[HDOJ1160]FatMouse's Speed（DP）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1160

FatMouse believes that the fatter a mouse is, the faster it runs. To disprove this, you want to take the data on a collection of mice and put as large a subset of this data as possible into a sequence so that the weights are increasing, but the speeds are decreasing.

给一组w s，找出一个最长的序列，使得w是严格单调递增而且s是严格单调递减的。

两种做法，分别是关注w和关注s。

关注w：相当于是在s上求最长下降子序列。

 #include <algorithm>
 #include <iostream>
 #include <iomanip>
 #include <cstring>
 #include <climits>
 #include <complex>
 #include <fstream>
 #include <cassert>
 #include <cstdio>
 #include <bitset>
 #include <vector>
 #include <deque>
 #include <queue>
 #include <stack>
 #include <ctime>
 #include <set>
 #include <map>
 #include <cmath>

 using namespace std;

 typedef struct Node {
     int w;
     int s;
     int idx;
 }Node;

 const int maxn = ;
 Node mice[maxn];
 int n, ans;
 int dp[maxn];
 int pre[maxn];
 int st[maxn];
 int top;

 bool cmp(Node a, Node b) {
     if(a.w == b.w) return a.s > b.s;
     return a.w < b.w;
 }

 int main() {
     // freopen("in", "r", stdin);
     // freopen("out", "w", stdout);
     n = ;
     while(~scanf("%d %d", &mice[n].w, &mice[n].s)) {
         mice[n].idx = n;
         n++;
     }
     n--;
     sort(mice + , mice + n + , cmp);
     ans = ;
     int pos;
     memset(dp, , sizeof(dp));
     memset(pre, -, sizeof(pre));
     for(int i = ; i <= n; i++) {
         dp[i] = ;
         for(int j = ; j < i; j++) {
             if(dp[i] < dp[j] +  &&
                 mice[i].s < mice[j].s &&
                 mice[i].w > mice[j].w) {
                 dp[i] = dp[j] + ;
                 pre[mice[i].idx] = mice[j].idx;
             }
         }
         if(ans < dp[i]) {
             ans = dp[i];
             pos = mice[i].idx;
         }
     }
     top = ;
     for(int i = pos; ~i; i=pre[i]) st[top++] = i;
     printf("%d\n", ans);
     while(top) printf("%d\n", st[--top]);
     return ;
 }

关注s：相当于是在w上求最长上升子序列。

 #include <algorithm>
 #include <iostream>
 #include <iomanip>
 #include <cstring>
 #include <climits>
 #include <complex>
 #include <fstream>
 #include <cassert>
 #include <cstdio>
 #include <bitset>
 #include <vector>
 #include <deque>
 #include <queue>
 #include <stack>
 #include <ctime>
 #include <set>
 #include <map>
 #include <cmath>

 using namespace std;

 typedef struct Node {
     int w;
     int s;
     int idx;
 }Node;

 const int maxn = ;
 Node mice[maxn];
 int n, ans;
 int dp[maxn];
 int pre[maxn];
 int st[maxn];
 int top;

 bool cmp(Node a, Node b) {
     if(a.s == b.s) return a.w < b.w;
     return a.s > b.s;
 }

 int main() {
     // freopen("in", "r", stdin);
     // freopen("out", "w", stdout);
     n = ;
     while(~scanf("%d %d", &mice[n].w, &mice[n].s)) {
         mice[n].idx = n;
         n++;
     }
     n--;
     sort(mice + , mice + n + , cmp);
     ans = ;
     int pos;
     memset(dp, , sizeof(dp));
     memset(pre, -, sizeof(pre));
     for(int i = ; i <= n; i++) {
         dp[i] = ;
         for(int j = ; j < i; j++) {
             if(dp[i] < dp[j] +  &&
                mice[i].w > mice[j].w) {
                 dp[i] = dp[j] + ;
                 pre[mice[i].idx] = mice[j].idx;
             }
         }
         if(ans < dp[i]) {
             ans = dp[i];
             pos = mice[i].idx;
         }
     }
     top = ;
     for(int i = pos; ~i; i=pre[i]) st[top++] = i;
     printf("%d\n", ans);
     while(top) printf("%d\n", st[--top]);
     return ;
 }

注意小心关注w时s相等的情况和关注s时w相等的情况。不知道为什么，关注w时没有注意s相等的代码可以AC但是关注s的时候必须要注意w相等要continue掉。应该是数据水了吧。