Created
March 22, 2018 12:03
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Consider 2 dimensional space
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| const coordsDigitsCalcSum = coords => | |
| coords | |
| .reduce( | |
| (acc, el) => | |
| Math.abs(el) | |
| .toString(10) | |
| .split("") | |
| .map(num => Number(num)) | |
| .concat(acc), | |
| [] | |
| ) | |
| .reduce((acc, val) => acc + val, 0); | |
| function countStepsImperatively(startCoords, digitsSumLimit = 21) { | |
| const queue = []; | |
| let startCoordsDigitsSum = coordsDigitsCalcSum(startCoords); | |
| if (startCoordsDigitsSum > digitsSumLimit) return 0; | |
| let steps = 0; | |
| queue.push(startCoords); | |
| const processedNodes = { [startCoords]: [startCoords] }; | |
| while (queue.length > 0) { | |
| let coords = queue.pop(); | |
| ++steps; | |
| coords.forEach((coord, index, coordsArray) => { | |
| const newCoordsPlus = coordsArray.slice(); | |
| newCoordsPlus[index] = coord + 1; | |
| let coordsPlusDigitsSum = coordsDigitsCalcSum(newCoordsPlus); | |
| if ( | |
| coordsPlusDigitsSum <= digitsSumLimit && | |
| !processedNodes[newCoordsPlus] | |
| ) { | |
| queue.push(newCoordsPlus); | |
| processedNodes[newCoordsPlus] = newCoordsPlus; | |
| } | |
| const newCoordsMinus = coordsArray.slice(); | |
| newCoordsMinus[index] = coord - 1; | |
| let coordsMinusDigitsSum = coordsDigitsCalcSum(newCoordsMinus); | |
| if ( | |
| coordsMinusDigitsSum <= digitsSumLimit && | |
| !processedNodes[newCoordsMinus] | |
| ) { | |
| queue.push(newCoordsMinus); | |
| processedNodes[newCoordsMinus] = newCoordsMinus; | |
| } | |
| }); | |
| } | |
| return steps; | |
| } | |
| function countStepsRecursively( | |
| coords, | |
| digitsSumLimit = 21, | |
| processedNodes = {} | |
| ) { | |
| if (processedNodes[coords]) { | |
| return 0; | |
| } | |
| processedNodes[coords] = coords; | |
| const digitsSum = coordsDigitsCalcSum(coords); | |
| if (digitsSum > digitsSumLimit) { | |
| return 0; | |
| } | |
| const [x, y] = coords; | |
| return ( | |
| 1 + | |
| coords | |
| .map((coord, index, coordsArray) => { | |
| const newCoordsPlus = coordsArray.slice(); | |
| newCoordsPlus[index] = coord + 1; | |
| const newCoordsMinus = coordsArray.slice(); | |
| newCoordsMinus[index] = coord - 1; | |
| return ( | |
| (processedNodes[newCoordsPlus] | |
| ? 0 | |
| : countStepsRecursively( | |
| newCoordsPlus, | |
| digitsSumLimit, | |
| processedNodes | |
| )) + | |
| (processedNodes[newCoordsMinus] | |
| ? 0 | |
| : countStepsRecursively( | |
| newCoordsMinus, | |
| digitsSumLimit, | |
| processedNodes | |
| )) | |
| ); | |
| }) | |
| .reduce((acc, val) => acc + val, 0) | |
| ); | |
| } | |
| console.log( | |
| "countStepsImperatively([0,0], 1) gives", | |
| countStepsImperatively([0], 1) | |
| ); | |
| //gives 3, trivial points with coordinates [0],[-1],[1] | |
| console.log( | |
| "countStepsImperatively([0,0], 1) gives", | |
| countStepsImperatively([0, 0], 1) | |
| ); | |
| //gives 3, trivial points with coordinate [0,0], [0,1], [0,-1], [-1,0] | |
| console.log( | |
| "countStepsImperatively([0,0], 21) gives", | |
| countStepsImperatively([0, 0], 21) | |
| ); |
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