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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。
1 #include <algorithm> 2 #include <iostream> 3 #include <iomanip> 4 #include <cstring> 5 #include <climits> 6 #include <complex> 7 #include <fstream> 8 #include <cassert> 9 #include <cstdio> 10 #include <bitset> 11 #include <vector> 12 #include <deque> 13 #include <queue> 14 #include <stack> 15 #include <ctime> 16 #include <set> 17 #include <map> 18 #include <cmath> 19 20 using namespace std; 21 22 typedef struct Node { 23 int w; 24 int s; 25 int idx; 26 }Node; 27 28 const int maxn = 1111; 29 Node mice[maxn]; 30 int n, ans; 31 int dp[maxn]; 32 int pre[maxn]; 33 int st[maxn]; 34 int top; 35 36 bool cmp(Node a, Node b) { 37 if(a.w == b.w) return a.s > b.s; 38 return a.w < b.w; 39 } 40 41 int main() { 42 // freopen("in", "r", stdin); 43 // freopen("out", "w", stdout); 44 n = 1; 45 while(~scanf("%d %d", &mice[n].w, &mice[n].s)) { 46 mice[n].idx = n; 47 n++; 48 } 49 n--; 50 sort(mice + 1, mice + n + 1, cmp); 51 ans = 0; 52 int pos; 53 memset(dp, 0, sizeof(dp)); 54 memset(pre, -1, sizeof(pre)); 55 for(int i = 1; i <= n; i++) { 56 dp[i] = 1; 57 for(int j = 1; j < i; j++) { 58 if(dp[i] < dp[j] + 1 && 59 mice[i].s < mice[j].s && 60 mice[i].w > mice[j].w) { 61 dp[i] = dp[j] + 1; 62 pre[mice[i].idx] = mice[j].idx; 63 } 64 } 65 if(ans < dp[i]) { 66 ans = dp[i]; 67 pos = mice[i].idx; 68 } 69 } 70 top = 0; 71 for(int i = pos; ~i; i=pre[i]) st[top++] = i; 72 printf("%d\n", ans); 73 while(top) printf("%d\n", st[--top]); 74 return 0; 75 }
关注s：相当于是在w上求最长上升子序列。
1 #include <algorithm> 2 #include <iostream> 3 #include <iomanip> 4 #include <cstring> 5 #include <climits> 6 #include <complex> 7 #include <fstream> 8 #include <cassert> 9 #include <cstdio> 10 #include <bitset> 11 #include <vector> 12 #include <deque> 13 #include <queue> 14 #include <stack> 15 #include <ctime> 16 #include <set> 17 #include <map> 18 #include <cmath> 19 20 using namespace std; 21 22 typedef struct Node { 23 int w; 24 int s; 25 int idx; 26 }Node; 27 28 const int maxn = 1111; 29 Node mice[maxn]; 30 int n, ans; 31 int dp[maxn]; 32 int pre[maxn]; 33 int st[maxn]; 34 int top; 35 36 bool cmp(Node a, Node b) { 37 if(a.s == b.s) return a.w < b.w; 38 return a.s > b.s; 39 } 40 41 int main() { 42 // freopen("in", "r", stdin); 43 // freopen("out", "w", stdout); 44 n = 1; 45 while(~scanf("%d %d", &mice[n].w, &mice[n].s)) { 46 mice[n].idx = n; 47 n++; 48 } 49 n--; 50 sort(mice + 1, mice + n + 1, cmp); 51 ans = 0; 52 int pos; 53 memset(dp, 0, sizeof(dp)); 54 memset(pre, -1, sizeof(pre)); 55 for(int i = 1; i <= n; i++) { 56 dp[i] = 1; 57 for(int j = 1; j < i; j++) { 58 if(dp[i] < dp[j] + 1 && 59 mice[i].w > mice[j].w) { 60 dp[i] = dp[j] + 1; 61 pre[mice[i].idx] = mice[j].idx; 62 } 63 } 64 if(ans < dp[i]) { 65 ans = dp[i]; 66 pos = mice[i].idx; 67 } 68 } 69 top = 0; 70 for(int i = pos; ~i; i=pre[i]) st[top++] = i; 71 printf("%d\n", ans); 72 while(top) printf("%d\n", st[--top]); 73 return 0; 74 }
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。
[HDOJ1160]FatMouse's Speed（DP）
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原文地址：http://www.cnblogs.com/vincentX/p/5398026.html
