added more cat-in-the-hat test cases and renamed file

wk1/107-cat-hat/cat-hat.cpp

@@ -0,0 +1,72 @@
+/**
+ * Problem 107 - The Cat in the Hat
+ *
+ * Natalie Barillario & Jordan Scales
+ * for CS370
+ * Jan 27, 2014
+ */
+#include <iostream>
+#include <cmath>
+#include <stdio.h>
+
+int main() {
+    std::string input;
+    int i, initialHeight, workingCats;
+    double n;
+    double x;
+    int totalCats, totalHeight, nonWorkingCats;
+    bool shouldBreak;
+
+    while(scanf("%d %d\n", &initialHeight, &workingCats)) {
+        if (initialHeight == 0 && workingCats == 0) {
+            break;
+        }
+
+        /* Handle edge case for 1 1 */
+        if (initialHeight == 1 && workingCats == 1) {
+            std::cout << 0 << " " << 1 << std::endl;
+            continue;
+        }
+
+        /**
+         * Working cats: n^x
+         * Height of first cat: (n+1)^x
+         *
+         * Find x and n
+         */
+        for (n = 1; n <= workingCats; n++) {
+            shouldBreak = false;
+            for (x = 1; pow(n+1, x) <= initialHeight; x++) {
+                if (pow(n, x) == workingCats && pow(n+1, x) == initialHeight) {
+                    shouldBreak = true;
+                    break;
+                }
+            }
+
+            if (shouldBreak) break;
+        }
+
+        /**
+         * Compute the non-working cats (totalCats - workingCats)
+         *     Total cats: n^0 + n^1 + ... + n^x
+         *     Non-working Cats: Total cats - n^x
+         *
+         * Compute the height of everyone
+         *     (n+1)^x * n^0 + (n+1)^(x-1) * n^1 + ... + (n+1)^1 * n^(x-1) + n^x
+         */
+        totalCats = 0;
+        totalHeight = 0;
+
+        for (i = 0; i <= x; i++) {
+            totalCats += pow(n, i);
+            totalHeight += pow(n+1, x-i) * pow(n, i);
+        }
+        nonWorkingCats = totalCats - workingCats;
+
+        std::cout << nonWorkingCats << " " << totalHeight << std::endl;
+    }
+    return 0;
+}
+
+
+

wk1/107-cat-hat/test.in

@@ -0,0 +1,16 @@
+1 1
+216 125
+5764801 1679616
+1024 243
+2 1
+4 1
+1024 1
+371293 248832
+11 10
+1 1
+1048576 59049
+483736625 481890304
+125 64
+64 1
+81 64
+0 0