# Tree Recursion Traditional Approach. Tree Recursion Consider the Fibonacci Number Sequence: Time: 0 1 2 3 4 5 6 7 8 0, 1, 1, 2, 3, 5, 8, 13, 21,... /

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Tree Recursion Consider the Fibonacci Number Sequence: Time: 0 1 2 3 4 5 6 7 8 0, 1, 1, 2, 3, 5, 8, 13, 21,... / 0when n = 0 fib(n) = | 1when n = 1 \ fib(n - 1) + fib(n - 2)otherwise

Tree Recursion (cont.) As code this is: int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) fib(2) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) fib(2) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) fib(2) fib(1) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) fib(2) fib(1) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

5 3 2 2111 111010 10 1 111 1 0 00 What happens when computing fib(5)?

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Tree Recursion MS Agent Approach

Tree Recursion Consider the Fibonacci Number Sequence: Time: 0 1 2 3 4 5 6 7 8 0, 1, 1, 2, 3, 5, 8, 13, 21,...  This sequence is defined by the rule: / 0when n = 0 fib(n) = | 1when n = 1 \ fib(n - 1) + fib(n - 2)otherwise

Tree Recursion (cont.) As code this is: int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

What happens when computing fib(5)? fib(5) int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) fib(2) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) fib(2) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

fib(5) fib(4) fib(3) fib(2) fib(1) What happens when computing fib(5)? int fib ( int n ) { if ( n <= 0 ) return 0; else if ( n = 1 ) return 1; else return fib ( n - 1 ) + fib ( n - 2 ) ; }

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