Explanation for B. Pairs↵
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### The answer I submitted for B. Pairs was too slow to pass the tests, so I went back after the contest to view others solutions. Then I discovered that I was missing some key assumptions.↵
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#### Assumption 1.↵
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If there is an answer, one of the numbers from the solution pair will be one of the two numbers in the very first given pair↵
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#### Assumption 2.↵
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If you choose a number K from the first pair using Assumption 1, that number will either occur in every single following pair, or there will be a point↵
where you encounter a pair where K is not one of the numbers. At this point you must choose a second number L which will be again one of the two numbers in the currently encountered ↵
pair.↵
↵
#### Assumption 3.↵
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The answer is "YES" If and only if for every pair you encounter, at least one of the chosen numbers K or L are one of the two numbers in the current pair↵
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### Logic↵
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#### Step 1↵
Capture all the pairs given.↵
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#### Step 2↵
Use Assumption 1 to choose one of the two numbers from the first pair (K). (Choose the one you haven't used if you've done this step before).↵
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#### Step 3↵
~~~~~↵
Iterate through all the pairs until.↵
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- a.) you reach the end of the pairs which means go to step #SUCCESS.↵
- b.) you encounter a pair where K is not in the pair.↵
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#### Step 4↵
Choose one of the two numbers from the current pair (L) (Choose the one use didn't use last time [first number or second number]).↵
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#### Step 5↵
Continue iterating through pairs while at least one of the numbers in the current pair is K or L.↵
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#### Step 6↵
- a) you reached the end of the pairs, go to step #7↵
- b) you encountered a pair where neither K or L are one of the two numbers, go to step #4 if you still haven't tried another number for L.↵
- c) you've tried both numbers for L, but you still haven't tried a different number for K, go back to step #2.↵
- d) you've tried both numbers for K, and both numbers for L for every K. Nothing left to do, go to #8.↵
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#### Step 7↵
Print "YES" and exit program↵
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#### Step 8↵
Print "NO" and exit program↵
------------------↵
↵
### The answer I submitted for B. Pairs was too slow to pass the tests, so I went back after the contest to view others solutions. Then I discovered that I was missing some key assumptions.↵
↵
#### Assumption 1.↵
↵
If there is an answer, one of the numbers from the solution pair will be one of the two numbers in the very first given pair↵
↵
#### Assumption 2.↵
↵
If you choose a number K from the first pair using Assumption 1, that number will either occur in every single following pair, or there will be a point↵
where you encounter a pair where K is not one of the numbers. At this point you must choose a second number L which will be again one of the two numbers in the currently encountered ↵
pair.↵
↵
#### Assumption 3.↵
↵
The answer is "YES" If and only if for every pair you encounter, at least one of the chosen numbers K or L are one of the two numbers in the current pair↵
↵
↵
### Logic↵
↵
#### Step 1↵
Capture all the pairs given.↵
↵
#### Step 2↵
Use Assumption 1 to choose one of the two numbers from the first pair (K). (Choose the one you haven't used if you've done this step before).↵
↵
#### Step 3↵
~~~~~↵
Iterate through all the pairs until.↵
~~~~~↵
- a
- b
↵
#### Step 4↵
Choose one of the two numbers from the current pair (L) (Choose the one use didn't use last time [first number or second number]).↵
↵
#### Step 5↵
Continue iterating through pairs while at least one of the numbers in the current pair is K or L.↵
↵
#### Step 6↵
- a) you reached the end of the pairs, go to step #7↵
- b) you encountered a pair where neither K or L are one of the two numbers, go to step #4 if you still haven't tried another number for L.↵
- c) you've tried both numbers for L, but you still haven't tried a different number for K, go back to step #2.↵
- d) you've tried both numbers for K, and both numbers for L for every K. Nothing left to do, go to #8.↵
↵
#### Step 7↵
Print "YES" and exit program↵
↵
#### Step 8↵
Print "NO" and exit program↵
