Recursive

Recursive F(n) = F(n-1) + F(n-2) n! = (n-1)! x n C(m,n) = C(m-1,n-1)+C(m-1,n)......

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 8 ************************** n = ?

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 9 ************************** n = ?

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 10 ************************** n = 3

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 factorial(n) = ?

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 factorial(n) = ? Function: factorial Line: 2 ************************** n = 3

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 3 ************************** n = 3

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 5 ************************** n = 3

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 6 ************************** n = 3 Return n x …

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 6 ************************** n = 3 Return n x … Function: factorial Line: 2 ************************** n = 2

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 3 ************************** n = 3 Function: factorial Line: 3 ************************** n = 2

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 5 ************************** n = 3 Function: factorial Line: 5 ************************** n = 2

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 6 ************************** n = 3 Return n x … Function: factorial Line: 6 ************************** n = 2 Return n x …

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 6 ************************** n = 3 Return n x … Function: factorial Line: 6 ************************** n = 2 Return n x … Function: factorial Line: 2 ************************** n = 1

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 3 ************************** n = 3 Function: factorial Line: 3 ************************** n = 2 Function: factorial Line: 3 ************************** n = 1

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 3 ************************** n = 3 Function: factorial Line: 6 ************************** n = 2 Return n x … Function: factorial Line: 4 ************************** n = 1 Return 1

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 3 ************************** n = 3 Function: factorial Line: 6 ************************** n = 2 Return n x 1

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 Function: factorial Line: 6 ************************** n = 3 Return n x 2 Function: factorial Line: 6 ************************** n = 2 Return 2

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 factorial(n) = ? Function: factorial Line: 6 ************************** n = 3 Return 6

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 factorial(n) = ?

Recursive #include int factorial(int n){ if(n<=1) return 1; else return n * factorial(n-1); } int main() { int n = 3; printf("%d! = %d\n", n, factorial(n) ); return 0; } Function: mian Line: 11 ************************** n = 3 factorial(n) = 6

Hanoi Tower

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Hanoi Tower If you want to move n disks from SRC to DES…. Step 1: Move top n-1 from SRC to TMP Step 2: Move top 1 from SRC to DES Step 3: Move top n-1 from TMP to DES SRCTMPDES

Hanoi Tower How to Move top n-1 from SRC to TMP? This time, TMP become DES, DES become TMP. Step 1: Move top n-2 from SRC to TMP Step 2: Move top 1 from SRC to DES Step 3: Move top n-2 from TMP to DES SRCTMPDES

Hanoi Tower #include void hanoi(int n, int startRod, int tempRod, int targetRod){ if(n>0){ hanoi(n-1, startRod, targetRod, tempRod); printf(" 將 %d 盤從 %d 柱移動到 %d 柱 \n", n, startRod, targetRod); hanoi(n-1, tempRod, startRod, targetRod); } int main() { hanoi(3,1,2,3); return 0; }