Merge pull request #16 from arsalanc-v2/non-det-examples

Add non-det SICP JS solutions

Author: martin-henz

src/source-3-non-det-examples/__tests__/fast-multiple-dwelling.test.js

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+// chapter=3 variant=non-det executionMethod=interpreter
+const md = multiple_dwelling();
+let res = '';
+for (let i = 0; i < length(md); i=i+1) {
+    const person_floor = list_ref(md, i);
+    const person = head(person_floor);
+    const floor = stringify(head(tail(person_floor))); 
+    res = res + person + floor + ',';
+}
+res;
+// 'baker3,cooper2,fletcher4,miller5,smith1,'

src/source-3-non-det-examples/__tests__/liars.test.js

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+// chapter=3 variant=non-det executionMethod=interpreter
+const liars = list(list('betty', betty), list('ethel', ethel), list('joan', joan),
+list('kitty', kitty), list('mary', mary));
+let res = '';
+for (let i = 0; i < length(liars); i=i+1) {
+    const person_rank = list_ref(liars, i);
+    const person = head(person_rank);
+    const rank = stringify(head(tail(person_rank))); 
+    res = res + person + rank + ',';
+}
+res;
+// 'betty3,ethel5,joan2,kitty1,mary4,'

src/source-3-non-det-examples/__tests__/queens.test.js

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+// chapter=3 variant=non-det executionMethod=interpreter
+const queens = queens_fast(8, 8);
+let res = '';
+for (let i = 0; i < length(queens); i=i+1) {
+    const position = list_ref(queens, i);
+    const x = stringify(head(position));
+    const y = stringify(tail(position)); 
+    res = res + '(' + x + ',' + y + '),';
+}
+res;
+// '(4,8),(2,7),(7,6),(3,5),(6,4),(8,3),(5,2),(1,1),'

src/source-3-non-det-examples/fast-multiple-dwelling.js

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+/* SICP JS Exercise 4.31
+   
+   This file contains a fast(er) solution to the multiple dwelling puzzle.
+   The key idea is that we perform every 'require' check immediately once
+   the information it needs is available. This minimises wasteful backtracking.
+*/
+
+function distinct(items) {
+    return is_null(items)
+        ? true
+        : is_null(tail(items))
+        ? true
+        : is_null(member(head(items), tail(items)))
+            ? distinct(tail(items))
+            : false;
+  }
+  
+  function multiple_dwelling() {
+      const baker = amb(1, 2, 3, 4, 5);
+      require(!(baker === 5));
+      const cooper = amb(1, 2, 3, 4, 5);
+      require(!(cooper === 1));
+      const fletcher = amb(1, 2, 3, 4, 5);
+      require(!(fletcher === 5));
+      require(!(fletcher === 1));
+      require(!(math_abs(fletcher - cooper) === 1));
+      const miller = amb(1, 2, 3, 4, 5);
+      require(miller > cooper);
+      const smith = amb(1, 2, 3, 4, 5);
+      require(!(math_abs(smith - fletcher) === 1));
+      require(distinct(list(baker, cooper, fletcher, miller, smith)));
+  
+  
+      return list(list("baker", baker),
+                  list("cooper", cooper),
+                  list("fletcher", fletcher),
+                  list("miller", miller),
+                  list("smith", smith));
+  }
+  // multiple_dwelling();

src/source-3-non-det-examples/liars.js

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+/*
+  SICP JS Exercise 4.33
+
+  This file contains a solution to the Liars' puzzle
+*/
+
+function distinct(items) {
+  return is_null(items)
+      ? true
+      : is_null(tail(items))
+      ? true
+      : is_null(member(head(items), tail(items)))
+          ? distinct(tail(items))
+          : false;
+}
+
+const kitty = amb(1, 2, 3, 4, 5);
+const mary = amb(1, 2, 3, 4, 5);
+require(amb(kitty === 2, mary === 4));
+const betty = amb(1, 2, 3, 4, 5);
+require(amb(kitty === 2, betty === 3));
+require(amb(mary === 4, betty === 1));
+const ethel = amb(1, 2, 3, 4, 5);
+const joan = amb(1, 2, 3, 4, 5);
+require(amb(ethel === 1, joan === 2));
+require(amb(joan === 3, ethel === 5));
+
+require(distinct(list(betty, ethel, joan, kitty, mary)));
+
+// list(list('betty', betty), list('ethel', ethel), list('joan', joan),
+// list('kitty', kitty), list('mary', mary));

src/source-3-non-det-examples/queens.js

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+/*
+  SICP JS Exercise 4.35
+
+  This file contains two solutions for the n-queens puzzle using non-determinism.
+  Each of them makes use of the generate-and-test paradigm.
+  
+  The first (queens_slow) uses non-determinism for generating both the row and column
+  for each position. It does so in an optimized manner, testing the corresponding condition
+  as soon as the choice is generated, thereby reducing the search space. However, this is not
+  enough to yield a quick solution when N = 8.
+  This solution also gives repeated solutions (i.e different permutations that have all the same positions) upon backtracking.
+
+  The second (queens_fast) uses non-determinism in picking only the row and not the column of each position, with the
+  columns being fixed. This further reduces the search space, yielding a quick solution when N = 8.
+*/
+
+const N = 8; // the number of queens and the size of the board
+const empty_positions = null;
+
+/******************************************************************************/
+/* Slow version which uses non-determinism for both the columns and rows,     */
+/* perform testing of a required condition as soon as the choice is generated */
+/******************************************************************************/
+
+// const result_queens_slow = queens_slow(N, N);
+// pretty_print(result_queens_slow, N);
+// generate more solutions by entering 'try again' in the REPL
+
+function queens_slow(board_size, num_queens) {
+  require(num_queens <= board_size);
+  const possible_positions = enum_list(1, board_size);
+
+  const result = accumulate(
+    (_, so_far) => {
+      const row = an_element_of(possible_positions);
+      require(is_row_safe(row, so_far));
+
+      const col = an_element_of(possible_positions);
+      require(is_col_safe(col, so_far));
+
+      const new_position = pair(row, col);
+      require(is_diagonal_safe(new_position, so_far));
+
+      const new_positions = pair(new_position, so_far);
+      return new_positions;
+    },
+    empty_positions,
+    enum_list(1, num_queens)
+  );
+
+  return result;
+}
+
+function is_row_safe(new_row, queen_positions) {
+  const rows = map(position => head(position), queen_positions);
+  return member(new_row, rows) === null;
+}
+
+function is_col_safe(new_col, queen_positions) {
+  const cols = map(position => tail(position), queen_positions);
+  return member(new_col, cols) === null;
+}
+
+function is_diagonal_safe(new_position, queen_positions) {
+  const new_sum = head(new_position) + tail(new_position);
+  const new_sub = head(new_position) - tail(new_position);
+  const sums = map(
+    position => head(position) + tail(position),
+    queen_positions
+  );
+
+  return (
+    member(new_sum, sums) === null &&
+    member(
+      new_sub,
+      map(position => head(position) - tail(position), queen_positions)
+    ) === null
+  );
+}
+
+/******************************************************************************/
+/* Fast version which uses non-determinism only for the rows,                 */
+/* with the columns being hardcoded.                                          */
+/******************************************************************************/
+
+// const result_queens_fast = queens_fast(N, N);
+// pretty_print(result_queens_fast, N);
+// generate more solutions by entering 'try again' in the REPL
+
+function queens_fast(board_size, num_queens) {
+  require(num_queens <= board_size);
+  const possible_positions = enum_list(1, board_size);
+
+  function queen_cols(k) {
+    if (k === 0) {
+      return empty_positions;
+    } else {
+      const so_far = queen_cols(k - 1);
+
+      const new_row = an_element_of(possible_positions);
+      const new_position = pair(new_row, k);
+      require(is_safe(new_position, so_far));
+
+      const new_positions = pair(new_position, so_far);
+      return new_positions;
+    }
+  }
+  return queen_cols(num_queens);
+}
+
+function is_safe(new_position, positions) {
+  const new_row = head(new_position);
+  const new_col = tail(new_position);
+
+  return accumulate(
+    (position, so_far) => {
+      const row = head(position);
+      const col = tail(position);
+
+      return (
+        so_far &&
+        new_row - new_col !== row - col &&
+        new_row + new_col !== row + col &&
+        new_row !== row
+      );
+    },
+    true,
+    positions
+  );
+}
+
+
+/* Pretty prints a solution to the n-queens puzzle */
+function pretty_print(result, board_size) {
+  function member_eq(v, xs) {
+    return is_null(xs)
+      ? null
+      : equal(v, head(xs))
+      ? xs
+      : member_eq(v, tail(xs));
+  }
+  const possible_positions = enum_list(1, board_size);
+
+  let col_index_str = "  ";
+  for_each(i => {
+    col_index_str = col_index_str + stringify(i) + " ";
+  }, possible_positions);
+  display(col_index_str);
+
+  for_each(row => {
+    let row_str = stringify(row) + " ";
+    for_each(col => {
+      const position = pair(row, col);
+      const contains_position = member_eq(position, result) !== null;
+      if (contains_position) {
+        row_str = row_str + "Q ";
+      } else {
+        row_str = row_str + ". ";
+      }
+    }, possible_positions);
+
+    display(row_str);
+  }, possible_positions);
+}