Minimum number of operations required to sum to binary string S | Function to return the minimum operations required to sum to a number reprented by the binary string S ; Reverse the string to consider it from LSB to MSB ; initialise the dp table ; If S [ 0 ] = '0' , there is no need to perform any operation ; If S [ 0 ] = '1' , just perform a single operation ( i . e Add 2 ^ 0 ) ; Irrespective of the LSB , dp [ 0 ] [ 1 ] is always 1 as there is always the need of making the suffix of the binary string of the form "11 . . . . 1" as suggested by the definition of dp [ i ] [ 1 ] ; Transition from dp [ i - 1 ] [ 0 ] ; 1. Transition from dp [ i - 1 ] [ 1 ] by just doing 1 extra operation of subtracting 2 ^ i 2. Transition from dp [ i - 1 ] [ 0 ] by just doing 1 extra operation of subtracting 2 ^ ( i + 1 ) ; Transition from dp [ i - 1 ] [ 1 ] ; 1. Transition from dp [ i - 1 ] [ 1 ] by just doing 1 extra operation of adding 2 ^ ( i + 1 ) 2. Transition from dp [ i - 1 ] [ 0 ] by just doing 1 extra operation of adding 2 ^ i ; Swap values of left and right ; Driver Code
function findMinOperations ( S ) { S = reverse ( S ) ; let n = S . length ; let dp = new Array ( n + 1 ) ; for ( let i = 0 ; i < dp . length ; i ++ ) { dp [ i ] = new Array ( 2 ) ; for ( let j = 0 ; j < 2 ; j ++ ) { dp [ i ] [ j ] = 0 ; } } if ( S [ 0 ] == ' ' ) { dp [ 0 ] [ 0 ] = 0 ; } else { dp [ 0 ] [ 0 ] = 1 ; } dp [ 0 ] [ 1 ] = 1 ; for ( let i = 1 ; i < n ; i ++ ) { if ( S [ i ] == ' ' ) { dp [ i ] [ 0 ] = dp [ i - 1 ] [ 0 ] ; dp [ i ] [ 1 ] = 1 + Math . min ( dp [ i - 1 ] [ 1 ] , dp [ i - 1 ] [ 0 ] ) ; } else { dp [ i ] [ 1 ] = dp [ i - 1 ] [ 1 ] ; dp [ i ] [ 0 ] = 1 + Math . min ( dp [ i - 1 ] [ 0 ] , dp [ i - 1 ] [ 1 ] ) ; } } return dp [ n - 1 ] [ 0 ] ; } function reverse ( input ) { let temparray = input . split ( " " ) ; let left , right = 0 ; right = temparray . length - 1 ; for ( left = 0 ; left < right ; left ++ , right -- ) { let temp = temparray [ left ] ; temparray [ left ] = temparray [ right ] ; temparray [ right ] = temp ; } return ( temparray ) . join ( " " ) ; } let S = " " ; document . write ( findMinOperations ( S ) + " " ) ; S = " " ; document . write ( findMinOperations ( S ) + " " ) ;