cpp-algo-cases/chapter_dynamic_programming/knapsack.cpp

#include <algorithm>
#include <iostream>
#include <vector>

using namespace std;

/* 0-1 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> */
int knapsackDFS(vector<int> &wgt, vector<int> &val, int i, int c) {
    // <20><><EFBFBD><EFBFBD>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ʒ<EFBFBD>򱳰<EFBFBD><F2B1B3B0><EFBFBD>ʣ<EFBFBD><CAA3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>򷵻ؼ<F2B7B5BB>ֵ 0
    if (i == 0 || c == 0) {
        return 0;
    }
    // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֻ<EFBFBD><D6BB>ѡ<EFBFBD>񲻷<EFBFBD><F1B2BBB7>뱳<EFBFBD><EBB1B3>
    if (wgt[i - 1] > c) {
        return knapsackDFS(wgt, val, i - 1, c);
    }
    // <20><><EFBFBD>㲻<EFBFBD><E3B2BB><EFBFBD><EFBFBD><EFBFBD>ͷ<EFBFBD><CDB7><EFBFBD><EFBFBD><EFBFBD>Ʒ i <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵ
    int no = knapsackDFS(wgt, val, i - 1, c);
    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];
    // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD><EFBFBD>м<EFBFBD>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB>
    return max(no, yes);
}

/* 0-1 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>仯<EFBFBD><E4BBAF><EFBFBD><EFBFBD> */
int knapsackDFSMem(vector<int> &wgt, vector<int> &val, vector<vector<int>> &mem, int i, int c) {
    // <20><><EFBFBD><EFBFBD>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ʒ<EFBFBD>򱳰<EFBFBD><F2B1B3B0><EFBFBD>ʣ<EFBFBD><CAA3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>򷵻ؼ<F2B7B5BB>ֵ 0
    if (i == 0 || c == 0) {
        return 0;
    }
    // <20><><EFBFBD><EFBFBD><EFBFBD>м<EFBFBD>¼<EFBFBD><C2BC><EFBFBD><EFBFBD>ֱ<EFBFBD>ӷ<EFBFBD><D3B7><EFBFBD>
    if (mem[i][c] != -1) {
        return mem[i][c];
    }
    // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֻ<EFBFBD><D6BB>ѡ<EFBFBD>񲻷<EFBFBD><F1B2BBB7>뱳<EFBFBD><EBB1B3>
    if (wgt[i - 1] > c) {
        return knapsackDFSMem(wgt, val, mem, i - 1, c);
    }
    // <20><><EFBFBD>㲻<EFBFBD><E3B2BB><EFBFBD><EFBFBD><EFBFBD>ͷ<EFBFBD><CDB7><EFBFBD><EFBFBD><EFBFBD>Ʒ i <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵ
    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);
    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];
    // <20><>¼<EFBFBD><C2BC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD><EFBFBD>м<EFBFBD>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB>
    mem[i][c] = max(no, yes);
    return mem[i][c];
}

/* 0-1 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>̬<EFBFBD>滮 */
int knapsackDP(vector<int> &wgt, vector<int> &val, int cap) {
    int n = wgt.size();
    // <20><>ʼ<EFBFBD><CABC> dp <20><>
    vector<vector<int>> dp(n + 1, vector<int>(cap + 1, 0));
    // ״̬ת<CCAC><D7AA>
    for (int i = 1; i <= n; i++) {
        for (int c = 1; c <= cap; c++) {
            if (wgt[i - 1] > c) {
                // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ѡ<EFBFBD><D1A1>Ʒ i
                dp[i][c] = dp[i - 1][c];
            } else {
                // <20><>ѡ<EFBFBD><D1A1>ѡ<EFBFBD><D1A1>Ʒ i <20><><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD><EFBFBD>Ľϴ<C4BD>ֵ
                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);
            }
        }
    }
    return dp[n][cap];
}

/* 0-1 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ռ<EFBFBD><D5BC>Ż<EFBFBD><C5BB><EFBFBD><EFBFBD>Ķ<EFBFBD>̬<EFBFBD>滮 */
int knapsackDPComp(vector<int> &wgt, vector<int> &val, int cap) {
    int n = wgt.size();
    // <20><>ʼ<EFBFBD><CABC> dp <20><>
    vector<int> dp(cap + 1, 0);
    // ״̬ת<CCAC><D7AA>
    for (int i = 1; i <= n; i++) {
        // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
        for (int c = cap; c >= 1; c--) {
            if (wgt[i - 1] <= c) {
                // <20><>ѡ<EFBFBD><D1A1>ѡ<EFBFBD><D1A1>Ʒ i <20><><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD><EFBFBD>Ľϴ<C4BD>ֵ
                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
            }
        }
    }
    return dp[cap];
}

/* Driver Code */
int main() {
    vector<int> wgt = {10, 20, 30, 40, 50};
    vector<int> val = {50, 120, 150, 210, 240};
    int cap = 50;
    int n = wgt.size();

    // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
    int res = knapsackDFS(wgt, val, n, cap);
    cout << "<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ʒ<EFBFBD><EFBFBD>ֵΪ " << res << endl;

    // <20><><EFBFBD>仯<EFBFBD><E4BBAF><EFBFBD><EFBFBD>
    vector<vector<int>> mem(n + 1, vector<int>(cap + 1, -1));
    res = knapsackDFSMem(wgt, val, mem, n, cap);
    cout << "<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ʒ<EFBFBD><EFBFBD>ֵΪ " << res << endl;

    // <20><>̬<EFBFBD>滮
    res = knapsackDP(wgt, val, cap);
    cout << "<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ʒ<EFBFBD><EFBFBD>ֵΪ " << res << endl;

    // <20>ռ<EFBFBD><D5BC>Ż<EFBFBD><C5BB><EFBFBD><EFBFBD>Ķ<EFBFBD>̬<EFBFBD>滮
    res = knapsackDPComp(wgt, val, cap);
    cout << "<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ʒ<EFBFBD><EFBFBD>ֵΪ " << res << endl;

    return 0;
}