Find Coins (25)

题目描述

Eva loves to collect coins from all over the universe, including some other planets like Mars.  One day she visited a universal shopping mall which could accept all kinds of coins as payments.  However, there was a special requirement of the payment: for each bill, she could only use exactly two coins to pay the exact amount.  Since she has as many as 105 coins with her, she definitely needs your help.  You are supposed to tell her, for any given amount of money, whether or not she can find two coins to pay for it.

输入描述:

Each input file contains one test case.  For each case, the first line contains 2 positive numbers: N (<=105, the total number of coins) and M(<=103, the amount of money Eva has to pay).  The second line contains N face values of the coins, which are all positive numbers no more than 500.  All the numbers in a line are separated by a space.


输出描述:

For each test case, print in one line the two face values V1 and V2 (separated by a space) such that V1 + V2 = M and V1 <= V2.  If such a solution is not unique, output the one with the smallest V1.  If there is no solution, output "No Solution" instead.

输入例子:

8 15
1 2 8 7 2 4 11 15

输出例子:

4 11

我的代码:

(此代码只能在牛客网上通过)

#include<iostream>
#include<algorithm>
using namespace std;
struct Coin
{
    int v1,v2;
}c[1001];
int cmp(Coin x,Coin y)
{
    return x.v1<y.v1;
}
int n,m,i,j,a[100001],k=0;
int main()
{
    cin>>n>>m;
    for(i=0;i<n;i++)
    {
        cin>>a[i];
        for(j=0;j<i;j++)
        {
            if(a[j]+a[i]==m)
            {
                c[k].v1=a[j];
				c[k].v2=a[i];
                k++;
                break;
            }
        }
    }
    if(k==0) puts("No Solution");
    else
    {
        sort(c,c+k,cmp);
        cout<<c[0].v1<<" "<<c[0].v2<<endl;
    }
    return 0;
}

提交结果:


### 关于分割硬币的公平分配算法 在计算机科学和数学领域,分割硬币的问题通常可以被建模为一种优化问题或动态规划问题。目标通常是找到一种方式来最小化两个集合之间的差异或者最大化某种公平性标准。 #### 动态规划解决方案 对于分割硬币使其尽可能均匀分布的情况,可以采用动态规划的方法解决此问题。假设我们有一组硬币 `coins` 和它们的价值分别为 `[c1, c2, ..., cn]`,我们需要将其分成两部分使得这两部分价值之差最小[^2]。 以下是基于动态规划的一个实现方案: ```python def min_difference_partition(coins): total_sum = sum(coins) n = len(coins) dp = [[False]*(total_sum//2 + 1) for _ in range(n+1)] # Initialize DP table for i in range(n+1): dp[i][0] = True for i in range(1, n+1): for j in range(1, total_sum//2 + 1): if coins[i-1] <= j: dp[i][j] = dp[i-1][j] or dp[i-1][j-coins[i-1]] else: dp[i][j] = dp[i-1][j] # Find the largest value that can be achieved less than half of total sum for j in range(total_sum//2, -1, -1): if dp[n][j]: return abs((total_sum - j) - j) ``` 该函数通过构建一个二维布尔数组 `dp` 来记录子集总和的可能性,并最终返回能够达到的最大接近一半总和的值,从而计算出两者间的最小差距[^3]。 #### 贪婪算法近似解法 如果追求更高效的解决方案而允许一定的误差范围,则可以考虑贪婪策略。这种方法并不总是能找到最优解,但在某些情况下表现良好。基本思路是从最大面额开始依次选取直到无法再选为止[^4]。 ```python def greedy_divide_coins(coins): coins.sort(reverse=True) group_a = [] group_b = [] for coin in coins: if sum(group_a) < sum(group_b): group_a.append(coin) else: group_b.append(coin) return (group_a, group_b), abs(sum(group_a)-sum(group_b)) ``` 尽管如此,在实际应用中需注意验证其适用性和局限性。
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