I am gonna make account of good observations and ideas which I come across while solving problems. The proofs of below statements will not be mentioned here, Its advised to do such proofs on own for exercise. ↵
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- Lets say I have a set $S$ consisting of integers, denote its $lcm(S) = L$, I add a new element $x$ to this set $S$ , ↵
Lets deonte the new set as $S'$,where $S' = union(S , x)$ and its $lcm(S') = L'$. Can we deduce a relation between $L$ and $L'$. We can observe that either $L = L'$ or $L' >= 2*L$. ↵
- Lets say we want to find 2 numbers in an array $A[]$ which have maximum common prefix bits in binary representation. Its easy to show that those 2 numbers always occur as adjacent numbers in $sorted(A[])$ ↵
- The number of distinct gcd prefixed / suffixed at a index in array will never exceed $log(A_{max})$ ↵
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- Lets say I have a set $S$ consisting of integers, denote its $lcm(S) = L$, I add a new element $x$ to this set $S$ , ↵
Lets deonte the new set as $S'$,where $S' = union(S , x)$ and its $lcm(S') = L'$. Can we deduce a relation between $L$ and $L'$. We can observe that either $L = L'$ or $L' >= 2*L$. ↵
- Lets say we want to find 2 numbers in an array $A[]$ which have maximum common prefix bits in binary representation. Its easy to show that those 2 numbers always occur as adjacent numbers in $sorted(A[])$ ↵
- The number of distinct gcd prefixed / suffixed at a index in array will never exceed $log(A_{max})$ ↵
