Mathematical Modeling: Common Models and MATLAB Code

% years, service, and wage are the original data
years = 1950:10:1990;
service = 10:10:30;
wage = [ 150.697  199.592  187.625  179.323  195.072;
250.287  203.212  179.092  322.767  226.505;
153.706  426.730  249.633  120.281  598.243];
[X, Y] = meshgrid(years, service);
% % 3D curve
% plot3(X, Y, wage)
% 3D surface
% figuresurf(X, Y, wage)
% interp2 is the 2D interpolation function in MATLAB, the first two parameters are known positions, the last two are unknown positions, w is the interpolation result at the unknown position
w = interp2(service,years,wage,15,1975);

#include<iostream>  #include<cstdio>  #include<cstdlib>  #include<cmath>  #include<cstring>  #include<algorithm>  #include<vector>  #include<fstream>  using namespace std;
const int maxnum = 100;  const int maxint = 2147483647;  int dist[maxnum];     // Represents the shortest path length from the current point to the source point  int prev[maxnum];     // Records the previous node of the current point  int c[maxnum][maxnum];   // Records the path length between two points in the graph  int n, line;             // n represents the number of nodes in the graph, line represents the number of paths  void Dijkstra(int n, int v, int *dist, int *prev, int c[maxnum][maxnum]){  bool s[maxnum];    // Determines whether the point has been added to the set S  for(int i=1; i<=n; ++i)      {          dist[i] = c[v][i];          s[i] = 0;     // Initially, none of the points have been used  if(dist[i] == maxint)              prev[i] = 0;  else            prev[i] = v;      }      dist[v] = 0;      s[v] = 1;  // Sequentially take the point with the smallest dist[] value from the points not in set S and add it to set S  // Once S contains all points in V, dist records the shortest path lengths from the source point to all other points  for(int i=2; i<=n; ++i)      {  int tmp = maxint;  int u = v;  // Find the minimum dist[j] value among the currently unused points j  for(int j=1; j<=n; ++j)  if((!s[j]) && dist[j]<tmp)              {                  u = j;              // u saves the number of the point with the minimum distance among the adjacent points                  tmp = dist[j];              }          s[u] = 1;    // Indicates that the point u has been added to set S  // Update dist  for(int j=1; j<=n; ++j)  if((!s[j]) && c[u][j]<maxint)              {  int newdist = dist[u] + c[u][j];  if(newdist < dist[j])                  {                      dist[j] = newdist;                      prev[j] = u;                  }              }      }  }  void searchPath(int *prev,int v, int u){  int que[maxnum];  int tot = 1;      que[tot] = u;      tot++;  int tmp = prev[u];  while(tmp != v)      {          que[tot] = tmp;          tot++;          tmp = prev[tmp];      }      que[tot] = v;  for(int i=tot; i>=1; --i)  if(i != 1)  cout << que[i] << " -> ";  elsecout << que[i] << endl;  }  int main(){  //freopen("input.txt", "r", stdin);  // Each array starts from index 1  // Input the number of nodes  cin >> n;  // Input the number of paths  cin >> line;  int p, q, len;          // Input points p, q and their path lengths  // Initialize c[][] to maxint  for(int i=1; i<=n; ++i)  for(int j=1; j<=n; ++j)              c[i][j] = maxint;  for(int i=1; i<=line; ++i)      {  cin >> p >>> q >>> len;  if(len < c[p][q])       // There are multiple edges          {              c[p][q] = len;      // p points to q              c[q][p] = len;      // q points to p, indicating an undirected graph          }      }  for(int i=1; i<=n; ++i)          dist[i] = maxint;  for(int i=1; i<=n; ++i)      {  for(int j=1; j<=n; ++j)  printf("%-16d", c[i][j]);  printf("\n");      }      Dijkstra(n, 1, dist, prev, c);   // Call the function to find the distances from the source point to other points 改法:Dijkstra(n, x, dist, prev, c);  where x=1,2,3,4,...,n  //    for(int i=1; i<=n; ++i)   // dist stores the distances from the source point to other points  //    {  //        printf("%-16d", dist[i]);  //    }  printf("\n");  // Shortest path length  cout << "The shortest path length from the source point to the last vertex: " << dist[n] <<< endl;  // Path  cout << "The path from the source point to the last vertex is: ";      searchPath(prev, 1, n);  return 0;  }  

/* Input data:  5  7  1 2 10  1 4 30  1 5 100  2 3 50  3 5 10  4 3 20  4 5 60  Output data:  999999 10 999999 30 100  10 999999 50 999999 999999  999999 50 999999 20 10  30 999999 20 999999 60  100 999999 10 60 999999  The shortest path length from the source point to the last vertex: 60  The path from the source point to the last vertex is: 1 -> 4 -> 3 -> 5 */