经典dp问题
自上向下dp
#include<iostream>
#include<cstring>
using namespace std;
const int N = 510, INF = 0x3f3f3f3f;
int f[N][N], a[N][N];
int n;
int main(){
memset(f, 128, sizeof f);
cin >> n;
for(int i = 1; i <= n; i ++)
for(int j = 1; j <= i; j ++)
cin >> a[i][j];
f[1][1] = a[1][1];
for(int i = 2; i <= n; i ++)
for(int j = 1; j <= i; j ++)
f[i][j] = max(f[i - 1][j - 1], f[i - 1][j]) + a[i][j];
int res = -INF;
for(int i = 1; i <= n; i ++) res = max(res, f[n][i]);
cout << res;
return 0;
}
自下向上dp
#include<iostream>
#include<cstring>
using namespace std;
const int N = 510;
int f[N][N], a[N][N];
int n;
int main(){
cin >> n;
for(int i = 1; i <= n; i ++)
for(int j = 1; j <= i; j ++)
cin >> a[i][j];
for(int i = n; i >= 0; i --) f[n][i] = a[n][i];
for(int i = n - 1; i >= 1; i --)
for(int j = 1; j <= i; j ++)
f[i][j] = max(f[i + 1][j], f[i + 1][j + 1]) + a[i][j];
cout << f[1][1];
return 0;
}
记忆化搜索
#include<iostream>
#include<cstring>
using namespace std;
const int N = 510;
int f[N][N], a[N][N], st[N][N];
int n;
int dfs(int x, int y){
if(x == n) return a[x][y];
if(!st[x][y]){
st[x][y] = 1;
f[x][y] = max(dfs(x + 1, y), dfs(x + 1, y + 1)) + a[x][y];
}
return f[x][y];
}
int main(){
// memset(f, 128, sizeof f);
cin >> n;
for(int i = 1; i <= n; i ++)
for(int j = 1; j <= i; j ++)
cin >> a[i][j];
cout << dfs(1, 1);
return 0;
}