如何证明找零钱问题的贪婪算法总能产生具有最少硬币数的零钱

    private static final int[] m = {100,50,20,10,5,2,1};
public static void main(String[] args) {
Scanner scanner  = new Scanner(System.in);
int f = scanner.nextInt();
int[] amount = new int[f];
for(int i = 0 ; i < f;i++){
amount[i] = giveChange(scanner.nextInt());
}
for(int i = 0 ; i < amount.length;i++){
System.out.println(amount[i]);
}
}
public static int giveChange(int n)  { 
int num=0;  
for(int i=0;inum+=n/m[i];  
n=n%m[i];  
}  
return num;  
}