POJ 4131 Charm Bracelet

题目

总时间限制: 1000ms 内存限制: 65536kB
描述
Bessie has gone to the mall’s jewelry store and spies a charm bracelet. Of course, she’d like to fill it with the best charms possible from the N(1 ≤ N≤ 3,402) available charms. Each charm iin the supplied list has a weight Wi(1 ≤ Wi≤ 400), a ‘desirability’ factor Di(1 ≤ Di≤ 100), and can be used at most once. Bessie can only support a charm bracelet whose weight is no more than M(1 ≤ M≤ 12,880).
Given that weight limit as a constraint and a list of the charms with their weights and desirability rating, deduce the maximum possible sum of ratings.

输入
Line 1: Two space-separated integers: N and M
Lines 2..N+1: Line i+1 describes charm i with two space-separated integers: Wi and Di
输出
Line 1: A single integer that is the greatest sum of charm desirabilities that can be achieved given the weight constraints
样例输入
4 6
1 4
2 6
3 12
2 7
样例输出
23

思路

F(i,j)表示在前i种物品中取若干种，在其总体积不超过M的条件下所能获得的最大价值。
F(i,j)=⎧⎩⎨max{F(i−1,j),F(i−1,j−W[i])+D[i]},i>1,D[1],i=1 and W[1]≤j0,others

代码

while True:    try:        N, M = input().split()        N = int(N); M = int(M)        W = []; D = []        for _ in range(N):            w, d = input().split()            W.append(int(w))            D.append(int(d))        dp = [0 for _ in range(M + 1)]        for i in range(N):            for j in range(1, M + 1)[::-1]:                if W[i] <= j:                    dp[j] = max(dp[j - W[i]] + D[i], dp[j])        print(dp[M])    except:        break