POJ 1678 I Love this Game

题目链接：http://poj.org/problem?id=1678

动态博弈。用dp[i]来表示如果先行者首先选择第i个数字的话能取得的最大差值。由于每次选择的数字一定比上一次选择的数字大，所以先对数组进行排序。然后对于每个数字，如果先行者首先选择这个数字的话，dp[i] 初始化的值为num[i].然后在num[i]之后的序列中，如果有符合条件的数字的话，那么选择dp值最大的那个数字。最后对所有的数字进行for loop，寻找符合条件的并且差值最大的数字。代码如下：

 1 //============================================================================
 2 // Name        : test.cpp
 3 // Author      :
 4 // Version     :
 5 // Copyright   : Your copyright notice
 6 // Description : Hello World in C++, Ansi-style
 7 //============================================================================
 8
 9 #include <iostream>
10 #include <math.h>
11 #include <stdio.h>
12 #include <cstdio>
13 #include <algorithm>
14 #include <string.h>
15 #include <string>
16 #include <sstream>
17 #include <cstring>
18 #include <queue>
19 #include <vector>
20 #include <functional>
21 #include <cmath>
22 #include <set>
23 #define SCF(a) scanf("%d", &a)
24 #define IN(a) cin>>a
25 #define FOR(i, a, b) for(int i=a;i<b;i++)
26 #define Infinity 999999999
27 #define NInfinity -999999999
28 #define PI 3.14159265358979323846
29 typedef long long Int;
30 using namespace std;
31
32 int main()
33 {
34     int t;
35     int n, a, b;
36     SCF(t);
37     int num[10005];
38     int dp[10005];
39     while (t--)
40     {
41         SCF(n);
42         SCF(a);
43         SCF(b);
44         FOR(i, 0, n)
45             SCF(num[i]);
46
47         sort(num, num + n);
48
49         for (int i = n - 1; i >= 0; i--)
50         {
51             dp[i] = num[i];
52             bool first = true;
53             int maxNum = 0;
54             for (int j = i + 1; j < n; j++)
55             {
56                 int diff = num[j] - num[i];
57                 if (diff >= a && diff <= b)
58                 {
59                     if (first)
60                     {
61                         maxNum = dp[j];
62                         first = false;
63                     }
64                     else
65                         maxNum = max(maxNum, dp[j]);
66                 }
67             }
68             dp[i] = dp[i] - maxNum;
69         }
70         int maxAns = 0;
71         bool found = false;
72         for (int i = n - 1; i >= 0; i--)
73         {
74             if (num[i] >= a && num[i] <= b)
75             {
76                 if (!found)
77                 {
78                     maxAns = dp[i];
79                     found = true;
80                 }
81                 else
82                 {
83                     if (dp[i] > maxAns)
84                         maxAns = dp[i];
85                 }
86             }
87         }
88         printf("%d\n", maxAns);
89     }
90     return 0;
91 }