/* heat.c */

#include "heatSupport.h"

void main() {
  double p[V][H];
  setTemperatureOfAllElementsToZero(p);
  p[V/2][H/2] = 1; /* set temperature of source element */
  simulateHeatDiffusion(1000, p);
  displayHeatDistribution(p);
}


/* heatSupport.h */

/* number of rows (V) and columns (H) of elements */
#define V 20 
#define H 30 

/* set element temperatures to zero */
void setTemperatureOfAllElementsToZero(double p[V][H]);

/* simulate heat diffusion on p for given number of time steps */
void simulateHeatDiffusion(int numberOfTimeSteps, double p[V][H]);

/* display on screen the temperature distribution of p */
void displayHeatDistribution(double p[V][H]);


/* heatSupport.c */

#include "heatSupport.h"
#include "heatSupportPrivate.h"
#include "numericUtilities.h"
#include <string.h>
#include <stdio.h>

void setTemperatureOfAllElementsToZero(double p[V][H]) {
  int i, j;
  for (i = 0; i < V; i = i + 1) {
    for (j = 0; j < H; j = j + 1) {
      p[i][j] = 0;
    }
  }
}

void simulateHeatDiffusion(int numberOfTimeSteps, double p[V][H]) {
  int t;
  for (t = 0; t < numberOfTimeSteps; t = t + 1) {
    updateInteriorTemperatures(p);
  }
}

void displayHeatDistribution(double p[V][H]) {
  int i, j;
  for (i = 0; i < V; i = i + 1) {  
    for (j = 0; j < H; j = j + 1) {
      printf("%c", digitalDisplay(" -+*", 0, 1, p[i][j]));
    }
    printf("\n");
  }
}


/* heatSupportPrivate.h */

/* update temperatures of interior elements of p */
void updateInteriorTemperatures(double p[V][H]);


/* heatSupportPrivate.c */

#include "heatSupport.h"
#include "heatSupportPrivate.h"

void updateInteriorTemperatures(double p[V][H]) {
  int i, j;
  double sourceElementTemperature;
  sourceElementTemperature = p[V/2][H/2];
  for (i = 1; i < V - 1; i = i + 1) {
    for (j = 1; j < H - 1; j = j + 1) {
      p[i][j] = (p[i-1][j] + p[i][j+1] + p[i+1][j] + p[i][j-1])/4;
    }
  }
  p[V/2][H/2] = sourceElementTemperature; /* restore source element */
}


/* numericUtilities.h */

/* deliver the larger of two integers */
int maxInt(int x, int y); 

/* deliver the smaller of two integers */
int minInt(int x, int y);

/* digitize x
   according to a uniform partition of the range (a, b)
   into n digital levels
   assuming a < x < b
   truncating out-of-range x's to appropriate exteme   */
int digitize(int n, double a, double b, double x);

/* deliver digital representation of x
   selected from a given sequence of display characters
   assuming a < x < b
   truncating out-of-range x's to appropriate exteme   */
char digitalDisplay(char displayChars[ ],
                    double a, double b, double x);


/* numericUtilities.c */

#include "numericUtilities.h"
#include <string.h>

int maxInt(int x, int y) {
  return(x < y ? y : x);
}

int minInt(int x, int y) {
  return(-maxInt(-x, -y));
}

int digitize(int n, double a, double b, double x) {
  return(maxInt(0, minInt(n - 1, n*(x - a)/(b - a))));
}

char digitalDisplay(char displayChars[ ],
                    double a, double b, double x) {
  return(displayChars[digitize(strlen(displayChars), a, b, x)]);
}