concatenate binary of first N integers and return decimal value

问题

Example,

N = 3 The first N integers for value 3 is 1, 2, 3

Binary of

1 is 1

2 is 10

3 is 11

Concatenations of N=3 of binary values will be 11011

And the decimal value returned for the binary value 11011 is 27

The code I am using below only works for first integers N<=15

    String input = "";
    for(int i = 1;i<=n;i++) {
        input += (Integer.toBinaryString(i));
    }
    return Integer.parseInt(input,2);

For larger N numbers, any ideas on solving using modulo 10^9 + 7 (since concatenation is large)

回答1:

Note that working with string representation is not necessary (moreover, is not useful after task changing). Look at approach with bitwise arithmetics (Python, but principle is the same)

With new condition concerning modulo 1000000007 we have just add modulo operation to result calculation line at every step, because shift left and or-ing is equivalent to multiplication by power of two and adding, these operations are obeyed to equivalence relations for modulo properties. Note that intermediate results don't exceed 1000000007*n, so long type is suitable here for reasonable n values.

n = 100  
size = 0   #bit length of addends
result = 0   # long accumulator
for i in range(1, n + 1):    
    if i & (i - 1) == 0:    #for powers of two we increase bit length
        size += 1
    result = ((result << size) | i) % 1000000007   #shift accumulator left and fill low bits with new addend
print(result)

variant without bitwise operations:

pow2 = 1
nextpow = 2
result = 0   # long accumulator
for i in range(1, n + 1):
    if i == nextpow:    #for powers of two we increase bit length
        pow2 = nextpow
        nextpow = nextpow * 2
    result = (result * pow2  + i) % 1000000007  #shift accumulator left and fill low bits with new addend

回答2:

String input = "";

    for(int i = 1;i<=n;i++) {
        input += (Integer.toBinaryString(i));
    }
    return new BigInteger(input, 2);

来源：https://stackoverflow.com/questions/62631840/concatenate-binary-of-first-n-integers-and-return-decimal-value

标签

java

math

binary