A + B Again

A + B Again
Time Limit: 1000ms, Special Time Limit:2500ms, Memory Limit:32768KB
Total submit users: 201, Accepted users: 182
Problem 10281 : No special judgement
Problem description
Reads in positive integers A and B,calculates A + B.Pay attention:A and B is composed by simple English word. [0-9]:"zero","one","two","three","four","five","six","seven","eight","nine";
Input
Standard input will contain multiple test cases.Each testcase occupies a line.the form is "A + B =",the neighboring two characters string has a blank space.When A and B is 0 at the same time ,inputs finished.You shouldn't output the result 0.
Output
For each testcase outputs 1 line,The result of A + B,by simple English word too.Each word is separated with a single space.There's no space after the last word.
Sample Input
one + two =
three four + five six =
zero + zero =
Sample Output
three
nine zero
Problem Source
HNU Contest 
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本人自己的解法,相当麻烦:

 
  1. #include<iostream>
  2. #include<string>
  3. #include<map>
  4. using namespace std;
  5. int pow(int x, int y)
  6. {
  7.      int sum = x;
  8.      for(int i=0; i<y; i++)
  9.      {
  10.          sum*=10;
  11.      }
  12.      return sum;
  13. }
  14. int main(int argc, char* argv[])
  15. {    
  16.     int i = 0;
  17.     int len;
  18.     int r=0;
  19.     int l=0;
  20.     char *ptr;
  21.     int t[1000];
  22.     string*s = new string[1000];
  23.     map<string,int> m;
  24.     map<int,string> m1;
  25.     m["zero"] = 0;
  26.     m["one"] = 1;
  27.     m["two"] = 2;
  28.     m["three"] = 3;
  29.     m["four"] = 4;
  30.     m["five"] = 5;
  31.     m["six"] = 6;
  32.     m["seven"] = 7;
  33.     m["eight"] = 8;
  34.     m["nine"] = 9;
  35.     m1[0] = "zero" ;
  36.     m1[1] = "one";
  37.     m1[2] = "two";
  38.     m1[3] = "three";
  39.     m1[4] = "four";
  40.     m1[5] = "five";
  41.     m1[6] = "six";
  42.     m1[7] = "seven";
  43.     m1[8] = "eight";
  44.     m1[9] = "nine";
  45.     
  46.     char in[100000];
  47.     while(gets(in))
  48.     {
  49.        len = strlen(in)+1;
  50.        ptr = strtok(in, " ");
  51.        while(ptr)
  52.        {
  53.          if(ptr[0]!='+'&&ptr[0]!='=')
  54.          {
  55.             t[i] = m[ptr];
  56.             i++;
  57.          }
  58.          else
  59.          {
  60.             
  61.              for(int k=i-1,f=0; k>=0; k--,f++)
  62.              {
  63.                  r+=pow(t[f],k);
  64.             
  65.              }
  66.             
  67.              i=0;
  68.          }
  69.          ptr = strtok(NULL," ");
  70.        }
  71.     
  72.        if(r == 0)
  73.            return 0;
  74.        int temp = r;
  75.        int count = 0;
  76.        while(r)
  77.        {
  78.           s[count++]=m1[r%10];
  79.           
  80.           r = r/10;
  81.           l++;
  82.         
  83.        } 
  84.        for(int p=count-1; p>=0; p--)
  85.        {
  86.            cout<<s[p];
  87.            if(p>0)
  88.               cout<<" ";
  89.        }
  90.        cout<<endl;
  91.         
  92.      
  93.        l=0;
  94.        r=0;
  95.       
  96.     }
  97.     
  98.     return 0;
  99. }
  100. /*在其中学会了如何使用一个函数:
  101. 原型:extern char *strtok(char *s, char *delim);
  102.         
  103.   用法:#include <string.h>
  104.   
  105.   功能:分解字符串为一组标记串。s为要分解的字符串,delim为分隔符字符串。
  106.   
  107.   说明:首次调用时,s必须指向要分解的字符串,随后调用要把s设成NULL。
  108.         strtok在s中查找包含在delim中的字符并用NULL('/0')来替换,直到找遍整个字符串。
  109.         返回指向下一个标记串。当没有标记串时则返回空字符NULL。
  110.   
  111.   举例:
  112.       // strtok.c
  113.       
  114.       #include <syslib.h>
  115.       #include <string.h>
  116.       #include <stdio.h>
  117.       main()
  118.       {
  119.         char *s="Golden Global View";
  120.         char *d=" ";
  121.         char *p;
  122.         
  123.         clrscr();
  124.         
  125.         p=strtok(s,d);
  126.         while(p)
  127.         {
  128.           printf("%s/n",s);
  129.           strtok(NULL,d);
  130.         }
  131.         getchar();
  132.         return 0;
  133.       }*/
{"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} 写一个脚本,将以上字符串格式化为以下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 }
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08-17
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