Ripple-Carry AdderProblem code: RIPPLE |
All submissions for this problem are available.
Amortized analysis deals with analyzing the average amount of work done per operation over a series of operations. In some cases, the average amount of work done per operation is dramatically less than the worst case analysis indicates.
A typical example is counting the number of times a bit is flipped in a ripple-carry counter. A ripple-carry counter is an implementation of a binary counter where incrementing from B to B+1 is done in the following manner. Say the binary number is represented as B = bn-1b_n-2...b_1b0 where bi is the bit corresponding to 2i. B is increased to B+1 in the following manner:
i := 0
while bi == 1
bi := 0
i := i+1
bi := 1
This doesn't account for overflow when increasing from 2n-1 to 2n, but we'll ignore that error for this problem.
Each time a bit is changed from 0 to 1 or from 1 to 0 we say the bit is "flipped". In the worst case, we may have to flip every bit. However, a standard result says the average number of bits flipped per increment when counting from 0 to 2n-1 is less than 2.
Being the curious sort, you decide to explore this result in a slightly more general setting. That is, you want to know how many bits are flipped when the counter is incremented from a number a to b where a < b.
Input
The first line denotes the number of test cases (about 20).
Each test case consists of three lines. The first contains a single integer n between 1 and 100,000 denoting the number of bits in the counter. The second line contains the number a written in binary and the third line contains the number b written in binary. Both a and b are described using exactly n bits.
Output
The output for each test case consists of a single line that describes the total number of bits flipped when the counter is increased from a to b. This number should be expressed in binary with the most significant bit being 1 (i.e. no leading zeros should pad the output).
Example
Input:
3
1
0
1
2
00
11
3
011
100
Output:
1
100
11
| Author: | friggstad |
| Date Added: | 8-05-2010 |
| Time Limit: | 3 sec |
| Source Limit: | 50000 Bytes |
| Languages: | ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT, WSPC |
Comments
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