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In some applications (such as cryptography), we need to use very long integers.These integers cannot be stored in an int type variable. So we must...
In some applications (such as cryptography), we need to use very long integers.These integers cannot be stored in an int type variable. So we must use an array A[1..n] torepresent such long integers. (For simplicity, each element in A is used for 1 digit, and A[n] isthe most significant digit.) (For example, in the Crypto++ library widely used in cryptographyapplications, a special class is defined for such integers.) The basic arithmetic operations forsuch long integers can no longer be computed in constant time.Let A[1..n] and B[1..n] be two n-digit integers. It is easy to see the sum of A and B canbe computed in (n) time. The multiplication procedure (you learned from elementary school)takes (n2) time.Describe an algorithm for multiplication, with O(nlog2 3) = O(n1.585) run time. (The algorithmis similar to Strassen's algorithm in nature. But much more simpler.)
