brute_force_zero_sum.js

function create_empty_is_visited_matrix(numberOfRows, numberOfColumns) {
    var result = [];
    for(var i = 0; i < numberOfRows; i++) {
        result[i] = [];
        for(var j = 0; j < numberOfColumns; j++) {
            result[i][j] = false;
        }
    }
    return result;
}

function clone_matrix(matrix) {
    var result = [];
    for(var i = 0; i < matrix.length; i++) {
        result[i] = [];
        for(var j = 0; j < matrix[i].length; j++) {
            result[i][j] = matrix[i][j];
        }
    }
    return result;
}

function has_zero_sum(matrix, row, column, currentSum, isVisitedMatrix) {
    
    if(row > 0) {
        var up = row - 1;
        if(isVisitedMatrix[up][column] === false) {
            var clone = clone_matrix(isVisitedMatrix);
            clone[up][column] = true;
            var updatedSum = currentSum - matrix[up][column];
            console.log(up, column, updatedSum);
            if (updatedSum === 0) {
                return true;
            }
            var result = has_zero_sum(matrix, up, column, updatedSum, clone);
            if (result === true) {
                return true;
            }
        }
    }
    if(row < matrix.length - 1) {
        var down = row + 1;
        if(isVisitedMatrix[down][column] === false) {
            var clone = clone_matrix(isVisitedMatrix);
            clone[down][column] = true;
            var updatedSum = currentSum - matrix[down][column];
            console.log(down, column, updatedSum);
            if (updatedSum === 0) {
                return true;
            }
            var result = has_zero_sum(matrix, down, column, updatedSum, clone);
            if (result === true) {
                return true;
            }
        }
    }
    if(column > 0) {
        var left = column - 1;
        if(isVisitedMatrix[row][left] === false) {
            var clone = clone_matrix(isVisitedMatrix);
            clone[row][left] = true;
            var updatedSum = currentSum + matrix[row][left];
            console.log(row, left, updatedSum);
            if (updatedSum === 0) {
                return true;
            }
            var result = has_zero_sum(matrix, row, left, updatedSum, clone);
            if (result === true) {
                return true;
            }
        } 
    }
    if(column < matrix[row].length - 1) {
        var right = column + 1;
        if(isVisitedMatrix[row][right] === false) {
            var clone = clone_matrix(isVisitedMatrix);
            clone[row][right] = true;
            var updatedSum = currentSum + matrix[row][right];
            console.log(row, right, updatedSum);
            if (updatedSum === 0) {
                return true;
            }
            var result = has_zero_sum(matrix, row, right, updatedSum, clone);
            if (result === true) {
                return true;
            }
        }
    }
    console.log('end of path');
    return false;
}

function does_matrix_have_zero_sum(matrix) {
    for(var i = 0; i < matrix.length; i++) {
        for(var j = 0; j < matrix[i].length; j++) {
            var isVistedMatrix = create_empty_is_visited_matrix(matrix.length, matrix[i].length);
            isVistedMatrix[i][j] = true;
            console.log('starting new' ,i, j, matrix[i][j]);
            var result = has_zero_sum(matrix, i, j, matrix[i][j], isVistedMatrix);
            if (result === true) {
                return true;
            }
        }
    }
    return false;
}

var matrix = [];
matrix[0] = [1,2,3];
matrix[1] = [3,2,1];
matrix[2] = [1,4,2];

var isVistedMatrix = create_empty_is_visited_matrix(matrix.length, matrix[2].length);
isVistedMatrix[2][0] = true;
console.log(does_matrix_have_zero_sum(matrix));