大数的加减乘除

高精度加法

public class 高精度加法 {
    public static  void add(ArrayList<Integer> a,ArrayList<Integer> b){
        int tmp = 0;
        ArrayList C = new ArrayList();
        for (int i=0;i<a.size()||i<b.size();i++){
            if(i<a.size()) tmp += a.get(i);
            if(i<b.size()) tmp += b.get(i);
            C.add(tmp%10);
            tmp = tmp/10;
        }
        if(tmp!=0){C.add(1);}
        for(int i=C.size()-1;i>=0;i--){
            System.out.print(C.get(i));
        }
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String A = sc.next();
        String B = sc.next();

        ArrayList<Integer> a = new ArrayList();
        ArrayList<Integer> b = new ArrayList();

        for(int i=A.length()-1;i>=0;i--){
            a.add(A.charAt(i)-'0');
        }
        for (int j=B.length()-1;j>=0;j--){
            b.add(B.charAt(j)-'0');
        }
        add(a,b);
    }
}

高精度减法

public class 高精度减法 {
    public static boolean cmp(ArrayList<Integer> a,ArrayList<Integer> b){
        if(a.size()!=b.size()) return a.size()>b.size();
        for(int i=0;i<a.size();i++){
            if(a.get(i)!=b.get(i)) return a.get(i)>b.get(i);
        }
        return true;
    }
    public static ArrayList<Integer> jianfa(ArrayList<Integer> a, ArrayList<Integer> b){
        ArrayList<Integer> C = new ArrayList<>();
        for(int i=0,t=0;i<a.size();i++){
            t = a.get(i)-t;
            if(i<b.size()) t -= b.get(i);
            C.add((t+10)%10);
            if(t<0) t=1;
            else t=0;
        }
        while (C.size()>0&&C.get(C.size()-1)==0) C.remove(C.size()-1);
        return C;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String A = sc.next();
        String B = sc.next();

        ArrayList<Integer> a = new ArrayList();
        ArrayList<Integer> b = new ArrayList();

        for(int i=A.length()-1;i>=0;i--){
            a.add(A.charAt(i)-'0');
        }
        for (int j=B.length()-1;j>=0;j--){
            b.add(B.charAt(j)-'0');
        }
        ArrayList<Integer> C = new ArrayList<>();
        if(cmp(a,b)){
            C = jianfa(a,b);
            for (int i=C.size()-1;i>=0;i--){
                System.out.print(C.get(i));
            }
        }else{
            System.out.print("-");
            C = jianfa(b,a);
            for (int i=C.size()-1;i>=0;i--){
                System.out.print(C.get(i));
            }
        }
    }
}

高精度乘法

public class 高精度乘法 {
    public static void mul(ArrayList<Integer> a,int b){
        int t = 0;
        ArrayList<Integer> C = new ArrayList<>();
        for(int i=0;i<a.size()||(t!=0);i++){
            if(i<a.size())t += a.get(i)*b;
            C.add(t%10);
            t /=10;
        }
        for(int i=C.size()-1;i>=0;i--){
            System.out.print(C.get(i));
        }
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String A = sc.nextLine();

        ArrayList<Integer> a = new ArrayList();
        int b;

        for(int i=A.length()-1;i>=0;i--){
            a.add(A.charAt(i)-'0');
        }
        b = sc.nextInt();
        mul(a,b);
    }
}

高精度除法

public class 高精度除法 {
    public static void chu(ArrayList<Integer> a,int b){
        ArrayList<Integer> C = new ArrayList<>();
        String t = "0";
        for(int i=0;i<a.size();i++){
            int tmp = (Integer.parseInt(t)*10)+a.get(i);
            C.add(tmp/b);
            t = (tmp%b)+"";
        }
        while (C.size()>0&&C.get(0)==0) C.remove(0);
        for (int i=0;i<C.size();i++){
            System.out.print(C.get(i));
        }
        System.out.println();
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String A = sc.nextLine();

        ArrayList<Integer> a = new ArrayList();
        int b;

        for(int i=0;i<A.length();i++){
            a.add(A.charAt(i)-'0');
        }
        b = sc.nextInt();
        chu(a,b);
    }
}

前缀和

一维前缀和

public class 前缀和 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        int[] str1 = new int[N+1];
        int[] str2 = new int[N+1];
        for(int i=1;i<=N;i++){
            str1[i]=sc.nextInt();
        }
        for(int i=1;i<=N;i++){
            str2[i] = str2[i-1]+str1[i];
        }
        for(int i=0;i<M;i++){
            int l = sc.nextInt();
            int r = sc.nextInt();
            System.out.println(str2[r]-str2[l-1]);
        }
    }
}

二位前缀和

public class 二维前缀和 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int q = sc.nextInt();
        int[][] str1 = new int[n+1][m+1];
        int[][] str2 = new int[n+1][m+1];
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                str1[i][j]=sc.nextInt();
            }
        }
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                str2[i][j]=str2[i-1][j]+str2[i][j-1]-str2[i-1][j-1]+str1[i][j];
            }
        }
        for(int i=0;i<q;i++){
            int x1 = sc.nextInt();
            int y1 = sc.nextInt();
            int x2 = sc.nextInt();
            int y2 = sc.nextInt();
            System.out.println(str2[x2][y2]-str2[x1-1][y2]-str2[x2][y1-1]+str2[x1-1][y1-1]);
        }
    }
}

差分

一维差分

public class 差分 {
    public static void insert(int l,int r,int c,int[] b){
        b[l] += c;
        b[r+1] -=c;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        int[] a = new int[N+2];
        int[] b = new int[N+2];
        for(int i=1;i<=N;i++){
            a[i]=sc.nextInt();
        }
        for(int i=1;i<=N;i++){ insert(i,i,a[i],b);}
        for(int i=0;i<M;i++){
            int l,r,c;
            l = sc.nextInt();
            r = sc.nextInt();
            c = sc.nextInt();
            insert(l,r,c,b);
        }
        for(int i=1;i<=N;i++){
            b[i] += b[i-1];
        }
        for(int i=1;i<=N;i++){
            System.out.print(b[i]+" ");
        }
    }
}

二维差分

public class 差分矩阵 {
    public static void insert(int x1,int y1,int x2,int y2,int c,int[][] b){
        b[x1][y1]+=c;
        b[x1][y2+1]-=c;
        b[x2+1][y1]-=c;
        b[x2+1][y2+1]+=c;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int q = sc.nextInt();
        int[][] a = new int[n+2][m+2];
        int[][] b = new int[n+2][m+2];
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                a[i][j] = sc.nextInt();
            }
        }
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                insert(i,j,i,j,a[i][j],b);
            }
        }
        for(int i=0;i<q;i++){
            int x1 = sc.nextInt();
            int y1 = sc.nextInt();
            int x2 = sc.nextInt();
            int y2 = sc.nextInt();
            int c = sc.nextInt();
            insert(x1,y1,x2,y2,c,b);
        }
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                b[i][j]+=b[i-1][j]+b[i][j-1]-b[i-1][j-1];
            }
        }
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                System.out.print(b[i][j]+" ");
            }
            System.out.println();
        }
    }
}