Jumping Cows
Farmer John's cows would like to jump over the moon, just like the cows in their favorite nursery rhyme. Unfortunately, cows can not jump. The local witch doctor has mixed up P (1 <= P <= 150,000) potions to aid the cows in their quest to jump. These potions must be administered exactly in the order they were created, though some may be skipped.
Each potion has a 'strength' (1 <= strength <= 500) that enhances the cows' jumping ability. Taking a potion during an odd time step increases the cows' jump; taking a potion during an even time step decreases the jump. Before taking any potions the cows' jumping ability is, of course, 0.
No potion can be taken twice, and once the cow has begun taking potions, one potion must be taken during each time step, starting at time 1. One or more potions may be skipped in each turn.
Determine which potions to take to get the highest jump.
Input
* Line 1: A single integer, P
* Lines 2..P+1: Each line contains a single integer that is the strength of a potion. Line 2 gives the strength of the first potion; line 3 gives the strength of the second potion; and so on.
Output
* Line 1: A single integer that is the maximum possible jump.
Sample Input
8
7
2
1
8
4
3
5
6
Sample Output
17
Source
题目类型：线性DP
算法分析：dp[0][i]表示前i个数经过偶数次跳跃增加的最大能量值，dp[1][i]表示前i个数经过奇数次跳跃增加的最大能量值，初始化dp[0][0] = 0，状态转移方程为dp[0][i] = max(dp[0][i-1], dp[1][i-1] - a[i])，dp[1][i] = max(dp[1][i-1], dp[0][i-1] + a[i])，最后输出dp[0][P]和dp[1][P]的最大值即可
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/************************************************** filename :f.cpp author :maksyuki created time :2017/3/4 10:34:52 last modified :2017/3/4 11:02:52 file location :C:\Users\abcd\Desktop\TheEternalPoet ***************************************************/ #pragma comment(linker, "/STACK:102400000,102400000") #include <set> #include <bitset> #include <list> #include <map> #include <stack> #include <queue> #include <deque> #include <string> #include <vector> #include <ios> #include <iostream> #include <fstream> #include <sstream> #include <iomanip> #include <algorithm> #include <utility> #include <complex> #include <numeric> #include <functional> #include <cmath> #include <ctime> #include <climits> #include <cstdarg> #include <cstdio> #include <cstdlib> #include <cstring> #include <cctype> #include <cassert> using namespace std; #define CFF freopen ("in", "r", stdin) #define CPPFF ifstream cin ("in") #define DB(ccc) cout << #ccc << " = " << ccc << endl #define PB push_back #define MP(A, B) make_pair(A, B) typedef long long LL; typedef unsigned long long ULL; typedef double DB; typedef pair <int, int> PII; typedef pair <int, bool> PIB; const int INF = 0x7F7F7F7F; const int MOD = 1e9 + 7; const double EPS = 1e-10; const double PI = 2 * acos (0.0); const int maxn = 1e5 + 66666; int a[maxn], dp[2][maxn]; int main() { //CFF; //CPPFF; int P; scanf("%d", &P); for(int i = 1; i <= P; i++) scanf("%d", &a[i]); for(int i = 0; i < maxn; i++) dp[0][i] = dp[1][i] = -INF; dp[0][0] = 0; for(int i = 1; i <= P; i++) { dp[1][i] = max(dp[1][i-1], dp[0][i-1] + a[i]); dp[0][i] = max(dp[0][i-1], dp[1][i-1] - a[i]); } printf("%d\n", max(dp[0][P], dp[1][P])); return 0; } |
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