Informatics Olympiad One Pass 1.6: Functions (2)

​The first part of C++ language

Chapter 6 Functions

Section 2 Recursive Algorithm

1158 Find 1+2+3+...

#include <iostream>
using namespace std;

int f(int x) {
    if (x == 1) return 1;
    return f(x-1) + x;
}

int main() {
    int n;
    cin >> n;

    cout << f(n);

    return 0;
}

1159 Fibonacci Sequence

#include <iostream>
using namespace std;

int f(int x) {
    if (x == 1) return 0;
    if (x == 2) return 1;
    return f(x-1) + f(x-2);
}

int main() {
    int n;
    cin >> n;

    cout << f(n);

    return 0;
}

1160 Reversed number

#include <iostream>
using namespace std;

void f(int x) {
    if (x == 0) return;

    cout << x % 10;
    return f(x/10);
}

int main() {
    int n;
    cin >> n;

    f(n);

    return 0;
}

1161 Conversion

#include <iostream>
using namespace std;

void f(int x, int m) {
    if (x == 0) return;

    f(x/m, m);

    int t = x % m;
    if (t < 10) cout << t;
    else cout << char(t - 10 + 'A');
}

int main() {
    int x, m;
    cin >> x >> m;

    f(x, m);

    return 0;
}

1162 string reverse order

#include <iostream>
using namespace std;

string s;

void f(int i) {
    if (s[i] == '!') return;

    f(i+1);
    cout << s[i++];
}

int main() {
    cin >> s;

    f(0);

    return 0;
}

1163 Ackmann function

#include <iostream>
using namespace std;

int A(int m, int n) {
    if (m == 0) return n + 1;

    else if (m > 0 && n == 0) return A(m-1, 1);

    else return A(m-1, A(m, n-1));
}

int main() {
    int m, n;
    cin >> m >> n;

    cout << A(m, n);

    return 0;
}

1164 digit function

#include <iostream>
using namespace std;

void digit(int n, int k) {
    if (k == 1) cout << n % 10;
    else digit(n/10, k-1);
}

int main() {
    int n, k;
    cin >> n >> k;

    digit(n, k);

    return 0;
}

1165 Hermite polynomial

#include <cstdio>
#include <iostream>
using namespace std;

double h(int n, double x) {
    if (n == 0) return 1;
    else if (n == 1) return 2*x;
    else return 2 * x * h(n-1, x) - 2 * (n-1) * h(n-2, x);
}

int main() {
    int n;
    double x;
    cin >> n >> x;
    printf("%.2lf\n",h(n,x));

    return 0;
}

1166 Find f(x,n)

#include <cstdio>
#include <iostream>
#include <cmath>
using namespace std;

double f(double x, int n) {
    if (n == 1) return sqrt(1 + x);

    else return sqrt(n + f(x, n-1));
}

int main() {
    int n;
    double x;
    cin >> x >> n;

    printf("%.2lf\n",f(x, n));

    return 0;
}

1167 Find f(x,n) again

#include <cstdio>
#include <iostream>
using namespace std;

double f(double x, int n) {
    if (n == 1) return x / (1 + x);

    else return x / (n + f(x, n-1));
}

int main() {
    int n;
    double x;
    cin >> x >> n;

    printf("%.2lf\n",f(x, n));

    return 0;
}

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