C 解法, 执行用时: 2ms, 内存消耗: 800KB, 提交时间: 2022-06-07

#include "stdio.h"
#include "stdlib.h"
#include "string.h"
  
int WeightMap[1000000] = {0};
int Sum[100000] = {0};
int main()
{
    int n,i,k;
    int weight[11];
    int num[11];
    scanf("%d\n", &n);
    //输入
    for(i=0; i<n; i++)
    {
        scanf("%d\n", &weight[i]);
    }
    for(i=0; i<n; i++)
    {
        scanf("%d\n", &num[i]);
    }
    //初始化第一个元素
    Sum[0] = weight[0];
    num[0]--;
    WeightMap[Sum[0]] = 1;
    int count = 1;
    int last_count = 1;
    //每种重量
    for(i=0; i<n; i++)
    {
        k = 0;
        if(WeightMap[weight[i]] != 1)
            {
                WeightMap[weight[i]] = 1;
                Sum[count++] = weight[i];
            }
        //每种重量的数目
        for(;num[i] > 0; num[i]--)
        {
            
            //上一次不重复的所有元素
            for(;k<last_count; k++)
            {
                if(WeightMap[Sum[k] + weight[i]] != 1)
                {
                    WeightMap[Sum[k] + weight[i]] = 1;
                    Sum[count++] = Sum[k] + weight[i];
                }
            }
            last_count = count;
        }
    }
    printf("%d\n", (count+1));
    return 0;
}

C 解法, 执行用时: 3ms, 内存消耗: 512KB, 提交时间: 2022-07-27

#include <stdio.h>

int main(){
    int n = 0;                                // 砝码种类数n
    scanf("%d", &n);
    int* weights = (int*)malloc(4*n);         
    int* cnts = (int*)malloc(4*n);            
    for(int i = 0; i < n; ++i){
        scanf("%d", weights+i);               // 砝码重量数组weights
    }
    for(int i = 0; i < n; ++i){
        scanf("%d", cnts+i);                  // 砝码个数数组cnts
    }
    int max = 0;
    for(int i = 0; i < n; ++i){
        max += weights[i] * cnts[i];          // 计算最大能称重的重量，哈希表的数组大小 max
    }
    char * hash = (char*)malloc(max+1);       // 哈希表，判断是否重复
    int maxSize = 1;                          // 计算可能的最多组合数
    for(int i = 0; i < n; ++i) maxSize *= cnts[i];
    int * sums = (int*)malloc(4*maxSize);     // sums用来存放不重复的前面元素的计算和
    sums[0] = 0;                              // 首元素为0
    int num = 1;                              // num 记录数量
    for(int i = 0; i < n; ++i){
        int cnt = cnts[i];                    // 当前遍历到的砝码数量和重量
        int weight = weights[i];
        int size = num;                       // 遍历该砝码之前，已经存在的和数组的大小size
        for(int j = 1; j <= cnt; ++j){        // 用sums数组的数逐个和 k 个 weight 进行组合相加，得到 sum
            for(int k = 0; k < size; ++k){
                int sum = sums[k] + j * weight;
                if(hash[sum] != '1'){         // sum不重复，则用哈希表记录，并存储到sums值，个数num++
                    sums[num++] = sum;
                    hash[sum] = '1';
                }   
            }
        }
    }
    printf("%d", num);
        free(weights);
    free(cnts);
    free(hash);
    free(sums);
    return 0;
}