HDU-5616 Jam's balance(母函数)

╰半橙微兮° 2022-06-07 22:35 144阅读 0赞

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 <a href="http://blog.csdn.net/m0_37953323?viewmode=contents" style="color:red; text-decoration:none" rel="nofollow">友情链接</a> 
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 <td align="center"> <h1 style="color:rgb(26,92,200)">Jam's balance</h1> Time Limit: 2000/1000 MS (Java/Others)&nbsp;&nbsp;&nbsp;&nbsp;Memory Limit: 65536/65536 K (Java/Others) Total Submission(s): 2093&nbsp;&nbsp;&nbsp;&nbsp;Accepted Submission(s): 861 
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 Problem Description 
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 Jim has a balance and N weights.&nbsp; 
 
 <span style="display:inline; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:relative; border-top-width:0px; border-right-width:0px; border-bottom-width:0px; border-style:initial; border-color:initial; padding:0px; margin:0px; vertical-align:0px; width:5.816em; height:0px; font-size:14.28px; border-left-width:0px!important">(1≤N≤20)<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.146em"> 
 The balance can only tell whether things on different side are the same weight. 
 Weights can be put on left side or right side arbitrarily. 
 Please tell whether the balance can measure an object of weight M. 
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 Input 
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 The first line is a integer&nbsp; 
 
 <span style="display:inline; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:relative; border-top-width:0px; border-right-width:0px; border-bottom-width:0px; border-style:initial; border-color:initial; padding:0px; margin:0px; vertical-align:0px; width:5.816em; height:0px; font-size:14.28px; border-left-width:0px!important">T(1≤T≤5)<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.146em"> , means T test cases. 
 For each test case : 
 The first line is&nbsp; 
 
 <span style="display:inline; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:relative; border-top-width:0px; border-right-width:0px; border-bottom-width:0px; border-style:initial; border-color:initial; padding:0px; margin:0px; vertical-align:0px; width:0.914em; height:0px; font-size:14.28px; border-left-width:0px!important">N<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:0.861em"> , means the number of weights. 
 The second line are&nbsp; 
 
 <span style="display:inline; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:relative; border-top-width:0px; border-right-width:0px; border-bottom-width:0px; border-style:initial; border-color:initial; padding:0px; margin:0px; vertical-align:0px; width:0.914em; height:0px; font-size:14.28px; border-left-width:0px!important">N<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:0.861em"> &nbsp;number, i'th number&nbsp; 
 
 <span style="display:inline; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:relative; border-top-width:0px; border-right-width:0px; border-bottom-width:0px; border-style:initial; border-color:initial; padding:0px; margin:0px; vertical-align:0px; width:7.426em; height:0px; font-size:14.28px; border-left-width:0px!important">wi(1≤wi≤100)<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.146em"> &nbsp;means the i'th weight's weight is&nbsp; 
 
 <span style="display:inline; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:relative; border-top-width:0px; border-right-width:0px; border-bottom-width:0px; border-style:initial; border-color:initial; padding:0px; margin:0px; vertical-align:0px; width:0.984em; height:0px; font-size:14.28px; border-left-width:0px!important">wi<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.211em; overflow:hidden; width:0px; height:0.789em"> . 
 The third line is a number&nbsp; 
 
 <span style="display:inline; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:relative; border-top-width:0px; border-right-width:0px; border-bottom-width:0px; border-style:initial; border-color:initial; padding:0px; margin:0px; vertical-align:0px; width:1.054em; height:0px; font-size:14.28px; border-left-width:0px!important">M<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:0.861em"> .&nbsp; 
 
 <span style="display:inline; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:relative; border-top-width:0px; border-right-width:0px; border-bottom-width:0px; border-style:initial; border-color:initial; padding:0px; margin:0px; vertical-align:0px; width:1.054em; height:0px; font-size:14.28px; border-left-width:0px!important">M<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:0.861em"> &nbsp;is the weight of the object being measured. 
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 Output 
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 You should output the "YES"or"NO". 
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 Sample Input 
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 1
2
1 4
3
2
4
5
 
 
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 Sample Output 
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 NO
YES
YES

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 Hint 
 </div> For the Case 1:Put the 4 weight alone For the Case 2:Put the 4 weight and 1 weight on both side 
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题意：有一个天平，给你n个砝码，问你能否量出某个质量的物品。

思路：这道题可以用普通型母函数去做，不过因为是天平，所以每个砝码可以放左边也可以放右边，也就是说每个砝码的质量可以加也可以减，所以说在进行b\[k + j\*v\[i\]\] += a\[k\];这一步的时候，要考虑减的情况，加上b\[abs(k - j\*v\[i\])\] += a\[k\];这一步就行了，这题没有给砝码个数的数据范围，但是总质量不会超过1000。

#include <bits\stdc++.h>
 #define N 1000
 using namespace std;
 
 int Num,n1[N],n2[N],v[N],P,a[N],b[N],L;
 void solve()
 {
 a[0] = 1;
 L = 0;
 for (int i = 1; i <= Num; i++)
 {
 int R = min(L + n2[i] * v[i], P);
 memset(b, 0, sizeof(int)*(R + 1));
 for (int j = n1[i]; j <= n2[i] && j*v[i] <= R; j++)
 for (int k = 0; k <= L&&k + j*v[i] <= R; k++)
 {
 b[k + j*v[i]] = b[k + j*v[i]] + a[k];
 b[abs(k - j*v[i])] += a[k];
 }
 memcpy(a,b,sizeof(int)*(R + 1));
 L = R;
 }
 }
 int main()
 {
 int T,Q,x;
 scanf("%d", &T);
 while (T--)
 {
 P = 0;
 scanf("%d", &Num);
 for (int i = 1; i <= Num; i++)
 {
 n1[i] = 0;
 n2[i] = 1;
 scanf("%d", &v[i]);
 P += v[i];
 }
 solve();
 scanf("%d", &Q);
 while (Q--)
 {
 scanf("%d", &x);
 printf("%s\n",a[x]&&x<=L?"YES":"NO");
 }
 }
 }