动态规划-背包问题python实现

背包问题解析
python实现:

#0-1背包问题
'''
四样物体(things):wight:[2,3,4,5]
        value:[3,4,5,6]
        bag capacity:8
填表:
   things/bag capacity 0,  1   2   3   4   5   6   7   8
                    0  0,  0,  0,  0,  0,  0,  0,  0,  0
                    1  0,  0,  3,  3,  3,  3,  3,  3,  3
                    2  0,  0,  3,  4,  4,  7,  7,  7,  7
                    3  0,  0,  3,  4,  5,  7,  8,  9,  9
                    4  0,  0,  3,  4,  5,  7,  8,  9, 10
'''
import numpy as np
def dpbag(weight, value, capacity):

    #创建二维数组保存
    results = np.zeros((len(weight) + 1 , capacity + 1), dtype = int)

    #第0行的每一个赋0
    results[0, :] = 0

    #第0列的每一个赋0
    results[:, 0] = 0

    for i in range(1, len(weight) + 1):
        for j in range(1, capacity + 1):
            #如果该数比num要大,则此时需要考虑上一个数
            if weight[i-1] > j:
                results[i, j] = results[i-1, j]
            else:
                #不选weight[i - 1]
                A = results[i - 1,j]
                #选择weight[i - 1]
                B = results[i - 1, j - weight[i - 1]] + value[i - 1]
                #取AB中最大值
                results[i, j] = max(A , B)
    return results[-1, -1]

dpbag([2,3,4,5],[3,4,5,6],8)

推荐大佬学习视频:
动态规划1
动态规划2