898. 数字三角形

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;
}