ZOJ 1108 FatMouse's Speed（dp+路径还原）

FatMouse's Speed

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Time Limit: 2 Seconds      Memory Limit: 65536 KB      Special Judge

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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.

Input Specification

Input contains data for a bunch of mice, one mouse per line, terminated by end of file.

The data for a particular mouse will consist of a pair of integers: the first representing its size in grams and the second representing its speed in centimeters per second. Both integers are between 1 and 10000. The data in each test case will contain information for at most 1000 mice.

Two mice may have the same weight, the same speed, or even the same weight and speed.

Output Specification

Your program should output a sequence of lines of data; the first line should contain a number n; the remaining n lines should each contain a single positive integer (each one representing a mouse). If these n integers are m[1], m[2],..., m[n]then it must be the case that

   W[m[1]] < W[m[2]] < ... < W[m[n]]

and

   S[m[1]] > S[m[2]] > ... > S[m[n]]

In order for the answer to be correct, n should be as large as possible.

All inequalities are strict: weights must be strictly increasing, and speeds must be strictly decreasing. There may be many correct outputs for a given input, your program only needs to find one.

Sample Input

6008 13006000 2100500 20001000 40001100 30006000 20008000 14006000 12002000 1900

Output for Sample Input

44597

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Source: Zhejiang University Training Contest 2001

思路：LIS，不过要先把重量或速度排序。

AC代码：

#include <bits/stdc++.h>using namespace std;struct mouse { int weight, speed, id;//老鼠的体重，速度和编号 } mice[1001]; int dp[1001];int path[1001];bool cmp(mouse a,mouse b){if(a.weight == b.weight)//重量相同按速度降序return a.speed > b.speed;return a.weight < b.weight;//重量不同按升序} void output(int path[], int pos){if(pos == 0) return;output(path, path[pos]);printf("%d\n", mice[pos].id);}int main(){int n = 1;   while(scanf("%d%d", &mice[n].weight, &mice[n].speed)!=EOF){mice[n].id = n;//记录编号 n++;}sort(mice,mice+n,cmp);memset(dp,0,sizeof(dp));for(int i = 1; i < n; i++)//LIS {for(int j = 1; j < i; j++)if(mice[i].weight > mice[j].weight && mice[i].speed < mice[j].speed)//严格递增重量和递减速度 if(dp[i] < dp[j]){dp[i] = dp[j];path[i] = j;//记录前驱 }dp[i]++;}int max = 0;int pos;for(int i = 1; i < n; i++)if(dp[i] > max){max = dp[i];pos = i;}printf("%d\n", max);output(path, pos);return 0;}