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diffusion.c

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+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+
+//TODO
+//Implement the below function
+//Simulate one particle moving n steps in random directions
+//Use a random number generator to decide which way to go at every step
+//When the particle stops at a final location, use the memory pointed to by grid to 
+//record the number of particles that stop at this final location
+//Feel free to declare, implement and use other functions when needed
+
+void one_particle(int *grid, int n)
+{
+    int x, y, z, r, num;
+    x = 0;
+    y = 0;
+    z = 0;
+    num = 0;
+    while (num < n){
+        r = rand() % 6;
+
+        if (r == 0){    
+            x -= 1;    
+        }
+        if (r == 1){    
+            x += 1;    
+        }
+
+        if (r == 2){    
+            y += 1;    
+        }
+
+        if (r == 3){    
+            y -= 1;    
+        }
+
+        if (r == 4){    
+            z += 1;    
+        }
+        if (r == 5){    
+            z -= 1;    
+        }
+
+        num += 1;
+    }
+    grid[(x*x) + (y*y) + (z*z)] += 1;
+}
+
+//TODO
+//Implement the following function
+//This function returns the fraction of particles that lie within the distance
+//r*n from the origin (including particles exactly r*n away)
+//The distance used here is Euclidean distance
+//Note: you will not have access to math.h when submitting on Mimir
+double density(int *grid, int n, double r)
+{
+    double sum = 0.0; 
+    double total = 0.0;
+    int dist1 = n * n + 1;
+    int dist2 = r * r * n * n;
+
+    for (int i = 0; i < dist1; i++){
+        if (grid[i] >= 1){
+            total += grid[i];
+            if (i <= dist2){
+                sum += grid[i];
+            }
+        }
+    }
+
+    float fract = sum / total;
+    return fract;
+}
+
+//use this function to print results
+void print_result(int *grid, int n)
+{
+    printf("radius density\n");
+    for(int k = 1; k <= 20; k++)
+    {
+        printf("%.2lf   %lf\n", 0.05*k, density(grid, n, 0.05*k));
+    }
+}
+
+//TODO
+//Finish the following function
+//See the assignment decription on Piazza for more details
+void diffusion(int n, int m)
+{
+	//fill in a few line of code below
+    int *grid;    
+    grid = (int *) calloc(n * n + 1, sizeof(int));
+
+	for (int i = 1; i <= m; i++) {
+        one_particle(grid, n);
+    }
+
+	print_result(grid, n);
+	//fill in some code below
+    free(grid);
+}
+
+int main(int argc, char *argv[])
+{
+
+	if(argc != 3)
+	{
+		printf("Usage: %s n m\n", argv[0]);
+		return 0; 
+	}
+	int n = atoi(argv[1]);
+	int m = atoi(argv[2]);
+
+	assert(n >= 1 && n <=50);
+	assert(m >= 1 && m <= 1000000);
+	srand(12345);
+	diffusion(n, m);
+	return 0;
+}