You're about to go on a trip around the world! On this trip you're bringing your trusted backpack, that anything fits into. The bad news is that the airline has informed you, that your luggage cannot exceed a certain amount of weight.

To make sure you're bringing your most valuable items on this journey you've decided to give all your items a score that represents how valuable this item is to you. It's your job to pack you bag so that you get the most value out of the items that you decide to bring.

Your input will consist of two arrays, one for the scores and one for the weights. You input will always be valid lists of equal length, so you don't have to worry about verifying your input.

You'll also be given a maximum weight. This is the weight that your backpack cannot exceed.

For instance, given these inputs:

    scores = [15, 10, 9, 5]
    weights = [1, 5, 3, 4]
    capacity = 8
    
The maximum score will be ``29``. This number comes from bringing items ``1, 3 and 4``.

Note: Your solution will have to be efficient as the running time of your algorithm will be put to a test.

Difficulty: introductory

Starter code:

def pack_bagpack(scores, weights, capacity):
	

Solutions:
def pack_bagpack(scores, weights, capacity):
    load = [0] * (capacity + 1)
    for score, weight in zip(scores, weights):
        load = [max(l, weight <= w and load[w - weight] + score)
                for w, l in enumerate(load)]
    return load[-1]

def pack_bagpack(S,W,C) :
    M = [0] * (1 + C)
    for F,V in enumerate(S) :
        M = [max(U,M[T - W[F]] + V if W[F] <= T else 0) for T,U in enumerate(M)]
    return M[-1]

def pack_bagpack(scores,weights,capacity):
    sols=[[0 for j in range(capacity+1)] for i in range(len(scores)+1)]
    scores.insert(0, 0)
    weights.insert(0, 0)
    for y,iy in enumerate(sols[1:],1):
        for x,ix in enumerate(iy[1:],1):
            if weights[y]<=x:
                sols[y][x]=max(scores[y]+sols[y-1][x-weights[y]],sols[y-1][x])
            else:
                sols[y][x]=sols[y-1][x]
    return sols[-1][-1]

import numpy as np

def pack_bagpack(scores, weights, capacity):
    print(len(scores))
    print(capacity)
    n = len(scores)
    dp = np.zeros((n + 1, capacity + 1))
    for i in range(1, n + 1):
        for j in range(capacity + 1):
            if j >= weights[i - 1]:
                dp[i][j] = (max(dp[i - 1][j], dp[i - 1][j - weights[i - 1]] + scores[i - 1]))
            else:
                dp[i][j] = dp[i - 1][j]
    return dp[n][capacity];           

import sys
print((sys.getrecursionlimit()))

def pack_bagpack(scores, weights, capacity):

    if capacity >= sum(weights):
        return sum(scores)

    print(('{},{},{}'.format(scores, weights, capacity)))
    items = [(i, j) for i, j in zip(scores, weights)]
    def fetchBestMax(toConsider, avail, memo = {}):
        if (len(toConsider), avail) in memo:
            result = memo[(len(toConsider), avail)]
        elif toConsider == [] or avail == 0:
            result = (0, ())
        elif toConsider[0][1] > avail:
            #Explore right branch only
            result = fetchBestMax(toConsider[1:], avail, memo)
        else:
            nextItem = toConsider[0]
            #Explore left branch
            withVal, withToTake =fetchBestMax(toConsider[1:], avail - nextItem[1], memo)
            withVal += nextItem[0]
            #Explore right branch
            withoutVal, withoutToTake = fetchBestMax(toConsider[1:], avail, memo)
            #Choose better branch
            if withVal > withoutVal:
                result = (withVal, withToTake + (nextItem,))
            else:
                result = (withoutVal, withoutToTake)
        memo[(len(toConsider), avail)] = result
        return result
    
    
    maxVal = fetchBestMax(items, capacity)
    print(("maxVal", maxVal))
    return maxVal[0]


def pack_bagpack(val, wt, W):
    n = len(val) 
    K = [[0 for x in range(W+1)] for x in range(n+1)] 
    for i in range(n+1): 
        for w in range(W+1): 
            if i==0 or w==0: 
                K[i][w] = 0
            elif wt[i-1] <= w: 
                K[i][w] = max(val[i-1] + K[i-1][w-wt[i-1]],  K[i-1][w]) 
            else: 
                K[i][w] = K[i-1][w] 
  
    return K[n][W]

def pack_bagpack(val, w, t):
    if sum(w) <= t : return sum(val)
    matrix = [[0 for _ in range(t + 1)] for _ in range(len(w) + 1)]
    for i in range(1, len(w) + 1):
        for j in range(1, t + 1):
            matrix[i][j] = matrix[i-1][j] if j<w[i-1] else max(matrix[i-1][j],val[i-1]+matrix[i-1][j-w[i-1]])
    return matrix[-1][-1]

import time
def pack_bagpack(scores, weights, capacity):
    """
    求最大分数
    :param scores:   行李评分列表
    :param weights:  行李重量列表
    :param capacity: 限制重量
    :return: 最大分数

    1）按照均分倒序排列
    2) 递归组合
        max_value = max(包含自己的最大值, 跳过自己的最大值)
    3) 得出最优
    """
    start_time = time.time()
    # 组合
    lst = list(zip(scores, weights))

    # 1) 倒序排列 >> 均分 = 分数/重量
    lst_sorted = sorted(lst, key=lambda x: x[0], reverse=True)

    cache_dict = {}

    def calc_item(index, weight_last):
        if index >= len(lst_sorted) or weight_last <= 0:
            return 0
        current = lst_sorted[index]

        cache_key = "{}-{}".format(index, weight_last)

        if cache_key not in cache_dict:
            # 算上当前的最大结果
            score_with_current = 0
            if weight_last >= current[1]:
                score_with_current = current[0] + calc_item(index + 1, weight_last - current[1])
            # 跳过当前的最大结果
            score_no_current = calc_item(index + 1, weight_last)

            # 缓存当前的位置和剩余重量的值, 让以后的递归不再重复计算类似结果
            cache_dict[cache_key] = max(score_with_current, score_no_current)
            
        return cache_dict[cache_key]

    final_score = calc_item(0, capacity)

    print("score: {}  duration---> {}".format(final_score,time.time() - start_time))
    # 3) 得出最优
    return final_score

def pack_bagpack(scores, weights, capacity):
    dp=[[0,[]] for i in range(capacity+1)]
    for j in range(1,len(scores)+1):
        r = [[0,[]] for i in range(capacity+1)]
        for i in range(1,capacity+1):
            c,p = weights[j-1], scores[j-1]
            if c<=i and p+dp[i-c][0]>dp[i][0]: r[i]=[p+dp[i-c][0], dp[i-c][1]+[j-1]]
            else: r[i]=dp[i]
        dp = r
    return dp[-1][0]

def pack_bagpack(scores, weights, capacity):
    loads = [0] * (capacity + 1)
    for score, weight in zip(scores, weights):
        loads = [max(l, weight <= w and loads[w - weight] + score) for w, l in enumerate(loads)]
    return loads[-1]