Find String Path in Matrix using objective-c

This is the classic case to solve with backtracking, The usual scenario is that you are faced with a number of options, and you must choose one of these. After you make your choice you will get a new set of options; just what set of options you get depends on what choice you made. This procedure is repeated over and over until you reach a final state. There is a nice explanation of backtracking here http://www.cis.upenn.edu/~matuszek/cit596-2012/NewPages/backtracking.html

/*
This part needs to be in the caller program, which will pass the original array and input. I have taken input as an array, you can use input as a string for your question, in the end for the algorithm it doesn't matter. 

NSArray* a1 = @[
    @[@"A", @"B", @"C", @"E"],
    @[@"S", @"F", @"C", @"S"],
    @[@"A", @"D", @"E", @"E"],
];

NSArray* input = @[ @"A", @"B", @"C", @"B" ];
BOOL result = [self checkPath:a1 andInput:input];
*/
 -(BOOL) checkPath:(NSArray*)a1 andInput:(NSArray*)input
{
// Create a test array to keep track of what options you have already used.
NSMutableArray* testArray =
[[NSMutableArray alloc] init];
[testArray addObject:[[NSMutableArray alloc] init]];
[testArray addObject:[[NSMutableArray alloc] init]];
[testArray addObject:[[NSMutableArray alloc] init]];

// Initialize all the elements of the test array to zero, You should replace zero with 1 when you match the element at a certain index.
for(int i = 0; i < 3; i++) {
    for (int j = 0; j< 4; j++) {
        testArray[i][j]  = @0;
    }
}

for(int i = 0; i < 3; i++) {
    for (int j = 0; j< 4; j++) {
        NSLog(@"%@", a1[i][j]);
    }
}

BOOL res = NO;

int i = 0, j = 0;

while (!res && i <3) {
    while (!res && j <4) {
        if( [input[0] isEqualToString:a1[i][j]])
        {
            testArray[i][j] = @1;
            res = [self doesPathExist:input dictionaryArray:a1 startIndexX:i andStartIndexY:j compareIndex:1 andMarkerTable:testArray];
            // Reset the test option incase the chosen option wasn't success
            testArray[i][j] = [NSNumber numberWithBool:res];
        }
        j++;
    }
    i++;
}
return res;
}
/**
*  Check if the path exist in array a1 starting at index x and y for elements of array input, starting at element c
*
*  @param input       input array for which you want to check path in a1
*  @param a1          array in which we want to check the path
*  @param x           row number to start with
*  @param y           column number to start with
*  @param c           index of elemnet to check in input array
*  @param markerTable table that decides which elements have already been used.
*
*  @return yes if path exist for array input in a1 otherwise No
*/
-(BOOL)doesPathExist:(NSArray*)input dictionaryArray:(NSArray*)a1 startIndexX:(int) x andStartIndexY:(int) y compareIndex:(int)c andMarkerTable:(NSMutableArray*) markerTable
{
NSUInteger n = markerTable.count;
NSUInteger m = ((NSArray*)markerTable[0]).count;

NSUInteger N = input.count;
if (c == N)
{
    NSLog(@"YES, Path Exists");
    return YES;
}
else
{
    BOOL result = NO;
while (c < N) {
    int left = y -1;
    int right = y + 1;
    int top = x - 1;
    int bottom = x + 1;

    if (left>=0 && ![markerTable[x][left]  isEqualToNumber: @1]) {

        if( [a1[x][left] isEqualToString:input[c]]){
            // set marker table value as 1 to mark the match
            markerTable[x][left] = @1;
         result = [self doesPathExist:input dictionaryArray:a1 startIndexX:x andStartIndexY:left compareIndex:c+1 andMarkerTable:markerTable];
        // reset the marker table based on result, we do a reset of marker
        // table at the index to make sure if this combination fails and there
        // is another combination involving this element it should be able to use this element.
        markerTable[x][left] = [NSNumber numberWithBool:result];
            return result;
        }
    }
    if (right<m && ![markerTable[x][right] isEqualToNumber:@1]) {
        if([a1[x][right] isEqualToString:input[c]]) {
            markerTable[x][right] = @1;
            result = [self doesPathExist:input dictionaryArray:a1 startIndexX:x andStartIndexY:right compareIndex:c+1 andMarkerTable:markerTable];
            markerTable[x][right] = [NSNumber numberWithBool:result];
            return result;
        }
    }
    if(top >=0 && ![markerTable[top][y] isEqualToNumber:@1]) {
        if([a1[top][y] isEqualToString:input[c]]) {
            markerTable[top][y] = @1;
            result = [self doesPathExist:input dictionaryArray:a1 startIndexX:top andStartIndexY:y compareIndex:c+1 andMarkerTable:markerTable];
            markerTable[top][y] = [NSNumber numberWithBool:result];
            return result;
        }
    }
    if(bottom < n && ![markerTable[bottom][y] isEqualToNumber:@1]) {
        if([a1[bottom][y] isEqualToString:input[c]]) {
            markerTable[bottom][y] = @1;
            result = [self doesPathExist:input dictionaryArray:a1 startIndexX:bottom andStartIndexY:y compareIndex:c+1 andMarkerTable:markerTable];
            markerTable[bottom][y] = [NSNumber numberWithBool:result];
            return result;
        }
    }
    c++;
}
    NSLog(@"Returning false");
     return NO;
}
}