Rokua P1004 Check Number "multithreading dp/four-dimensional dp/"

Title Description (https://www.luogu.org/problemnew/show/1004)

With N*n (n<=9), we fill some of these squares with positive integers, while the other squares

Person number 0. As shown (see examples):

A 0  0  0  0  0  0  0  0 0  0 13  0  0  6  0  0 0  0  0  0  7  0  0  0 0  0  0 14  0  0  0  0 0 21  0  0  0  4  0  0 0  0 15  0  0  0  0  0 0 14  0  0  0  0  0  0 0  0  0  0  0  0  0  0.                       B

Someone from a point in the upper left corner of the picture, you can walk down, or to the right, until you reach the lower right corner of B

Point. On the way, he can take the number in the squares (the squares will change to the number 0).

This person from point A to point B to walk two times, try to find out 2 such paths, so that the sum of the obtained number is the largest.

Input/output format

Input format:

The first behavior of the input is an integer n (a square chart representing n*n), followed by three integers per line, the first two

Represents the position, and the third number is the number placed at that position. A single line of 0 indicates the end of the input.

Output format:

Just output an integer that represents the maximum and the 2 paths that are obtained.

Input and Output sample input sample #: Copy

3 6 (  5)  4 145 2 215 6  3 157 2 0  0

Output Example # #: Replication

67

Description

NOIP 2000 Improvement Group Fourth question

"Analysis":

1th: Open four-dimensional array:

Take two paths as two people at the same time,

There are four coordinates, respectively, for two persons.

Vertical and horizontal coordinates, with the same four for loop.

2nd: Decision-making:

There are four ways to go:

(bottom, bottom), (bottom, right),

(right, bottom), (right, right).

are represented as:

S[I-1][J][H-1][K],S[I][J-1][H][K-1]

S[I-1][J][H][K-1],S[I][J-1][H-1][K]

(I,j is the first person, H,k is the second person)

The state transition equation can be obtained:

First Person: S[i][j][h][k]=max (TMP1,TMP2) +a[i][j];

A second person: s[i][j][h][k]+=a[h][k];

Note: If i=h&&j=k, it can only be added once.

"Code":

#include <bits/stdc++.h>using namespacestd;intn,x,y,val,maxn,f[ A][ A][ A][ A],a[ A][ A];//A[i][j][k][l] means that two people go at the same time, a walk i,j a walk k,lintMain () {CIN>>N; Memset (A,0,sizeofa);  while(cin>>x>>y>>val) {        if(x==0&&y==0&&val==0) Break; A[x][y]=Val; }     for(intI=1; i<=n;i++){         for(intj=1; j<=n;j++){             for(intk=1; k<=n;k++){                 for(intL=1; l<=n;l++){                    intOp1=max (f[i-1][j][k-1][l],f[i][j-1][k][l-1]); intOp2=max (f[i-1][j][k][l-1],f[i][j-1][k-1][l]); F[I][J][K][L]=max (OP1,OP2) +a[i][j]+A[k][l]; if(i==k&&j==l) f[i][j][k][l]-=A[i][j]; } }}} printf ("%d\n", F[n][n][n][n]); return 0;}

four-dimensional DP

Rokua P1004 Check Number "multithreading dp/four-dimensional dp/"