SICP 找零钱问题背后的思考

 1      #lang racket
 2      (define (count-change amount kinds-of-coins) 
 3           ( cond ((= amount 0) 1)
 4          ((or (< amount 0) (= kinds-of-coins 0))0)
 5          (else 
 6            (+(count-change amount (- kinds-of-coins 1)) (count-change (- amount (some-coin kinds-of-coins)) kinds-of-coins )) ) ) )
 7   
 8      (define (some-coin kinds-of-coins)
 9        ( cond ((= kinds-of-coins 1) 1)
10          ((= kinds-of-coins 2) 5)
11          ((= kinds-of-coins 3) 10)
12          ((= kinds-of-coins 4) 25)
13          ((= kinds-of-coins 5) 50)))
14 
15 　　(count-change 45 5)

 1  //cpp
 2           #include <iostream>
 3           #include <vector>
 4           using namespace std;
 5 
 6           int main ()
 7           {     
 8                  int amount = 55;
 9                  const int kind_of_coins = 5 ;
10                  int coin [ kind_of_coins] = { 1 , 5 , 10, 25 , 50 };
11                  vector< int > result ( amount + 1 , 0 );
12                  result [0 ] = 1;
13       
14                  for (int i = 0 ; i < kind_of_coins; ++ i ){
15                        int j = coin[ i ];
16                        for (; j <= amount; ++ j )
17                              result [j ] += result[ j - coin [ i]];
18                   }
19 
20               cout << result [amount ] << endl;
21               system ("pause" );
22       
23           }
24  

 1  //cpp
 2           #include <iostream>
 3           #include <vector>
 4           using namespace std;
 5 
 6           int main ()
 7           {     
 8                  int amount = 55;
 9                  const int kind_of_coins = 5 ;
10                  int coin [ kind_of_coins] = { 1 , 5 , 10, 25 , 50 };
11                  vector< int > result ( amount + 1 , 0 );
12                  result [0 ] = 1;
13       
14                  for (int i = 0 ; i < kind_of_coins; ++ i ){
15                        int j = coin[ i ];
16                        for (; j <= amount; ++ j )
17                              result [j ] += result[ j - coin [ i]];
18                   }
19 
20               cout << result [amount ] << endl;
21               system ("pause" );
22       
23           }