AcWing 1371. 货币系统(传送门)
思路分析:
闫式DP分析法,yxc yyds!!!
绿色为本题分析,其他颜色是DP整体思路
没有进行空间优化前,即状态表示是二维,依然是二维空间
AC代码:
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int N = 30, M = 10010;
int v, n;
ll f[N][M];
int main() {
while (cin >> v >> n) {
f[0][0] = 1;
for (int i = 1; i <= v; i++) {
int num;
cin >> num;
for (int j = 0; j <= n; j++) {
f[i][j] = f[i - 1][j];
if (j >= num)
f[i][j] += f[i][j - num];
}
}
cout << f[v][n] << endl;
}
return 0;
}
空间优化后,二维优化成一维(可能略有些难理解,主要是循环层数理解到位了,其实还好)
AC代码:
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int M = 10010;
int v, n;
ll f[M];
int main() {
while (cin >> v >> n) {
f[0] = 1;
for (int i = 1; i <= v; i++) {
int num;
cin >> num;
for (int j = num; j <= n; j++) {
f[j] = f[j] + f[j - num];
// 等价于 f[i][j] = f[i-1][j] + f[i][j-num];
}
}
cout << f[n] << endl;
}
return 0;
}