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cout << "The average of the first two is " << ave(w,x) << endl; cout << "The average of the first three is " << ave(w,x,y)<<endl; cout << "The average of all four is " << ave(w,x,y,z) << endl; } double ave(double x1, double x2, double x3, double x4) { double sum = x1 + x2 + x3 + x4; if (x2 == 0) return sum; if (x3 == 0) return sum/2.0; if (x4 == 0) return sum/3.0; return sum/4.0; } Enter four non-zero numbers: 44 88 22 66 The average of the first one is 44 The average of the first two is 66 The average of the first three is 51.3333 The average of all four is 55 This tests the factorial function: long fact(int n); int main() { for (int i=-1; i<20; i++) cout << "fact(" << i << ") = " << fact(i) << endl; } long fact(int n) { if (n < 2) return 1; long f=1; for (int i=2; i <= n; i++) f *= i; return f; } fact(-1) = 1 fact(0) = 1 fact(1) = 1 fact(2) = 2 fact(3) = 6 fact(4) = 24 fact(5) = 120 fact(6) = 720 fact(7) = 5040 fact(8) = 40320 fact(9) = 362880 fact(10) = 3628800 fact(11) = 39916800 fact(12) = 479001600 fact(13) = 1932053504 fact(14) = 1278945280 fact(15) = 2004310016 fact(16) = 2004189184 fact(17) = -288522240 fact(18) = -898433024 fact(19) = 109641728 This overflows when n = 13 on machines that implement the long type with 32-bits.
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This tests the permutation function: long perm(int n, int k); int main() { for (int i = -1; i < 6; i++) { for (int j = -1; j <= i+1; j++) cout << " " << perm(i,j); cout << endl; } } long perm(int n, int k) { if (n < 0 || k < 0 || k > n) return 0; int p = 1; for (int i = 1; i <= k; i++, n--) p *= n; return p; } 0 0 0 1 0 0 1 1 0 0 1 2 2 0 0 1 3 6 6 0 0 1 4 12 24 24 0 0 1 5 20 60 120 120 0 This tests the combination function: long comb(int n, int k); int main() { for (int i = -1; i < 6; i++) { for (int j = -1; j <= i+1; j++) cout << " " << comb(i,j); cout << endl; } } long fact(int n); long comb(int n, int k) { if (n < 0 || k < 0 || k > n) return 0; return fact(n)/(fact(k)*fact(n-k)); } long fact(int n) { if (n < 2) return 1; long f=1; for (int i=2; i <= n; i++) f *= i; return f; } 0 0 0 1 0 0 1 1 0 0 1 2 1 0 0 1 3 3 1 0 0 1 4 6 4 1 0 0 1 5 10 10 5 1 0 Note that the fact() function must be declared above the comb() function because it is used by comb(). But it does not need to be declared above main() because it is not used there.
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This tests the combination function: long comb(int n, int k); int main() { for (int i = -1; i < 9; i++) { for (int j = -1; j <= i+1; j++) cout << " " << comb(i,j); cout << endl; } } long perm(int,int); long fact(int); long comb(int n, int k) { if (n < 0 || k < 0 || k > n) return 0; return perm(n,k)/fact(k); } long perm(int n, int k) { if (n < 0 || k < 0 || k > n) return 0; int p = 1; for (int i = 1; i <= k; i++, n--) p *= n; return p; } long fact(int n) { if (n < 2) return 1; long f=1; for (int i=2; i <= n; i++) f *= i; return f; } The output is the same as for Problem 5.13. This tests the combination function: long comb(int n, int k); int main() { for (int i = -1; i < 9; i++) { for (int j = -1; j <= i+1; j++) cout << " " << comb(i,j); cout << endl; } } 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; } The output is the same as for Problem 5.13. This prints Pascal s Triangle: long comb(int n, int k); int main() { const m = 13; for (int i = 0; i < m; i++)
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