Exercise

可信软件

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Weiwen Chen 10152510217

Exercise 1

• Write a program in our language to compute the sum of natural numbers from 0 to n
• Write the corresponding program in C (with n = 10)
• Write the complete program in C, printing result and executing it.
• Use an approach similar to the one used in the example below

#include<stdio.h>
int sum(const int &n){
    int sum = 0;
    for (int i = 0; i <= n; i++){
        sum += i;
    }
}
int main(){
    printf("%d\n", sum(10));
    return 0;
}

// small Language

sum
    sum := 0;
    i:=1;
    while i<=n do
        res := res + a;
        a := a + 1;
    end

Exercise 2

• Translate "sumarray" in C using the same approach as below
• Take m = 10
• Initialise the array f with {1,2,3,4,5,6,7,8,9,10}
• Execute your C program

#include<stdio.h>
int f[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
int sumarray(const int &m){
    int res = 0;
    for (int i = 0; i < m; i++){
        res += f[i];
    }
    return res;
}
int main(){
    printf("%d\n", sumarray(10););
    return 0;
}

Exercise 3

• Let f be this function:
  f = {0 7→ 1,1 7→ 2,2 7→ 3,3 7→ 4,4 7→ 4}
• Give the values of:
  ran(f) = ?
  f[0 .. 4] = ?
  {3} ? f = ?
  f ? {4} = ?
  {3} ? − f = ?
  f ? − {4} = ?

$$ran(f) = {1, 2, 3, 4}$$

$$f[0..4] = {1, 2, 3, 4}$$

$${3} \triangleleft f = \{3 \rightarrow 4 \}$$

$$f \triangleright {4} = \{3 \rightarrow 4, 4 \rightarrow 4\}$$

$$\{ 3 \} ? f = \{ 0\rightarrow1, 1\rightarrow2, 2\rightarrow3, 4\rightarrow4 \}$$

$$f ? {4}={0\rightarrow1,1\rightarrow2,2\rightarrow3}$$