tasks a-s

Task/Pascals-triangle-Puzzle/D/pascals-triangle-puzzle.d

@@ -0,0 +1,69 @@
+import std.stdio, std.algorithm;
+
+void iterate(bool doPrint=true)(double[] v, double[] diff) {
+    static ref T E(T)(T[] x, in size_t row, in size_t col)
+    pure nothrow {
+        return x[row * (row + 1) / 2 + col];
+    }
+
+    double sum = 0.0;
+    do {
+        // enforce boundary conditions
+        E(v, 0, 0) = 151;
+        E(v, 2, 0) = 40;
+        E(v, 4, 1) = 11;
+        E(v, 4, 3) = 4;
+
+        // calculate difference from equilibrium
+        foreach (i; 1 .. 5) {
+            foreach (j; 0 .. i + 1) {
+                E(diff, i, j) = 0;
+                if (j < i)
+                    E(diff, i, j) += E(v, i - 1, j) -
+                                     E(v, i, j + 1) -
+                                     E(v, i, j);
+                if (j)
+                    E(diff, i, j) += E(v, i - 1, j - 1) -
+                                     E(v, i, j - 1) -
+                                     E(v, i, j);
+            }
+        }
+
+        foreach (i; 1 .. 4)
+            foreach (j; 0 .. i)
+                E(diff, i, j) += E(v, i + 1, j) +
+                                 E(v, i + 1, j + 1) -
+                                 E(v, i, j);
+
+        E(diff, 4, 2) += E(v, 4, 0) + E(v, 4, 4) - E(v, 4, 2);
+
+        // do feedback, check if we are close enough
+        // 4: scale down the feedback to avoid oscillations
+        v[] += diff[] / 4;
+        sum = reduce!q{a + b ^^ 2}(0.0, diff);
+
+        static if (doPrint)
+            writeln("dev: ", sum);
+
+        // sum(dx^2) < 0.1 means each cell is no more than 0.5 away
+        // from equilibrium. It takes about 50 iterations. After
+        // 700 iterations sum is < 1e-25, but that's overkill.
+    } while (sum >= 0.1);
+}
+
+void main() {
+    static void show(in double[] x) {
+        int idx;
+        foreach (i; 0 .. 5)
+            foreach (j; 0 .. i+1) {
+                printf("%4d%c", cast(int)(0.5 + x[idx]),
+                       j < i ? ' ' : '\n');
+                idx++;
+            }
+    }
+
+    double[15] v = 0.0;
+    double[15] diff = 0.0;
+    iterate(v, diff);
+    show(v);
+}