text: Find the n | Efficient C program to find n - th palindrome ; Construct the nth binary palindrome with the given group number , aux_number and operation type ; No need to insert any bit in the middle ; Length of the final binary representation ; Fill first and last bit as 1 ; Start filling the a [ ] from middle , with the aux_num binary representation ; Get the auxiliary number 's ith bit and  fill around middle ; Insert bit 0 in the middle ; Length of the final binary representation ; Fill first and last bit as 1 ; Start filling the a [ ] from middle , with the aux_num binary representation ; Get the auxiliary number 's ith bit and fill  around middle ; else Insert bit 1 in the middle ; Length of the final binary representation ; Fill first and last bit as 1 ; Start filling the a [ ] from middle , with the aux_num binary representation ; Get the auxiliary number 's ith bit and fill  around middle ; Convert the number to decimal from binary ; Will return the nth binary palindrome number ; Add number of elements in all the groups , until the group of the nth number is found ; Total number of elements until this group ; Element 's offset position in the group ; Finding which bit to be placed in the middle and finding the number , which we will fill from the middle in both directions ; We need to fill this auxiliary number in binary form the middle in both directions ; op = 0 ; Need to Insert 0 at middle ; op = 1 ; Need to Insert 1 at middle ; Driver code ; Function Call
code: #include <stdio.h> NEW_LINE #define INT_SIZE  32 NEW_LINE int constructNthNumber ( int group_no , int aux_num , int op ) { int a [ INT_SIZE ] = { 0 } ; int num = 0 , len_f ; int i = 0 ; if ( op == 2 ) { len_f = 2 * group_no ; a [ len_f - 1 ] = a [ 0 ] = 1 ; while ( aux_num ) { a [ group_no + i ] = a [ group_no - 1 - i ] = aux_num & 1 ; aux_num = aux_num >> 1 ; i ++ ; } } else if ( op == 0 ) { len_f = 2 * group_no + 1 ; a [ len_f - 1 ] = a [ 0 ] = 1 ; a [ group_no ] = 0 ; while ( aux_num ) { a [ group_no + 1 + i ] = a [ group_no - 1 - i ] = aux_num & 1 ; aux_num = aux_num >> 1 ; i ++ ; } } { len_f = 2 * group_no + 1 ; a [ len_f - 1 ] = a [ 0 ] = 1 ; a [ group_no ] = 1 ; while ( aux_num ) { a [ group_no + 1 + i ] = a [ group_no - 1 - i ] = aux_num & 1 ; aux_num = aux_num >> 1 ; i ++ ; } } for ( i = 0 ; i < len_f ; i ++ ) num += ( 1 << i ) * a [ i ] ; return num ; } int getNthNumber ( int n ) { int group_no = 0 , group_offset ; int count_upto_group = 0 , count_temp = 1 ; int op , aux_num ; while ( count_temp < n ) { group_no ++ ; count_upto_group = count_temp ; count_temp += 3 * ( 1 << ( group_no - 1 ) ) ; } group_offset = n - count_upto_group - 1 ; if ( ( group_offset + 1 ) <= ( 1 << ( group_no - 1 ) ) ) { aux_num = group_offset ; } else { if ( ( ( group_offset + 1 ) - ( 1 << ( group_no - 1 ) ) ) % 2 ) else aux_num = ( ( group_offset ) - ( 1 << ( group_no - 1 ) ) ) / 2 ; } return constructNthNumber ( group_no , aux_num , op ) ; } int main ( ) { int n = 9 ; printf ( " % d " , getNthNumber ( n ) ) ; return 0 ; }