大数计算(支持两个大数乘除)

作者： 作者的头像   szhang ,  2024-05-15 20:41:33 ,  所有人可见 ,  阅读 12

0


实用版本

#include <bits/stdc++.h>

using namespace std;

bool cmp(vector<int> A, vector<int> B) {
    if (A.size() != B.size()) return A.size() > B.size();
    for (int i = A.size() - 1; i >= 0; i--)
        if (A[i] != B[i])
            return A[i] > B[i];
    return true;
}

vector<int> add(vector<int> A, vector<int> B) {
    int t = 0;
    vector<int> C;
    for (int i = 0; i < A.size() || i < B.size(); i++) {
        if (i < A.size()) t += A[i];
        if (i < B.size()) t += B[i];
        C.push_back(t % 10);
        t /= 10;
    }
    if (t != 0) C.push_back(1);
    return C;
}

vector<int> sub(vector<int> A, vector<int> B) {
    vector<int> C;
    int t = 0;
    for (int i = 0; i < A.size(); i++) {
        t += A[i];
        if (i < B.size()) t -= B[i];
        C.push_back((t + 10) % 10);
        if (t >= 0) t = 0;
        else t = -1;
    }
    while (C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
}

vector<int> mul(vector<int> A, int b) {
    int t = 0;
    vector<int> C;
    for (int i = 0; i < A.size() || t; i++) {
        if (i < A.size()) t += A[i] * b;    
        C.push_back(t % 10);
        t /= 10;
    }
    while (C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
}

vector<int> MOD(string a, string b) {
    bool neg = false;
    if (a[0] == '-') {
        neg = true;
        a = a.substr(1);
    }

    vector<int> A, B;
    for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
    for (int i = b.size() - 1; i >= 0; i--) B.push_back(b[i] - '0');

    while (true) {
        int d = max(0, (int)(A.size() - B.size() - 1));
        vector<int> C(d, 0);
        for (int i : B) C.push_back(i);
        while (cmp(A, C)) A = sub(A, C);
        if (d == 0) {
            if (neg) A = sub(C, A);
            break;
        }
    }
    reverse(A.begin(), A.end());

    return A;
}

vector<int> MUL(string a, string b, bool& neg) {
    if (a[0] == '-') {
        neg ^= 1;
        a = a.substr(1);
    }
    if (b[0] == '-') {
        neg ^= 1;
        b = b.substr(1);
    }

    vector<int> A, B;
    for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
    for (int i = b.size() - 1; i >= 0; i--) B.push_back(b[i] - '0');

    vector<int> ans(1, 0);
    for (int i = 0; i < B.size(); i++) {
        vector<int> C(i, 0);
        for (int j : A) C.push_back(j);
        ans = add(ans, mul(C, B[i]));
    }
    reverse(ans.begin(), ans.end());
    return ans;
}

void DIV(string a, string b, bool& neg, vector<int>& ans1, vector<int>& ans2) {
    if (a[0] == '-') {
        neg ^= 1;
        a = a.substr(1);
    }
    if (b[0] == '-') {
        neg ^= 1;
        b = b.substr(1);
    }

    vector<int> A, B;
    for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
    for (int i = b.size() - 1; i >= 0; i--) B.push_back(b[i] - '0');

    vector<int> ans(1, 0);
    while (true) {
        int d = max(0, (int)(A.size() - B.size() - 1));
        vector<int> C(d, 0);
        for (int i : B) C.push_back(i);
        int cnt = 0;
        while (cmp(A, C)) {
            cnt++;
            A = sub(A, C);
        }
        vector<int> D(d, 0);
        D.push_back(cnt);
        ans = add(ans, D);
        if (d == 0) break;
    }

    reverse(ans.begin(), ans.end());
    reverse(A.begin(), A.end());
    ans1 = ans;
    ans2 = A;
}

int main() {
    string a, b;
    cin >> a >> b;

    bool neg = false;
    vector<int> ans1, ans2;
    DIV(a, b, neg, ans1, ans2);
    if (neg) cout << "-";
    for (int i : ans1) cout << i;
    cout << " ";
    if (neg && ans2[0]) cout << "-";
    for (int i : ans2) cout << i;

    return 0;
}

a ^ b % p

#include <bits/stdc++.h>

using namespace std;

bool cmp(vector<int> A, vector<int> B)
{
    if (A.size() != B.size()) {
        return A.size() > B.size();
    }

    for (int i = A.size() - 1; i >= 0; i--) {
        if (A[i] != B[i]) {
            return A[i] > B[i];
        }
    }

    return true;
}

vector<int> sub(vector<int> A, vector<int> B) {
    vector<int> C;
    int t = 0;
    for (int i = 0; i < A.size(); i++) {
        t += A[i];
        if (i < B.size()) t -= B[i];
        C.push_back((t + 10) % 10);
        if (t >= 0) t = 0;
        else t = -1;
    }
    while (C.size() > 1 && C.back() == 0) C.pop_back();

    return C;
}

vector<int> add(vector<int> A, vector<int> B) {
    int t = 0;
    vector<int> C;
    for (int i = 0; i < A.size() || i < B.size(); i++) {
        if (i < A.size()) t += A[i];
        if (i < B.size()) t += B[i];
        C.push_back(t % 10);
        t /= 10;
    }
    if (t) C.push_back(1);

    return C;
}

vector<int> mul(vector<int> A, int b) {
    int t = 0;
    vector<int> C;
    for (int i = 0; i < A.size() || t; i++) {
        if (i < A.size()) t += A[i] * b;    
        C.push_back(t % 10);
        t /= 10;
    }
    while (C.size() > 1 && C.back() == 0) C.pop_back();

    return C;
}

vector<int> div(vector<int> A, int b)
{
    vector<int> C;
    int r = 0;
    for (int i = A.size() - 1; i >= 0; i--)
    {
        r *= 10;
        r += A[i];
        C.push_back(r / b);
        r %= b;
    }
    reverse(C.begin(), C.end());

    while (C.size() > 1 && C.back() == 0) C.pop_back();

    return C;
}

vector<int> mul(vector<int> A, vector<int> B) {
    vector<int> ans(1, 0);
    for (int i = 0; i < B.size(); i++) {
        vector<int> C(i, 0);
        for (int j : A) C.push_back(j);
        ans = add(ans, mul(C, B[i]));
    }
    return ans;
}

vector<int> mod(vector<int> A, vector<int> B) {
    while (true) {
        int d = max(0, (int)(A.size() - B.size() - 1));
        vector<int> C(d, 0);
        for (int i : B) C.push_back(i);
        while (cmp(A, C)) A = sub(A, C);
        if (d == 0) break;
    }

    return A;
}

int main() {
    string a, b, p;
    cin >> a >> b >> p;

    vector<int> A, B, P;
    for (int i = a.size() - 1; i >= 0; i--) {
        A.push_back(a[i] - '0');
    }
    for (int i = b.size() - 1; i >= 0; i--) {
        B.push_back(b[i] - '0');
    }
    for (int i = p.size() - 1; i >= 0; i--) {
        P.push_back(p[i] - '0');
    }

    // res = a ^ (p - 2) % p
    vector<int> res(1, 1);
    while (!(B.size() == 1 && B[0] == 0)) {
        if (B[0] & 1) {
            res = mul(res, A);
            res = mod(res, P);
        }
        B = div(B, 2);
        A = mul(A, A);
        A = mod(A, P);
    }
    reverse(res.begin(), res.end());
    for (int i : res) cout << i;

    return 0;
}

大数的取模运算

#include <bits/stdc++.h>

using namespace std;

vector<int> A, B;

bool cmp(vector<int> A, vector<int> B) {
    if (A.size() != B.size()) return A.size() > B.size();
    for (int i = A.size() - 1; i >= 0; i--)
        if (A[i] != B[i])
            return A[i] > B[i];
    return true;
}

vector<int> sub(vector<int> A, vector<int> B) {
    vector<int> C;
    int t = 0;
    for (int i = 0; i < A.size(); i++) {
        t += A[i];
        if (i < B.size()) t -= B[i];
        C.push_back((t + 10) % 10);
        if (t >= 0) t = 0;
        else t = -1;
    }
    while (C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
}

int main() {
    string a, b;
    cin >> a >> b;

    bool neg = false;
    if (a[0] == '-') {
        neg = true;
        a = a.substr(1);
    }

    for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
    for (int i = b.size() - 1; i >= 0; i--) B.push_back(b[i] - '0');

    while (true) {
        int d = max(0, (int)(A.size() - B.size() - 1));
        vector<int> C(d, 0);
        for (int i : B) C.push_back(i);
        while (cmp(A, C)) A = sub(A, C);
        if (d == 0) {
            if (neg) A = sub(C, A);
            break;
        }
    }
    for (int i = A.size() - 1; i >= 0; i--) cout << A[i];

    return 0;
}

大数的乘法运算

#include <bits/stdc++.h>

using namespace std;

vector<int> add(vector<int> A, vector<int> B) {
    int t = 0;
    vector<int> C;
    for (int i = 0; i < A.size() || i < B.size(); i++) {
        if (i < A.size()) t += A[i];
        if (i < B.size()) t += B[i];
        C.push_back(t % 10);
        t /= 10;
    }
    if (t != 0) C.push_back(1);
    return C;
}

vector<int> mul(vector<int> A, int b) {
    int t = 0;
    vector<int> C;
    for (int i = 0; i < A.size() || t; i++) {
        if (i < A.size()) t += A[i] * b;    
        C.push_back(t % 10);
        t /= 10;
    }
    while (C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
}

int main() {
    string a, b;
    cin >> a >> b;

    bool neg = false;
    if (a[0] == '-') {
        neg ^= 1;
        a = a.substr(1);
    }
    if (b[0] == '-') {
        neg ^= 1;
        b = b.substr(1);
    }

    vector<int> A, B;
    for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
    for (int i = b.size() - 1; i >= 0; i--) B.push_back(b[i] - '0');

    vector<int> ans(1, 0);
    for (int i = 0; i < B.size(); i++) {
        vector<int> C(i, 0);
        for (int j : A) C.push_back(j);
        ans = add(ans, mul(C, B[i]));
    }
    if (neg) cout << "-";
    reverse(ans.begin(), ans.end());
    for (int i : ans) cout << i;

    return 0;
}

大数的除法运算

#include <bits/stdc++.h>

using namespace std;

bool cmp(vector<int> A, vector<int> B) {
    if (A.size() != B.size()) return A.size() > B.size();
    for (int i = A.size() - 1; i >= 0; i--)
        if (A[i] != B[i])
            return A[i] > B[i];
    return true;
}

vector<int> sub(vector<int> A, vector<int> B) {
    vector<int> C;
    int t = 0;
    for (int i = 0; i < A.size(); i++) {
        t += A[i];
        if (i < B.size()) t -= B[i];
        C.push_back((t + 10) % 10);
        if (t >= 0) t = 0;
        else t = -1;
    }
    while (C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
}

vector<int> add(vector<int> A, vector<int> B) {
    int t = 0;
    vector<int> C;
    for (int i = 0; i < A.size() || i < B.size(); i++) {
        if (i < A.size()) t += A[i];
        if (i < B.size()) t += B[i];
        C.push_back(t % 10);
        t /= 10;
    }
    if (t != 0) C.push_back(1);
    return C;
}

int main() {
    string a, b;
    cin >> a >> b;

    bool neg = false;
    if (a[0] == '-') {
        neg ^= 1;
        a = a.substr(1);
    }
    if (b[0] == '-') {
        neg ^= 1;
        b = b.substr(1);
    }

    vector<int> A, B;
    for (int i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
    for (int i = b.size() - 1; i >= 0; i--) B.push_back(b[i] - '0');

    vector<int> ans(1, 0);
    while (true) {
        int d = max(0, (int)(A.size() - B.size() - 1));
        vector<int> C(d, 0);
        for (int i : B) C.push_back(i);
        int cnt = 0;
        while (cmp(A, C)) {
            cnt++;
            A = sub(A, C);
        }
        vector<int> D(d, 0);
        D.push_back(cnt);
        ans = add(ans, D);
        if (d == 0) break;
    }

    if (neg) cout << "-";
    reverse(ans.begin(), ans.end());
    for (int i : ans) cout << i;
    cout << endl;
    reverse(A.begin(), A.end());
    if (neg && A[0]) cout << "-";
    for (int i : A) cout << i;
    cout << endl;

    return 0;
}

0 评论