Summary of Steps: 1, 2, (3,4,5,6), (3,4,5,6), (3,4,5,6), (3,4,5,6), (3,4,5,7), 8
Note the sequential execution, except for Conditional statements Goto statements iterative statements
Questions: Where is the “loop-body”? How many iteration of the loop-body? How many times is the loop-test done?
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 28© Leong Hon Wai, 2003-2008
Explore further (DIY)
We did Sum 1-to-5 (instead of Sum 1-to-100)
DIY: Simulate the execution for the original algorithm for Sum 1-to-100?
(Use the following “ending”-slides to help you.)
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 29© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-100;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 100)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 100Step 5.
(k <= 100)?(100 <= 100)?
= TRUE
CPU
sum 5050
Condition check: evaluate (k <= 100)? TRUE execute Step 6 next.
Executing Step 5. 99th loop-test
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 30© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-5;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 100)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
k 100 Step 6.Goto Repeat
(Step 3)
CPU
sum 4950
Goto Step 3 and Execute the loop-body again.
Executing Step 6. 99th round
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 31© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-100;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 100)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 100 Step 3.sum + k
= 4950 + 100
CPU
sum 5050
Add 100 to sum;The new value of sum is stored; the old value is gone.
Executing Step 3. 100th round of loop-body
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 32© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-100;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 100)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 101 Step 4.k + 1
= 100 + 1
CPU
sum 5050
Increment k;The new value of k is stored; the old value is gone.
Executing Step 4. 100th round of loop-body
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 33© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-100;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 100)
6. then Goto Step 3. Repeat
7. else Goto Finish
Finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 101Step 5.
(k <= 100)?(101 <= 100)?
= FALSE
CPU
sum 5050
Condition check: evaluate (k <= 100)? FALSE execute Step 7 next.
Executing Step 5. 100th loop-test
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 34© Leong Hon Wai, 2003-2008
Simulating an Algorithm
ALGORITHM Sum-1-to-100;
1. sum 0
2. k 1
3. Repeat: add k to sum
4. add 1 to k
5. if (k <= 100)
6. then Goto Step 3. Repeat
7. else Goto Finish
finish: print out the value of sum
0+1=1; 1+2=3; 3+3=6; 6+4=10; 10+5=15;
k 101 Step 7.Goto finish
(Step 8)
CPU
sum 5050
Goto finish (Step 8) (exit the iterative loop!)
Executing Step 7. & exit the iterative loop
LeongHW, SoC, NUS(UIT2201: Algorithms) Page 35© Leong Hon Wai, 2003-2008
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