Using divide-and-conquer method to realize multiplication, addition and subtraction of large numbers (Java implementation)

Large number multiplication is the problem of polynomial multiplication, the product C (x) of a (x) and B (x), the complexity of the Naïve solution O (n^2), the basic idea is to write the polynomial a (x) and B (x)

A (x) =a*x^m+b
B (x) =c*x^m+d

Where a,b,c,d is the polynomial of x.
Then a (x) *b (x) = (AC) *x^2m+ (AD+BC) *x^m+bd
by ad+bc= (a+b) (c+d)-AC-BD
The original 4 multiplication and 1 additions were replaced by 3 multiplication and 2 subtraction, which reduced one multiplication operation.
Apply the same method to the ABCD multiplication.

(The above content is excerpted from the Internet)

The following code is implemented in Java:

 Packagecom.kyy.sf; Public classBigInteger { PublicBigInteger () {}//The basic idea is to write the polynomial a (x) and B (x)//A (x) =a*x^m+b//B (x) =c*x^m+d//where a,b,c,d is the polynomial of x. //then A (x) *b (x) = (AC) *x^2m+ (AD+BC) *x^m+bd//by Ad+bc= (a+b) (c+d)-AC-BD//string Simulation multiplication Operation         Public Staticstring Mut (string x, string y) {//deep++;//Console.WriteLine ("-" + Deep + "-");String negative = ""; //x, y are positive or negative        if(X.startswith ("-") && Y.startswith ("-"))                || (!x.startswith ("-") &&!y.startswith ("-"))) {x= X.replaceall ("-", "" "); Y= Y.replaceall ("-", "" "); Negative= ""; }//x, Y, one positive and one negative        Else if(X.startswith ("-") &&!y.startswith ("-"))                || (!x.startswith ("-") && Y.startswith ("-"))) {x= X.replace ("-", "" "); Y= Y.replace ("-", "" "); Negative= "-"; }        //if the length is equal to 9, multiply directly and return to the line.         if(x.length () = = 1 && y.length () = = 1) {            //Calculate Product            intTMP = (integer.parseint (x) *integer.parseint (y)); if(TMP = = 0) {                returnTMP + ""; } Else {                returnNegative +tmp; }        }        //the ABCD in the formulaString A, B, C, D; if(x.length () = = 1) {a= "0"; b=x; } Else {            if(X.length ()% 2! = 0) {x= "0" +x; } A= x.substring (0, X.length ()/2); b= X.substring (X.length ()/2); }        if(y.length () = = 1) {C= "0"; D=y; } Else {            if(Y.length ()% 2! = 0) {y= "0" +y; } C= y.substring (0, Y.length ()/2); D= Y.substring (Y.length ()/2); }        //value by maximum number of digits to determine 0 number of complements        intn = x.length () >= y.length ()?x.length (): Y.length ();        String T1, T2, T3; //recursive invocation, which calculates the value based on the formula. String AC =Mut (A, c); String BD=Mut (b, D); T1=Mut (Sub (A, b), Sub (d, c)); T2=Add (Add (T1, AC), BD); T3= Add (Add (Power10 (AC, N), Power10 (T2, N/2)), BD). ReplaceAll ("^0+",                ""); if(T3 = = "")            return"0"; returnNegative +T3; }    Private Staticstring Add (string x, string y) {if(X.startswith ("-") &&!y.startswith ("-"))) {            returnSub (Y, X.replaceall ("^-", "" ")); } Else if(!x.startswith ("-") && Y.startswith ("-"))) {            returnSub (x, Y.replaceall ("^-", "" ")); } Else if(X.startswith ("-") && Y.startswith ("-"))) {            return"-" + Add (X.replaceall ("^-", ""), Y.replaceall ("^-", "" ")); }        if(X.length () >y.length ()) {y= Format (y, X.length (), "0"); } Else{x= Format (x, Y.length (), "0"); }        int[] sum =New int[X.length () + 1];  for(inti = X.length ()-1; I >= 0; i--) {            intTmpsum = Integer.parseint (X.charat (i) + "")                    + Integer.parseint (Y.charat (i) + "") + Sum[i + 1]; if(Tmpsum >= 10) {Sum[i+ 1] = tmpsum-10; Sum[i]= 1;//denotes rounding}Else{sum[i+ 1] =tmpsum; }} StringBuilder returnvalue=NewStringBuilder ();  for(inti:sum)        {returnvalue.append (i); }        if(Sum[0] = = 1) {            returnreturnvalue.tostring (); } Else {            returnReturnvalue.replace (0, 1, ""). toString (); }    }    //string emulation subtraction Operation    Private Staticstring Sub (string x, string y) {//x is positive, Y is positive        intFlag =Checkbigger (x, y); if(flag = = 0) {            return"0"; } Else if(Flag = =-1) {String tmp=y; Y=x; X=tmp; }        //guaranteed x>=y.y = Format (y, X.length (), "0");//y complement 0 and x align        int[] difference =New int[X.length ()];  for(inti = X.length ()-1; I >= 0; i--) {            inttmpdifference; Tmpdifference= Integer.parseint (X.charat (i) + "")                    -Integer.parseint (Y.charat (i) + "") +Difference[i]; if(Tmpdifference < 0) {tmpdifference+ = 10; Difference[i-1] =-1;//denotes rounding} Difference[i]=tmpdifference; } StringBuilder returnvalue=NewStringBuilder ();  for(inti:difference)        {returnvalue.append (i); } String RV= Returnvalue.tostring (). ReplaceAll ("^0+", "" "); if("". Equals (RV)) {            return"0"; }        if(Flag = =-1) {RV= "-" +RV; }        returnRV; }    //Compare Size    Private Static intCheckbigger (string x, string y) {if(X.length () >y.length ()) {            return1; } Else if(X.length () <y.length ()) {            return-1; } Else {             for(inti = 0; I < x.length (); i++) {                if(X.charat (i) >Y.charat (i)) {                    return1; } Else if(X.charat (i) <Y.charat (i)) {                    return-1; }            }            return0; }    }    //data Pre-fill 0    Private Staticstring format (String str,intLen, String Fu) {Len= Len-str.length ();  for(inti = 0; i < Len; i++) {str= Fu +str; }        returnstr; }    //Analog Shift     Public StaticString Power10 (String num,intN) { for(inti = 0; I < n; i++) {num+ = "0"; }        returnnum; }     Public Static voidMain (string[] args) {String x= "93859048059849086850986804750894758903278473894578397598475984784857487584758094875890475984955624146039530798877974 "; String y= "224343444859408590475847538946";                System.out.println (Mut (x, y)); System.out.println (Mut ("1111111111", "1111111111")); }}

Using divide-and-conquer method to realize multiplication, addition and subtraction of large numbers (Java implementation)