思路

思路很简单，照例是debug半天Orz
1. typeN 0表示数字，1表示公式，op 1表示sum，2表示avg, 3表示std
2. 字符串+正则处理 x1,x2,y1,y2为了图方便用了pair来存
3. dfs搜索时，遇到数字直接返回w的值，遇到公式则会进入下一层dfs进行计算
4. 全遍历输出dfs

代码

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<regex>
#include<math.h>
// #include<pair.h>

using namespace std;
#define x first
#define y second
typedef pair<int,int> PII;
typedef pair<PII,PII> PIIPII;

const int N = 55;
int n, m;
int typeN[N*N];  // 0 - number, 1 
double w[N*N];
int op[N*N];
PIIPII p[N*N];
regex patt1("\\d+");

double dfs(int x_y)
{
    if(typeN[x_y] == 0)
        return w[x_y];

    if(op[x_y] == 1)
    {
        int x1 = p[x_y].x.x, y1 = p[x_y].x.y, x2 = p[x_y].y.x, y2 = p[x_y].y.y;
        for(int i = x1; i<=x2; i++)
            for(int j = y1;j<=y2;j++)
                w[x_y] += dfs(i*m+j);
        typeN[x_y] = 0;
    }
    else if(op[x_y] == 2)
    {
        int x1 = p[x_y].x.x, y1 = p[x_y].x.y, x2 = p[x_y].y.x, y2 = p[x_y].y.y;
        for(int i = x1; i<=x2; i++)
            for(int j = y1;j<=y2;j++)
                w[x_y] += dfs(i*m+j);
        w[x_y] /= (x2-x1+1)*(y2-y1+1);
        typeN[x_y] = 0;
    }
    else if(op[x_y] == 3)
    {
        double mean = 0;
        int x1 = p[x_y].x.x, y1 = p[x_y].x.y, x2 = p[x_y].y.x, y2 = p[x_y].y.y;
        int cnt = (x2-x1+1)*(y2-y1+1);
        for(int i = x1; i<=x2; i++)
            for(int j = y1;j<=y2;j++)
                mean += dfs(i*m+j);
        mean /= cnt;
        x1 = p[x_y].x.x, y1 = p[x_y].x.y, x2 = p[x_y].y.x, y2 = p[x_y].y.y;
        for(int i = x1; i<=x2; i++)
            for(int j = y1;j<=y2;j++)
                w[x_y] += (dfs(i*m+j)-mean)*(dfs(i*m+j)-mean);
        w[x_y] = sqrt(w[x_y]/cnt);
        typeN[x_y] = 0;
    }

    return w[x_y];
}


int main()
{
    scanf("%d%d", &n,&m);
    string temp;
    for(int i = 0; i < n; i++)
        for(int j = 0; j < m; j++)
        {
            cin >> temp;
            if(0 <= temp[0]-'0' && temp[0]-'0'<=9) typeN[i*m+j] = 0, w[i*m+j] = (double)stoi(temp);
            else{

                typeN[i*m+j] = 1;

                if(temp.substr(0,3) == "SUM") op[i*m+j] = 1;
                else if(temp.substr(0,3) == "AVG") op[i*m+j] = 2;
                else op[i*m+j] = 3;
                string::const_iterator iterStart = temp.begin();
                string::const_iterator iterEnd = temp.end();
                int a[4], idx = 0;
                smatch result;
                while (regex_search(iterStart, iterEnd, result, patt1))
                {
                    a[idx++] = stoi(result[0]);
                    iterStart = result[0].second;   //更新搜索起始位置,搜索剩下的字符串
                }
                p[i*m+j].x.x = a[0]-1;
                p[i*m+j].x.y = a[1]-1;
                p[i*m+j].y.x = a[2]-1;
                p[i*m+j].y.y = a[3]-1;
            }
        }

    for(int i = 0; i < n; i++)
    {
        for(int j = 0; j <m ; j ++)
            printf("%.2lf ",dfs(i*m+j));
        printf("\n");
    }

}