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{ for (int j = 1; j cout << setw(2) for (int j = 0; j cout << setw(4) cout << endl; }
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< m-i; j++) << ""; // print whitespace <= i; j++) << comb(i,j);
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} long comb(int n, int k) { if (n < 0 || k < 0 || k > n) return 0; long c = 1; for (int i=1; i<=k; i++, n--) c = c*n/i; return c; } 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1 1 11 55 165 330 462 462 330 165 55 11 1 1 12 66 220 495 792 924 792 495 220 66 12 1 This tests a function that extracts a digit from an integer: int digit(long,int); int main() { int n, k; cout << "Integer: "; cin >> n; do { cout << "Digit: "; cin >> k; cout << "Digit number " << k << " of " << n << " is " << digit(n, k) << endl; } while (k > 0); } int digit(long n, int k) { for (int i = 0; i < k; i++) n /= 10; // remove right-most digit return n % 10; } Integer: 876543210 Digit: 4 Digit number 4 of 876543210 is 4 Digit: 7 Digit number 7 of 876543210 is 7 Digit: 0 Digit number 0 of 876543210 is 0
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This tests the greatest common divisor function: long gcd(long,long); int main() { int m, n; cout << "Enter two positive integers: "; cin >> m >> n; cout << "gcd(" << m << "," << n << ") = " << gcd(m,n) << endl; } long gcd(long m, long n) { // returns the greatest common divisor of m and n: if (m<n) swap(m,n); assert(n >= 0); while (n>0) { long r=m%n; m = n; n = r; } return m; } Enter two positive integers: 144 192 gcd(144,192) = 48 This tests the least common multiple function: long lcm(long,long); int main() { int m, n; cout << "Enter two positive integers: "; cin >> m >> n; cout << "lcm(" << m << "," << n << ") = " << lcm(m,n) << endl; } long gcd(long,long); long lcm(long m,long n) { return m*n/gcd(m,n); } long gcd(long m,long n) { if (m < n) swap(m,n); while (n>0) { int r = m%n; m = n; n = r; } return m; } Enter two positive integers: 144 192 lcm(144,192) = 576 This tests the power function: double pow(double,int); int main() { cout << "Enter a positive float x and an integer n: "; double x; int n; cin >> x >> n;
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cout << "pow(" << x << "," << n << ") = " << pow(x,n) << endl; } double pow(double x, int n) { if (x == 0) return 0; if (n == 0) return 1; double y=1; for (int i=0; i < n; i++) y *= x; for (int i=0; i > n; i--) y /= x; return y; } Enter a positive float x and an integer n: 2.0 -3 pow(2,-3) = 0.125 This tests a boolean function that tests integers for triangularity: int isTriangular(int); int main() { const int MAX=12; for (int i=0; i<MAX; i++) if (isTriangular(i)) cout << i << " is triangular.\n"; else cout << i << " is not triangular.\n"; } int isTriangular(int n) { int x=0, y=0, dy=1; while (y < n) y += dy++; if (y == n) return true; else return false; } 0 is triangular. 1 is triangular. 2 is not triangular. 3 is triangular. 4 is not triangular. 5 is not triangular. 6 is triangular. 7 is not triangular. 8 is not triangular. 9 is not triangular. 10 is triangular. 11 is not triangular. This tests a boolean function that tests integers for squares: int isSquare(int); int main() { const int MAX=20; for (int i=0; i<MAX; i++) if (isSquare(i)) cout << i << " is square.\n"; else cout << i << " is not square.\n"; } int isSquare(int n) { int i=0; while (i*i<n)
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