diff options
Diffstat (limited to 'csp.js')
| -rw-r--r-- | csp.js | 181 |
1 files changed, 181 insertions, 0 deletions
| @@ -0,0 +1,181 @@ | |||
| 1 | !function() { | ||
| 2 | |||
| 3 | var CSP = {}, | ||
| 4 | FAILURE = 'FAILURE', | ||
| 5 | stepCounter = 0; | ||
| 6 | |||
| 7 | CSP.solve = function solve(csp) { | ||
| 8 | // Solves a constraint satisfaction problem. | ||
| 9 | // `csp` is an object that should have the properties: | ||
| 10 | // `variables` : object that holds variable names and their domain. | ||
| 11 | // `constraints`: list of constraints where each element is an | ||
| 12 | // array of [head node, tail node, constraint function] | ||
| 13 | // `cb`: callback function for visualizing assignments. It is passed in | ||
| 14 | // an "assigned" object, an "unassigned" object, and `csp`. | ||
| 15 | // `timeStep`: milliseconds between invocations of `cb`. | ||
| 16 | |||
| 17 | csp.timeStep = csp.timeStep || 1; | ||
| 18 | var result = backtrack({}, csp.variables, csp); | ||
| 19 | if (result == FAILURE) { return result; } | ||
| 20 | // Unwrap values from array containers. | ||
| 21 | for (var key in result) { | ||
| 22 | result[key] = result[key][0]; | ||
| 23 | } | ||
| 24 | return result; | ||
| 25 | } | ||
| 26 | |||
| 27 | function backtrack(_assigned, unassigned, csp) { | ||
| 28 | // Backtracking search. | ||
| 29 | |||
| 30 | // Copying assigned in necessary because we modify it. Without copying | ||
| 31 | // the object over, modifying assigned would also change values for old | ||
| 32 | // assigned objects (which are used in callbacks). | ||
| 33 | var assigned = {}; | ||
| 34 | for (var key in _assigned) { assigned[key] = _assigned[key]; } | ||
| 35 | |||
| 36 | if (finished(unassigned)) { return assigned; } // Base case. | ||
| 37 | var nextKey = selectUnassignedVariable(unassigned), | ||
| 38 | values = orderValues(nextKey, assigned, unassigned, csp); | ||
| 39 | delete unassigned[nextKey]; | ||
| 40 | |||
| 41 | for (var i = 0; i < values.length; i++) { | ||
| 42 | stepCounter++; | ||
| 43 | assigned[nextKey] = [values[i]]; // Assign a value to a variable. | ||
| 44 | var consistent = enforceConsistency(assigned, unassigned, csp); | ||
| 45 | var newUnassigned = {}, newAssigned = {}; | ||
| 46 | for (var key in consistent) { | ||
| 47 | if (assigned[key]) { newAssigned[key] = assigned[key].slice(); } | ||
| 48 | else { newUnassigned[key] = consistent[key].slice(); } | ||
| 49 | } | ||
| 50 | if (csp.cb) { | ||
| 51 | setTimeout( | ||
| 52 | // Need a closure to fix values of newAssigned and newUnassigned. | ||
| 53 | // Otherwise, _every_ call of the callback takes the on values of the last iteration. | ||
| 54 | (function (newAssigned, newUnassigned) { | ||
| 55 | return function () { csp.cb(newAssigned, newUnassigned, csp); }; | ||
| 56 | })(newAssigned, newUnassigned), | ||
| 57 | stepCounter * csp.timeStep | ||
| 58 | ); | ||
| 59 | } | ||
| 60 | if (anyEmpty(consistent)) { continue; } // Empty domains means failure. | ||
| 61 | var result = backtrack(newAssigned, newUnassigned, csp); | ||
| 62 | if (result != FAILURE) { return result; } | ||
| 63 | } | ||
| 64 | |||
| 65 | return FAILURE; | ||
| 66 | } | ||
| 67 | |||
| 68 | function finished(unassigned) { | ||
| 69 | // Checks if there are no more variables to assign. | ||
| 70 | return Object.keys(unassigned).length == 0; | ||
| 71 | } | ||
| 72 | |||
| 73 | function anyEmpty(consistent) { | ||
| 74 | // Checks if any variable's domain is empty. | ||
| 75 | for (var key in consistent) { | ||
| 76 | if (consistent[key].length == 0) { return true; } | ||
| 77 | } | ||
| 78 | return false; | ||
| 79 | } | ||
| 80 | |||
| 81 | function partialAssignment(assigned, unassigned) { | ||
| 82 | // Combine unassigned and assigned for use in enforceConsistency. | ||
| 83 | var partial = {}; | ||
| 84 | for (var key in unassigned) { partial[key] = unassigned[key].slice(); } | ||
| 85 | for (var key in assigned) { partial[key] = assigned[key].slice(); } | ||
| 86 | return partial; | ||
| 87 | } | ||
| 88 | |||
| 89 | function enforceConsistency(assigned, unassigned, csp) { | ||
| 90 | // Enforces arc consistency by removing inconsistent values from | ||
| 91 | // every constraint's tail node. | ||
| 92 | |||
| 93 | function removeInconsistentValues(head, tail, constraint, variables) { | ||
| 94 | // Removes inconsistent values from the tail node. A value is | ||
| 95 | // inconsistent when if the `tail` is assigned that value, there are | ||
| 96 | // no values in `head`'s domain that satisfies the constraint. | ||
| 97 | var hv = variables[head], tv = variables[tail]; | ||
| 98 | var validTailValues = tv.filter(function (t) { | ||
| 99 | return hv.some(function (h) { | ||
| 100 | return constraint(h, t); | ||
| 101 | }); | ||
| 102 | }); | ||
| 103 | var removed = tv.length != validTailValues.length; | ||
| 104 | variables[tail] = validTailValues; | ||
| 105 | return removed; | ||
| 106 | } | ||
| 107 | |||
| 108 | function incomingConstraints(node) { | ||
| 109 | // Returns all the constraints where `node` is the head node. | ||
| 110 | return csp.constraints.filter(function (c) { | ||
| 111 | return c[0] == node; | ||
| 112 | }); | ||
| 113 | } | ||
| 114 | |||
| 115 | var queue = csp.constraints.slice(), | ||
| 116 | variables = partialAssignment(assigned, unassigned); | ||
| 117 | while (queue.length) { // While there are more constraints to test. | ||
| 118 | var c = queue.shift(), head = c[0], tail = c[1], constraint = c[2]; | ||
| 119 | if (removeInconsistentValues(head, tail, constraint, variables)) { | ||
| 120 | // If values from the tail have been removed, incoming constraints | ||
| 121 | // to the tail must be rechecked. | ||
| 122 | queue = queue.concat(incomingConstraints(tail)); | ||
| 123 | } | ||
| 124 | } | ||
| 125 | return variables; | ||
| 126 | } | ||
| 127 | |||
| 128 | function selectUnassignedVariable(unassigned) { | ||
| 129 | // Picks the next variable to assign according to the Minimum | ||
| 130 | // Remaining Values heuristic. Pick the variable with the fewest | ||
| 131 | // values remaining in its domain. This helps identify domain | ||
| 132 | // failures earlier. | ||
| 133 | var minKey = null, minLen = Number.POSITIVE_INFINITY; | ||
| 134 | for (var key in unassigned) { | ||
| 135 | var len = unassigned[key].length; | ||
| 136 | if (len < minLen) { minKey = key, minLen = len; } | ||
| 137 | } | ||
| 138 | return minKey; | ||
| 139 | } | ||
| 140 | |||
| 141 | function orderValues(nextKey, assigned, unassigned, csp) { | ||
| 142 | // Orders the values of an unassigned variable according to the | ||
| 143 | // Least Constraining Values heuristic. Perform arc consistency | ||
| 144 | // on each possible value, and order variables according to the | ||
| 145 | // how many values were eliminated from all the domains (fewest | ||
| 146 | // eliminated in the front). This helps makes success more likely | ||
| 147 | // by keeping future options open. | ||
| 148 | |||
| 149 | function countValues(vars) { | ||
| 150 | var sum = 0; | ||
| 151 | for (var key in vars) { sum += vars[key].length; } | ||
| 152 | return sum; | ||
| 153 | } | ||
| 154 | |||
| 155 | function valuesEliminated(val) { | ||
| 156 | assigned[nextKey] = [val]; | ||
| 157 | var newLength = countValues(enforceConsistency(assigned, unassigned, csp)); | ||
| 158 | delete assigned[nextKey]; | ||
| 159 | return newLength; | ||
| 160 | } | ||
| 161 | |||
| 162 | // Cache valuesEliminated to be used in sort. | ||
| 163 | var cache = {}, values = unassigned[nextKey]; | ||
| 164 | values.forEach(function(val) { | ||
| 165 | cache[val] = valuesEliminated(val); | ||
| 166 | }); | ||
| 167 | // Descending order based on the number of domain values remaining. | ||
| 168 | values.sort(function (a, b) { return cache[b] - cache[a]; }); | ||
| 169 | return values; | ||
| 170 | } | ||
| 171 | |||
| 172 | // Taken from d3 source. Makes `csp` usable in other scripts. | ||
| 173 | if (typeof define === 'function' && define.amd) { | ||
| 174 | define(CSP); | ||
| 175 | } else if (typeof module === 'object' && module.exports) { | ||
| 176 | module.exports = CSP; | ||
| 177 | } else { | ||
| 178 | this.csp = CSP; | ||
| 179 | } | ||
| 180 | |||
| 181 | }(); | ||
