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.↵
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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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1. Capture all the pairs given.↵
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).↵
3. Iterate through all the pairs until.↵
- 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.↵
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]).↵
5. Continue iterating through pairs while at least one of the numbers in the current pair is K or L.↵
6.↵
- a) you reached the end of the pairs, go to step #SUCCESS.↵
- 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 #FAILURE.↵
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- SUCCESS: print "YES" and exit program↵
- FAILURE: 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↵
↵
1. Capture all the pairs given.↵
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).↵
3. Iterate through all the pairs until.↵
- 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.↵
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]).↵
5. Continue iterating through pairs while at least one of the numbers in the current pair is K or L.↵
6.↵
- a) you reached the end of the pairs, go to step #SUCCESS.↵
- 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 #FAILURE.↵
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- SUCCESS: print "YES" and exit program↵
- FAILURE: print "NO" and exit program
