recursive backtracking for sudoku? - javascript
Im trying to make a sudoku solver algorithm to practice recursion and backtracking, so made this function 'backtrack' which is the main function that's supposed to solve it , and four other 'utility/helper' functions;the first one is 'getSubGrid' which returns the subgrid where the current number belongs,and then 'getColumn' which returns the column where the current number belongs, and 'getRow' which returns the row where the current number belongs, and the last helper function is 'subGridIncludes' to check whether a subgrid includes a specific number or not.The problem is that for some boards, this code works and solve them, but for some other boards it doesn't and it gives me 'too much recursion' error.Note that i tried to calculate how many recursive calls each board requires and i found that the boards that worked required less than 6000 calls , but the one of the boards that didnt work required more than 10000 call before i got the message 'too much recursion',and i want to know if the error is because i didnt set a base case that was present in the boards that were not solved and not present in the boards that were solved, or is it because the board is just big and i need to rewrite the script in a way that requires the least amount of recursive calls.
these are examples of the boards that were succesfully solved:
board 1:
[
[7,8,0,4,0,0,1,2,0],
[6,0,0,0,7,5,0,0,9],
[0,0,0,6,0,1,0,7,8],
[0,0,7,0,4,0,2,6,0],
[0,0,1,0,5,0,9,3,0],
[9,0,4,0,6,0,0,0,5],
[0,7,0,3,0,0,0,1,2],
[1,2,0,0,0,7,4,0,0],
[0,4,9,2,0,6,0,0,7]
]
board 2:
[
[0,2,0,0,0,8,0,0,4],
[0,9,0,1,0,0,6,0,0],
[0,0,3,0,0,0,0,1,0],
[9,0,1,4,0,0,0,0,8],
[0,0,0,0,0,0,3,0,2],
[0,0,5,0,8,3,0,0,7],
[0,0,4,0,0,0,9,2,0],
[7,0,0,3,0,0,8,5,0],
[0,0,0,2,5,6,4,0,3]
]
and this is an example of a board that the function didnt solve:
[
[1,0,0, 0,5,0, 0,4,0],
[0,0,0, 9,0,0, 0,0,1],
[0,0,0, 0,0,3, 8,0,0],
[0,5,0, 8,0,2, 4,0,0],
[0,0,0, 0,0,0, 0,0,0],
[4,0,0, 0,0,0, 7,5,3],
[5,0,0, 3,0,0, 0,6,0],
[0,2,0, 0,0,1, 3,7,0],
[0,6,0, 4,0,9, 0,0,0]
]
and this is the code:
let lastPopped; // variable to keep track of the last changed value
let addedVals = [[]]; // array of arrays to keep track of the indexes where the values were changed on each row,where the index of each subarray corresponds to the index of the row
backtrack()
function backtrack(currentRowIndex = 0, currentRow = board[currentRowIndex], testValue = 1, i = 0) {
// testValue is a value put under test to check if its included in the row, column,subgrid
if (currentRowIndex === board.length) {
// this condition checks the board is finished ,if so it stops the execution of the function.
return
} else if (i === currentRow.length) {
// this condition checks if we reached the end of the current row ,if so it takes us to the next row.
lastPopped = undefined
addedVals.push(new Array())
backtrack(currentRowIndex + 1, currentRow = board[currentRowIndex + 1], testValue = 1, i = 0)
} else if (testValue > 9) {
// this condition checks if the testValue is greater than 9,if so we know that we should set the current value to 0 and we backtrack to the previous value.
currentRow[i] = 0
if (i === 0 || (addedVals[currentRowIndex].length === 0)) {
// this condition checks whether we are at the start of a row or the previous values are original, if so we backtrack to the previous row.
lastPopped = addedVals[currentRowIndex - 1].pop()
backtrack(currentRowIndex - 1, currentRow = board[currentRowIndex - 1], testValue = board[currentRowIndex - 1][lastPopped] + 1, i = lastPopped)
} else {
// if the previous condtion is not satisfied we backtrack to the previous value plus one in the same row.
lastPopped = addedVals[currentRowIndex].pop()
backtrack(currentRowIndex, currentRow = board[currentRowIndex], testValue = currentRow[lastPopped] + 1, i = lastPopped)
}
} else {
if (currentRow[i] === 0 || i === lastPopped) {
// this condition checks if the current value is a value that was not original or equal to zero.
if (!getColumn(currentRow[i], currentRowIndex).includes(testValue) && !subGridIncludes(0, testValue, getSubGrid(currentRow[i], currentRowIndex)) && !getRow(currentRow[i], currentRowIndex).includes(testValue)) {
//this condition checks whether the testValue is included in the row, column,subgrid,if so it assigns it to the current index,and pushes the index to the addedVals array to indicate that the current index's value has bee changes and keep trakc of it for comming purposes
currentRow[i] = testValue;
addedVals[currentRowIndex].push(i);
if (currentRow[i] != 0 && i === 8) {
//this condition enables us to move to the next row when needed
lastPopped = undefined
addedVals.push(new Array())
backtrack(currentRowIndex + 1, currentRow = board[currentRowIndex + 1], testValue = 1, i = 0)
} else {
//this condition enables us to move to the next index when needed
backtrack(currentRowIndex, currentRow = board[currentRowIndex], testValue = 1, i + 1)
}
} else {
//this condition adds 1 to the test value with each call.
backtrack(currentRowIndex, currentRow = board[currentRowIndex], testValue + 1, i)
}
} else {
if (currentRow[i] != 0 && i === 8) {
//this condition enables us to move to the next row when needed
addedVals.push(new Array())
backtrack(currentRowIndex + 1, currentRow = board[currentRowIndex + 1], testValue = 1, i = 0)
} else {
//this condition enables us to move to the next index when needed
backtrack(currentRowIndex, currentRow = board[currentRowIndex], testValue = 1, i + 1)
}
}
}
}
for (property in board) {
console.log(".", JSON.stringify(board[property]));
}
//this function checks whether a subgrid includes a specific number or not
function subGridIncludes(index, value, subgrd) {
if (index === subgrd.length) {
return false
} else {
return subgrd[index].includes(value) ? true : subGridIncludes(index + 1, value, subgrd)
}
}
//this function returns the subgrid where the element belongs.
function getSubGrid(num, index) {
let arr = new Array(3).fill([])
let oneDimentionalIndex, twoDimentionalIndex, tdiSub, odiSub;
let [rightOrBelow, leftOrAbove, rightOrBelowAndleftOrAbove] = [[0, 3, 6], [2, 5, 8], [1, 4, 7]];
for (let j = 0; j < board[index].length; j++) {
if (board[index][j] === num) {
oneDimentionalIndex = index;
twoDimentionalIndex = j;
break
}
}
rightOrBelow.includes(oneDimentionalIndex) ? odiSub = 0 : leftOrAbove.includes(oneDimentionalIndex) ? odiSub = 2 : rightOrBelowAndleftOrAbove.includes(oneDimentionalIndex) ? odiSub = 1 : null;
rightOrBelow.includes(twoDimentionalIndex) ? tdiSub = 0 : leftOrAbove.includes(twoDimentionalIndex) ? tdiSub = 2 : rightOrBelowAndleftOrAbove.includes(twoDimentionalIndex) ? tdiSub = 1 : null;
arr = arr.map((_, ind) => board[(oneDimentionalIndex - odiSub) + ind].slice(twoDimentionalIndex - tdiSub, ((twoDimentionalIndex - tdiSub) + 3)))
return arr
}
//this function returns the column where the element belongs.
function getColumn(num, index) {
let twoDimentionalIndex;
let column = new Array(board.length);
for (let j = 0; j < board[index].length; j++) {
if (board[index][j] === num) {
twoDimentionalIndex = j;
break
}
}
for (let i = 0; i < board.length; i++) {
column[i] = board[i][twoDimentionalIndex];
}
return column
}
//this function returns the row where the element belongs.
function getRow(num, index) {
let oneDimentionalIndex;
let row = new Array(board.length);
for (let j = 0; j < board[index].length; j++) {
if (board[index][j] === num) {
oneDimentionalIndex = index;
break
}
}
for (let i = 0; i < board.length; i++) {
row[i] = board[oneDimentionalIndex][i];
}
return row
}
The code obviously has a lot of violations of the DRY principle because i havent had much practice with code cleaning,so im sorry.
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