程式碼：

#include <iostream>
#include <algorithm>
#include <set>
#include <map>
#include <string.h>
#include <queue>
#include <sstream>
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <string>

using namespace std;

const
 
 int MAXN = 1010000;//點數的最大值
const int MAXM = 6001000;//邊數的最大值
const int INF = 0x3f3f3f3f;

struct Edge
{
    int to, next, cap, flow;
}edge[MAXM];//注意是MAXM

int tol;
int head[MAXN];
int gap[MAXN], dep[MAXN], pre[MAXN], cur[MAXN];

void init()
{
    tol = 0;
    memset(head, -1, sizeof(head));
}
//加邊，單向圖三個引數，雙向圖四個引數
void
 
 addedge(int u, int v, int w, int rw = 0)
{
    edge[tol].to = v; edge[tol].cap = w; edge[tol].next = head[u];
    edge[tol].flow = 0; head[u] = tol++;
    edge[tol].to = u; edge[tol].cap = rw; edge[tol].next = head[v];
    edge[tol].flow = 0; head[v] = tol++;
}
//輸入引數：起點、終點、點的總數
//點的編號沒有影響，只要輸入點的總數

int Q[MAXN];

void
 
 BFS(int start,int end)
{
    memset(dep, -1, sizeof(dep));
    memset(gap, 0, sizeof(gap));
    gap[0] = 1;
    int front = 0, rear = 0;
    dep[end] = 0;
    Q[rear++] = end;
    while (front != rear)
    {
        int u = Q[front++];
        for (int i = head[u];i != -1;i = edge[i].next)
        {
            int v = edge[i].to;
            if (dep[v] != -1) continue;
            Q[rear++] = v;
            dep[v] = dep[u] + 1;
            gap[dep[v]]++;
        }
    }
}
int S[MAXN];
int sap(int start, int end, int N)
{
    BFS(start, end);
    memcpy(cur, head, sizeof(head));
    int u = start;
    int top = 0;
    int ans = 0;
    while (dep[start] < N)
    {
        if (u == end)
        {
            int Min = INF;
            int inser;
            for (int i = 0; i < top; i++)
                if (Min > edge[S[i]].cap - edge[S[i]].flow)
                {
                    Min = edge[S[i]].cap - edge[S[i]].flow;
                    inser = i;
                }
            for (int i = 0; i < top; i++)
            {
                edge[S[i]].flow += Min;
                edge[S[i] ^ 1].flow -= Min;
            }
            ans += Min;
            top = inser;
            u = edge[S[top] ^ 1].to;
            continue;
        }
        bool flag = false;
        int v;
        for (int i = cur[u]; i != -1; i = edge[i].next)
        {
            v = edge[i].to;
            if (edge[i].cap - edge[i].flow && dep[v] + 1 == dep[u])
            {
                flag = true;
                cur[u]  = i;
                break;
            }
        }
        if (flag)
        {
            S[top++] = cur[u];
            u = v;
            continue;
        }
        int Min = N;
        for (int i = head[u]; i != -1; i = edge[i].next)
            if (edge[i].cap - edge[i].flow && dep[edge[i].to] < Min)
            {
                Min = dep[edge[i].to];
                cur[u] = i;
            }
        gap[dep[u]]--;
        if (!gap[dep[u]])return ans;
        dep[u] = Min + 1;
        gap[dep[u]]++;
        if (u != start) u = edge[S[--top]^1].to;
    }
    return ans;
}

int n, m;
int a[110][110];
int dir[4][2] = {{1,0},{-1,0},{0,1},{0,-1}};

int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        m = n;
        int sum = 0;
        init();
        for(int i=1;i<=n;i++)
            for(int j=1;j<=m;j++)
           {
               scanf("%d",&a[i][j]);
               sum += a[i][j];
               if ((i+j) % 2 == 0)
                {
                    addedge(0,(i-1)*m+j,a[i][j]);
                }
                else
                {
                    addedge((i-1)*m+j,n*m+1,a[i][j]);
                }
           }

        for(int i=1;i<=n;i++)
            for(int j=1;j<=m;j++)
        {
            if ((i + j) % 2 == 0)
            for(int k=0;k<4;k++)
            {
                int x = i + dir[k][0];
                int y = j + dir[k][1];
                if (x>=1 && x<= n &&y>=1 && y<=m)
                {
                    addedge((i-1)*m+j,(x-1)*m+y,1e9+9);
                }
            }
        }

        int ans = sum - sap(0,n*m + 1,n*m + 2);
        printf("%d\n",ans);
    }
    return 0;
}