Add badness calculation

Current using the number of times someone is on-rota two days in a
row, multiplied by the standard deviation in the allocation
frequencies.

rotagen.c

@@ -1,10 +1,13 @@
 #include "rotagen.h"
 
+#include <math.h>
 #include <stdio.h>
 #include <stdlib.h>
+#include <string.h>
 #include <sys/time.h>
 
 #define POOL_SIZE 0x1000
+#define MAX_PEOPLE 32
 
 /* Hard-coded test data. */
 static const char *people[] = {
@@ -75,6 +78,9 @@ int main(void)
 	generate_rota(rota);
 	print_rota(rota);
 
+	const int badness = rota_badness(rota);
+	printf("Badness: %d\n", badness);
+
 	return 0;
 }
 
@@ -135,14 +141,54 @@ bool satisfies_slot_constraints(const struct slot_result *result)
 	return true;
 }
 
+int rota_badness(const struct slot_result *rota)
+{
+	int freqs[MAX_PEOPLE];
+	memset(freqs, 0, sizeof(freqs));
+	for (int slot = 0; slot < num_slots; ++slot) {
+		for (int job = 0; job < num_jobs; ++job)
+			++freqs[rota[slot].allocations[job].person];
+	}
+	const int total = num_slots * num_jobs;
+	int sum = 0;
+	double ps[MAX_PEOPLE];
+	for (int i = 0; i < num_people; ++i) {
+		ps[i] = (double)freqs[i] / total;
+		sum += freqs[i];
+	}
+	const double mean = (double)sum / total;
+	double variance = 0;
+	for (int i = 0; i < num_people; ++i) {
+		const double x = ps[i] - mean;
+		variance += x * x;
+	}
+	variance /= num_people;
+	const double stddev = sqrt(variance);
+
+	int adjacency_score = 0;
+	for (int i = 0; i < num_slots; ++i) {
+		for (int j = 0; j < num_jobs; ++j) {
+			const int p = rota[i].allocations[j].person;
+			for (int k = 0; k < num_jobs; ++k) {
+				if (p == rota[i].allocations[k].person)
+					++adjacency_score;
+			}
+		}
+	}
+
+	return adjacency_score * stddev;
+}
+
 void print_rota(const struct slot_result *rota)
 {
 	for (int slot = 0; slot < num_slots; ++slot) {
+		printf("----------------------------------------\n");
 		for (int job = 0; job < num_jobs; ++job) {
-			printf("%s\t%s\t%s\n",
+			printf("%s\t%s\t\t%s\n",
 			       job == 0 ? slots[slot] : "   ",
 			       jobs[job],
 			       people[rota[slot].allocations[job].person]);
 		}
 	}
+	printf("----------------------------------------\n");
 }

rotagen.h

@@ -33,6 +33,7 @@ void generate_rota(struct slot_result *rota_out);
 void generate_allocation(int slot, int job, struct allocation *allocation_out);
 bool satisfies_allocation_constraints(const struct allocation *allocation);
 bool satisfies_slot_constraints(const struct slot_result *slot);
+int rota_badness(const struct slot_result *rota);
 void print_rota(const struct slot_result *rota);
 
 #endif