01背包问题 二维

思路看了一遍，默写一下哈。甚至看了两遍，但是还没开始搞。。。振作起来！！！

目前看就是核心那一行有点问题，具体看备注吧，然后就是把验证代码也放上来了。

#include <iostream>
#include <vector>
using namespace ::std;
int main()
{int n;int bagweight;cin >> n;cin >> bagweight;// cout << "n是  " << n << endl;// cout << "bagweight  " << bagweight << endl;vector<int> weight(n, 0);vector<int> value(n, 0);for (int i = 0; i < n; i++){cin >> weight[i];}for (int i = 0; i < n; i++){cin >> value[i];}// test// for (int i = 0; i < n; i++)// {//     cout << "weight是  " << weight[i] << endl;//     cout << "value是  " << value[i] << endl;// }vector<vector<int>> dp(n, vector<int>(bagweight + 1, 0));for (int j = weight[0]; j <= bagweight; j++){dp[0][j] = value[0];}for (int i = 1; i < n; i++){for (int j = 0; j <= bagweight; j++){if (weight[i] > j){//这行实际上也做了第0列，第i行的赋值。dp[i][j] = dp[i - 1][j];}else{//要考虑 j - weight[i] 是前一个价值可能性dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - weight[i]] + value[i]); }}}// for (int i = 0; i < n; i++)// {//     for (int j = 0; j < bagweight; j++)//     {//         cout << " " << dp[i][j];//     }//     cout << endl;// }cout << dp[n-1][bagweight];return 0;
}

随想录的写法学习一下。

//二维dp数组实现
#include <bits/stdc++.h>
using namespace std;int n, bagweight;// bagweight代表行李箱空间
void solve() {vector<int> weight(n, 0); // 存储每件物品所占空间vector<int> value(n, 0);  // 存储每件物品价值for(int i = 0; i < n; ++i) {cin >> weight[i];}for(int j = 0; j < n; ++j) {cin >> value[j];}// dp数组, dp[i][j]代表行李箱空间为j的情况下,从下标为[0, i]的物品里面任意取,能达到的最大价值vector<vector<int>> dp(weight.size(), vector<int>(bagweight + 1, 0));// 初始化, 因为需要用到dp[i - 1]的值// j < weight[0]已在上方被初始化为0// j >= weight[0]的值就初始化为value[0]for (int j = weight[0]; j <= bagweight; j++) {dp[0][j] = value[0];}for(int i = 1; i < weight.size(); i++) { // 遍历科研物品for(int j = 0; j <= bagweight; j++) { // 遍历行李箱容量// 如果装不下这个物品,那么就继承dp[i - 1][j]的值if (j < weight[i]) dp[i][j] = dp[i - 1][j];// 如果能装下,就将值更新为 不装这个物品的最大值 和 装这个物品的最大值 中的 最大值// 装这个物品的最大值由容量为j - weight[i]的包任意放入序号为[0, i - 1]的最大值 + 该物品的价值构成else dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - weight[i]] + value[i]);}}cout << dp[weight.size() - 1][bagweight] << endl;
}int main() {while(cin >> n >> bagweight) {solve();}return 0;
}

#include <iostream>
#include <vector>
using namespace ::std;
int main()
{int n;int bagweight;cin >> n;cin >> bagweight;// cout << "n是  " << n << endl;// cout << "bagweight  " << bagweight << endl;vector<int> weight(n, 0);vector<int> value(n, 0);for (int i = 0; i < n; i++){cin >> weight[i];}for (int i = 0; i < n; i++){cin >> value[i];}// test// for (int i = 0; i < n; i++)// {//     cout << "weight是  " << weight[i] << endl;//     cout << "value是  " << value[i] << endl;// }vector<int> dp(bagweight + 1,0);for (int i = 0; i < n; i++){for (int j = bagweight; j >= weight[i]; j--){dp[j] = max(dp[j], dp[j - weight[i]] + value[i]); }}//for (int j = 0; j < bagweight; j++)//{//    cout << " " << dp[i][j];//}//cout << endl;cout << dp[bagweight];return 0;
}

class Solution {
public:bool canPartition(vector<int>& nums) {int sum = 0;for(int i = 0;i < nums.size();i++){sum += nums[i];}if(sum % 2 != 0)return false;vector<int>dp(sum/2 + 1,0);for(int i = 0;i < nums.size();i++){for(int j = sum/2;j >= nums[i];j--){dp[j] = max(dp[j],dp[j - nums[i]] + nums[i]);}}return (dp[sum/2] == sum/2);}
};