揹包問題 DP

4種寫法：

揹包0-1 

#include <iostream> 
using namespace std;


int w[101] = {0}, c[101] = {0}, dp[101][101] = {0}; 
int main(){
	int n, v;
	cin >> n >> v; 
	for(int i = 1; i <= n; i++){
		cin >> w[i] >> c[i];
	} 
	for(int i = 1; i <= n; i++){
		for(int j = v; j > 0; j--){
			if(w[i] <= j){
				dp[i][j] = max(dp[i-1][j], dp[i-1][j-w[i]] + c[i]);
			}else{
				dp[i][j] = f[i-1][j];
			}
 
		}
		
	}
	cout << dp[n][v] << endl;
	return 0;
}

------------------------------------------------------
#include <iostream> 
using namespace std;


int w[101] = {0}, c[101] = {0}, dp[101] = {0}; 
int main(){
	int n, v;
	cin >> n >> v; 
	for(int i = 1; i <= n; i++){
		cin >> w[i] >> c[i];
	} 
	for(int i = 1; i <= n; i++){
		for(int j = v; j >= w[i]; j--){
			if(dp[j-w[i]] + c[i] > dp[j]){
				dp[j] = dp[j-w[i]] + c[i];
			}
		} 
	}
	cout << dp[v] << endl;
	return 0;
}
-----------------------------------------------------------------------

完全揹包問題


#include <iostream> 
using namespace std;


int w[101] = {0}, c[101] = {0}, dp[101][101] = {0}; 
int main(){
	int n, v;
	cin >> n >> v; 
	for(int i = 1; i <= n; i++){
		cin >> w[i] >> c[i];
	} 
	for(int i = 1; i <= n; i++){
		for(int j = 1; j <= v; j++){
			if(w[i] <= j){
				dp[i][j] = max(dp[i-1][j], dp[i-1][j-w[i]] + c[i]);
			}else{
				dp[i][j] = dp[i-1][j];
			}
		}
	}
	cout << dp[n][v] << endl;
	return 0;
}

---------------------------------------------------------------

#include <iostream> 
using namespace std;


int w[101] = {0}, c[101] = {0}, dp[101][101] = {0}; 
int main(){
	int n, v;
	cin >> n >> v; 
	for(int i = 1; i <= n; i++){
		cin >> w[i] >> c[i];
	} 
	for(int i = 1; i <= n; i++){
		for(int j = 1; j <= v; j--){
			if(w[i] <= j){
				dp[i][j] = max(dp[i-1][j], dp[i-1][j-w[i]] + c[i]);
			}else{
				dp[i][j] = dp[i-1][j];
			}
		}
		
	}
	cout << dp[n][v] << endl;
	return 0;
}

--------------------------------------------------------------



#include <iostream> 
using namespace std;


int w[101] = {0}, c[101] = {0}, dp[101][101] = {0}; 
int main(){
	int n, v;
	cin >> n >> v; 
	for(int i = 1; i <= n; i++){
		cin >> w[i] >> c[i];
	} 
	for(int i = 1; i <= n; i++){
		for(int j = 1; j <= v; j--){
			if(w[i] <= j){
				dp[i][j] = max(dp[i-1][j], dp[i-1][j-w[i]] + c[i]);
			}else{
				dp[i][j] = dp[i-1][j];
			}
		}
		
	}
	cout << dp[n][v] << endl;
	return 0;
}



還差一種編譯不過


#include <bits/stdc++.h> 
using namespace std;


int w[101] = {0}, c[101] = {0}, dp[101][101] = {0}; 
int main(){
	int n, v;
	cin >> n >> v; 
	for(int i = 1; i <= n; i++){
		cin >> w[i] >> c[i];
	} 
	for(int i = 1; i <= n; i++){
		for(int j = w[i]; j <= v; j++){
			dp[j] = max(dp[j], dp[j-w[i]] + c[i]);
		}
	}
	cout << dp[v] << endl;
	return 0;
}