简单算法程序-C和C++

快速幂算法C++：用于以 log(n) 的复杂度求幂 $x^n$。

#include<iostream>
using namespace std;
long long fast_power(long long a, long long b){
    long long ans = 1;
    while(b){
        if (b&1)ans*=a;
        b >>= 1;
        a *= a;
    }
    return ans;
}

int main(){
    long long n=5, m=10;
    cout<<fast_power(n, m)<<endl;
    return 0;
}

快速幂余算法C语言：用于以 log(n) 的复杂度求 $x^n mod c$，以免先求幂在取余导致数值过大而产生数值溢出错误。

#include<stdio.h>
int fast_power_mode(int a, int b, int c){
    int ans = 1;
    a = a % c;
    while(b>0){
        if (b&1){
            ans=(ans*a)%c;
        };
        b >>= 1;
        a = (a * a) % c;
    }
    return ans;
}

int main(){
    int n=5, m=10, k=7;
    printf("%d\n", fast_power_mode(n, m, k));
    return 0;
}

快速排序算法C语言：用于以 nlog(n) 的时间复杂求对一个线性表排序。

#include<stdio.h>

void fastsort(int* numbers, int begin, int end){
    // int num_len = end - begin + 1;
    int num_len = sizeof(numbers);
    printf("sort array from index %d to %d, len: %d\n", begin, end, num_len);
    for(int i=0; i<num_len; i++)
        printf("%d, ", numbers[i]);
    printf("\n");
    // printf("the length of array \"numbers\": %d\n", num_len);
    if(begin >= 0 && begin < num_len && end >= 0 && end < num_len && begin < end){
        int i = begin, j = end;
        int vot = numbers[i];
        while (i != j){
            while(i<j && numbers[j]>=vot)j--;
            if(i<j) numbers[i++] = numbers[j];
            while(i<j && numbers[i]<=vot)i++;
            if(i<j) numbers[j--] = numbers[i];
        }
        numbers[i] = vot;
        fastsort(numbers, begin, j-1);
        fastsort(numbers,i+1, end);
    }
}
void fastsort_default(int* numbers){
    // why? line 1 return 2 but line 2 return 8
    // int num_len = sizeof(numbers) / sizeof(numbers[0]);  // line 1
    int num_len = sizeof(numbers);  // line 2
    printf("the length of array \"numbers\": %d\n", num_len);
    fastsort(numbers, 0, num_len-1);
    for(int i=0; i<num_len; i++)
        printf("%d, ", numbers[i]);
    printf("\n");
}
int main(){
    int numbers[] = {10, 7, 2, 4, 3, 8 ,9 ,19};
    // int num_len1 = sizeof(numbers) / sizeof(numbers[0]);
    // int num_len2 = sizeof(numbers);
    // printf("%d, %d\n", num_len1, num_len2);
    fastsort_default(numbers);
    // C language need not to free a static array, but dynamic array.
    // delete []numbers;
    return 0;
}

附编译执行的代码：

set filename=fastsortarray
set postfix1=.c
set postfix2=.exe
gcc -g %filename%%postfix1% -o %filename%%postfix2%
%filename%%postfix2%