Digital triangle model acwing 275 Pass a note

Digital triangle model AcWing 275. Pass slip

Original link

AcWing 275. Pass slip

Algorithm tags

Dynamic programming linear DP

Ideas

Optimization of row number value range

Code

#include<bits/stdc++.h>
#define int long long
#define rep(i, a, b) for(int i=a;i<b;++i)
#define Rep(i, a, b) for(int i=a;i>=b;--i)
using namespace std;
const int N = 105;
int f[2*N][N][N], a[N][N];
inline int read(){
   int s=0,w=1;
   char ch=getchar();
   while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
   while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
   return s*w;
}
void put(int x) {
    if(x<0) putchar('-'),x=-x;
    if(x>=10) put(x/10);
    putchar(x%10^48);
}
signed main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int n=read(),m=read();
    rep(i, 1, n+1){
        rep(j, 1, m+1){
            a[i][j]=read();  
        }
    }
    //  Sum of row and column values   The row determines the column 
    rep(k, 2, n+m+1){
        //  First time i That's ok 
        rep(i1, 1, n+1){
            //  Second time i That's ok 
            rep(i2, 1, n+1){
                // j1 It means the first time j Column  j2 It means the second time j Column 
                int j1=k-i1, j2=k-i2;
                if(j1>=1&&j1<=m&&j2>=1&&j2<=m){
                    int t=a[i1][j1];
                    if(i1-i2){
                        t+=a[i2][j2];
                    }
                    f[k][i1][i2]=max({f[k][i1][i2], f[k-1][i1-1][i2-1]+t, f[k-1][i1-1][i2]+t, f[k-1][i1][i2-1]+t, f[k-1][i1][i2]+t});
                }
            }
        } 
    }
    printf("%lld", f[n+m][n][n]);
    return 0;
}

Line number value range optimization code

#include<bits/stdc++.h>
#define int long long
#define rep(i, a, b) for(int i=a;i<b;++i)
#define Rep(i, a, b) for(int i=a;i>=b;--i)
using namespace std;
const int N = 105;
int f[2*N][N][N], a[N][N];
inline int read(){
   int s=0,w=1;
   char ch=getchar();
   while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
   while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
   return s*w;
}
void put(int x) {
    if(x<0) putchar('-'),x=-x;
    if(x>=10) put(x/10);
    putchar(x%10^48);
}
signed main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int n=read(),m=read();
    rep(i, 1, n+1){
        rep(j, 1, m+1){
            a[i][j]=read();  
        }
    }
    //  Sum of row and column values   The row determines the column 
    rep(k, 2, n+m+1){
        //  First time i That's ok 
        rep(i1, max(1ll, k-m), min(k, n)+1){
            //  Second time i That's ok 
            rep(i2, max(1ll, k-m), min(k, n)+1){
                // k-i1 Indicates the number of columns for the first time  k-i2 Indicates the number of secondary columns 
                int t=a[i1][k-i1];
                if(i1-i2){
                    t+=a[i2][k-i2];
                }
                f[k][i1][i2]=max({f[k][i1][i2], f[k-1][i1-1][i2-1]+t, f[k-1][i1-1][i2]+t, f[k-1][i1][i2-1]+t, f[k-1][i1][i2]+t});
            }
        } 
    }
    printf("%lld", f[n+m][n][n]);
    return 0;
}

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