NBUT-1521(+-字符串)

本文探讨了一个字符串操作问题,即如何通过交换加号和减号来将一个字符串转换为另一个字符串,同时提供了一段C语言实现的代码,用于计算最少的操作次数。

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题目

问题描述
Shiva得到了两个只有加号和减号的字符串。Shiva一次可以把一个加号和它相邻的减号交换。他想知道最少需要多少次操作才能把第一个字符串变换成第二个字符串。你现在要去帮助他完成那个这个问题。

输入

输入数据有两行,每行包含一个由”+”和”-“最成的字符串。每个子符串长度不超过5000。

输出

仅一个整数,输出最少需要操作的次数。如果答案不存在,输出-1。

样例输入

+±±-+
-+±-++

样例输出

4

这个题目没有说要多组输入,但是却要多组输入才能过,真的扎心了;

AC代码:

#include<stdio.h>
#include<string.h>
char a[5005];
char b[5005];
int main()
{
    int i,j;
    int x1,x2;
    int ans;
    while(~scanf("%s%s",a,b))
    {
        x1=0;
        x2=0;
        ans=0;
        if(strlen(a)!=strlen(b))
        {
            printf("-1");
            continue;
        }
        for(i=0; i<strlen(a); i++)
            if(a[i]=='+')
                x1++;
        for(i=0; i<strlen(b); i++)
            if(b[i]=='+')
                x2++;
        if(x1!=x2)
        {
            printf("-1");
            continue;
        }
        for(i=0; i<strlen(a); i++)
        {
            if(a[i]!=b[i])
            {
                for(j=i+1; j<strlen(b); j++)
                {
                    if(a[i]==b[j])
                    {
                        ans=ans+j-i;
                        b[j]=b[i];
                        break;
                    }
                }
            }
        }
        printf("%d\n",ans);
    }
}
json格式: {"id": "cmpl-e759f3d8-78e1-11f0-b2b4-1a85109d8f07", "choices": [{"finish_reason": "stop", "index": 0, "message": {"content": "<think>\nOkay, so I need to figure out how many whole-number divisors there are for the integer given by the expression $ a(2a + b) - 2a^2 + ab $, where $ a $ and $ b $ are different prime numbers greater than 2. Let me start by simplifying the expression step by step.\n\nFirst, let me write down the expression again to make sure I have it right: $ a(2a + b) - 2a^2 + ab $. Let me expand the first term, which is $ a(2a + b) $. If I distribute the $ a $, that becomes $ 2a^2 + ab $. So substituting that back into the original expression, we have:\n\n$ 2a^2 + ab - 2a^2 + ab $.\n\nNow let me combine like terms. The $ 2a^2 $ and $ -2a^2 $ cancel each other out, right? So that leaves me with $ ab + ab $, which is $ 2ab $. So the entire expression simplifies to $ 2ab $. \n\nWait, so the problem is asking for the number of whole-number divisors of $ 2ab $, where $ a $ and $ b $ are different primes greater than 2. Let me confirm that I simplified correctly. Let me check again:\n\nOriginal expression: $ a(2a + b) - 2a^2 + ab $.\n\nExpanding $ a(2a + b) $: $ 2a^2 + ab $. Then subtract $ 2a^2 $, so $ 2a^2 + ab - 2a^2 = ab $. Then add $ ab $, so $ ab + ab = 2ab $. Yes, that seems right. So the expression simplifies to $ 2ab $.\n\nAlright, so now I need to find the number of positive divisors of $ 2ab $. Since $ a $ and $ b $ are primes greater than 2, they are both odd primes. Let me recall that the number of divisors of a number is found by taking its prime factorization, adding one to each of the exponents, and multiplying those together.\n\nSo first, let me write the prime factorization of $ 2ab $. Since 2 is a prime number, and $ a $ and $ b $ are different primes, all three primes are distinct. Therefore, the prime factors of $ 2ab $ are 2, $ a $, and $ b $. Each of these primes has an exponent of 1 in the factorization. So the prime factorization is $ 2^1 \\times a^1 \\times b^1 $.\n\nTo find the number of divisors, I take each exponent (which are all 1s), add 1 to them, and multiply. That would be $ (1 + 1)(1 + 1)(1 + 1) = 2 \\times 2 \\times 2 = 8 $. Therefore, there are 8 positive divisors.\n\nBut let me verify this with an example to make sure I haven't made a mistake. Let me pick specific primes for $ a $ and $ b $. Let's take $ a = 3 $ and $ b = 5 $, which are both primes greater than 2 and different.\n\nCalculating $ 2ab $: $ 2 \\times 3 \\times 5 = 30 $. Now, the divisors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. That's 8 divisors. Yep, that matches the calculation. Let me try another example to be safe. Let me take $ a = 5 $, $ b = 7 $. Then $ 2ab = 2 \\times 5 \\times 7 = 70 $. Divisors of 70: 1, 2, 5, 7, 10, 14, 35, 70. Again, 8 divisors. Okay, so that seems consistent.\n\nBut let me think again if there's any possibility that 2 could be equal to $ a $ or $ b $. However, the problem states that $ a $ and $ b $ are primes greater than 2, so they are odd primes. Therefore, 2 is not among them. Therefore, 2, $ a $, and $ b $ are distinct primes. Therefore, the prime factorization is indeed three distinct primes each to the first power, leading to 2×2×2=8 divisors.\n\nBut let me check if there's a case where maybe $ a $ or $ b $ is 2. But the problem says they are greater than 2, so they can't be. Therefore, my reasoning holds.\n\nTherefore, the number of whole-number divisors is 8. Therefore, the answer is 8, which in boxed form is \\boxed{8}.\n\nWait, but let me just check once more. Suppose someone might think that maybe the original expression simplifies differently? Let me check again:\n\nOriginal expression: $ a(2a + b) - 2a^2 + ab $.\n\nFirst term: $ a(2a + b) = 2a^2 + ab $.\n\nSubtracting $ 2a^2 $: $ 2a^2 + ab - 2a^2 = ab $.\n\nAdding $ ab $: $ ab + ab = 2ab $. Yes, that's correct. So the expression simplifies to 2ab. So no issues there.\n\nAlternatively, maybe someone might misread the original problem? Let me check again. The problem says: \"the integer $ a(2a + b) - 2a^2 + ab $\". So yes, that's how it's written. So the steps are correct.\n\nTherefore, I think my answer is correct. The number of divisors is 8.\n\n**Final Answer**\n\\boxed{8}\n</think>\n\nWe are given an expression involving two distinct prime numbers $ a $ and $ b $, both greater than 2, and asked to find the number of whole-number divisors of the integer:\n\n$$\na(2a + b) - 2a^2 + ab\n$$\n\n---\n\n### Step 1: Simplify the Expression\n\nStart by expanding the first term:\n\n$$\na(2a + b) = 2a^2 + ab\n$$\n\nNow substitute this back into the full expression:\n\n$$\n2a^2 + ab - 2a^2 + ab\n$$\n\nSimplify by combining like terms:\n\n- $ 2a^2 - 2a^2 = 0 $\n- $ ab + ab = 2ab $\n\nSo the entire expression simplifies to:\n\n$$\n2ab\n$$\n\n---\n\n### Step 2: Prime Factorization of $ 2ab $\n\nSince $ a $ and $ b $ are distinct prime numbers greater than 2, and 2 is also a prime, the expression $ 2ab $ is the product of three **distinct** primes:\n\n$$\n2ab = 2^1 \\cdot a^1 \\cdot b^1\n$$\n\n---\n\n### Step 3: Count the Number of Divisors\n\nThe number of positive divisors of a number is determined by taking the product of one more than each exponent in its prime factorization.\n\nHere, the exponents are all 1:\n\n$$\n(1 + 1)(1 + 1)(1 + 1) = 2 \\cdot 2 \\cdot 2 = 8\n$$\n\n---\n\n### Final Answer\n\n$$\n\\boxed{8}\n$$", "role": "assistant", "reasoning_content": ""}, "review": {"gold": "8", "pred": "8", "result": true}}], "created": 1755157209, "model": "Qwen3-32B", "object": "chat.completion", "usage": {"completion_tokens": 1627, "prompt_tokens": 68, "total_tokens": 1695}, "model_spec": {"api_url": "http://0.0.0.0:9009/v1/chat/completions", "model_id": "Qwen3-32B", "api_key": "EMPTY"}, "answer_id": "answer-1a07ae97260436f698e63d4620d7cff0", "subset_name": "default", "raw_input": {"problem": "Suppose $a$ and $b$ are different prime numbers greater than 2. How many whole-number divisors are there for the integer $a(2a+b)-2a^{2}+ab$?", "solution": "Distributing and combining like terms, we have $a(2a+b)-2a^2+ab=2a^2+ab-2a^2+ab=2ab$. Now $a$ and $b$ are different prime numbers greater than 2, so $2ab=2^1\\cdot a^1\\cdot b^1$ has $(1+1)(1+1)(1+1)=\\boxed{8}$ divisors.", "answer": "8", "subject": "Number Theory", "level": 4, "unique_id": "test/number_theory/1287.json"}, "origin_prompt": {"data": ["Suppose $a$ and $b$ are different prime numbers greater than 2. How many whole-number divisors are there for the integer $a(2a+b)-2a^{2}+ab$?\nPlease reason step by step, and put your final answer within \\boxed{}."], "system_prompt": null, "raw_input": {"problem": "Suppose $a$ and $b$ are different prime numbers greater than 2. How many whole-number divisors are there for the integer $a(2a+b)-2a^{2}+ab$?", "solution": "Distributing and combining like terms, we have $a(2a+b)-2a^2+ab=2a^2+ab-2a^2+ab=2ab$. Now $a$ and $b$ are different prime numbers greater than 2, so $2ab=2^1\\cdot a^1\\cdot b^1$ has $(1+1)(1+1)(1+1)=\\boxed{8}$ divisors.", "answer": "8", "subject": "Number Theory", "level": 4, "unique_id": "test/number_theory/1287.json"}, "index": 0}, "reviewed": true, "review_id": "review-307a3dc16716316d92e62e1f3ae09703", "reviewer_spec": {"metric": ["AveragePass@1"], "reviewer": ["Evaluator"], "revision": ["default"]}, "review_time": 1755194244.6042051} 生成csv: 题目ID ID类型 原始答案(raw_input) 原始答案(review.gold) 原始答案一致性 模型答案(review.pred) 模型答案(boxed) 模型答案一致性 审核结果(review.result) 完成原因 原因分析 模型输出摘要 cmpl-e759f3d8-78e1-11f0-b2b4-1a85109d8f07 UUID 8 N/A N/A 8 8 是 N/A stop 正常完成 <think> Okay, so I need to figure out how many whole-number divisors there are for the integer given... 优化脚本
最新发布
08-16
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