一般DP-雙調取數問題

#include <iostream>
#include <sstream>
#include <stdio.h>
#include <algorithm>
#include <string.h>
#include <stack>
#include <queue>
#include <set>
#include <math.h>
#include <time.h>

/*=======================================
雙調取數問題
從A -> B只能向下或者向右走，獲取最大值

dp[i][j]表示從(0, 0) -> (i, j)可以獲取的最大值

dp[i][j][m][n] = max(dp[i][j - 1][m][n - 1], dp[i - 1][j][m - 1][n], dp[i - 1][j][m][n - 1], dp[i][j - 1][m - 1][n]) + w[i][j];

========================================*/
#define flush(arr, i) memset(arr, i, sizeof(arr))
typedef long long int64;
using namespace std;
const int MAX_ITEM = 20;
const int oo = 0x7fffffff;
//const int oo = 0x3f3f3f3f;

int dp[MAX_ITEM][MAX_ITEM][MAX_ITEM][MAX_ITEM], w[MAX_ITEM][MAX_ITEM];

int DP(int lx, int ly, int rx, int ry)
{
    if(lx <= 0 || ly <= 0 || rx <= 0 || ry <= 0)
        return 0;

    if(dp[lx][ly][rx][ry])
        return dp[lx][ly][rx][ry];

    int ans = max(max(DP(lx, ly - 1, rx, ry - 1), DP(lx - 1, ly, rx - 1, ry)), max(DP(lx, ly - 1, rx - 1, ry), DP(lx - 1, ly, rx, ry - 1)));

    if(lx == rx && ly == ry)
        ans += w[lx][ly];
    else
        ans = ans + w[lx][ly] + w[rx][ry];

    return dp[lx][ly][rx][ry] =  ans;
}

int main()
{
    freopen("0-data.txt", "r", stdin);
    int n, x, y, val;
    while(scanf("%d", &n) != EOF)
    {
        flush(w, 0), flush(dp, 0);
        while(true)
        {
            scanf("%d%d%d", &x, &y, &val);
            if(x + y + val == 0)
                break;
            w[x][y] = val;
        }
        printf("%d\n", DP(n - 1, n - 1, n - 1, n - 1));
    }
    return 0;
}

下面是簡化的獨立取數問題

#include <iostream>
#include <sstream>
#include <stdio.h>
#include <algorithm>
#include <string.h>
#include <stack>
#include <queue>
#include <set>
#include <math.h>
#include <time.h>

/*=======================================
取數問題
從A -> B只能向下或者向右走，獲取最大值

dp[i][j]表示從(0, 0) -> (i, j)可以獲取的最大值

dp[i][j] = max(dp[i][j - 1], dp[i - 1][j]) + w[i][j];

========================================*/
#define flush(arr, i) memset(arr, i, sizeof(arr))
typedef long long int64;
using namespace std;
const int MAX_ITEM = 110;
const int oo = 0x7fffffff;
//const int oo = 0x3f3f3f3f;

int dp[MAX_ITEM][MAX_ITEM], w[MAX_ITEM][MAX_ITEM];

int DP(int x, int y)
{
    if(x <= 0 || y <= 0)
        return 0;

    if(dp[x][y])
        return dp[x][y];

    return dp[x][y] = max(DP(x, y - 1), DP(x - 1, y)) + w[x][y];
}

int main()
{
    freopen("0-data.txt", "r", stdin);
    int n, x, y, val;
    while(scanf("%d", &n) != EOF)
    {
        flush(w, 0), flush(dp, 0);
        while(true)
        {
            scanf("%d%d%d", &x, &y, &val);
            if(x + y + val == 0)
                break;
            w[x][y] = val;
        }
        printf("%d\n", DP(n - 1, n - 1));
    }
    return 0;
}