The challenge at hand is quite straightforward: develop an algorithm that can determine if the target value exists within the given matrix. Here, I have devised two potential solutions. However, I am uncertain as to which one would be more efficient. Personally, I lean towards solution 1 due to its omission of building a new array. But, would this truly result in significantly faster performance?
Solution 1:
var searchMatrix = function(matrix, target) {
let cols = matrix[0].length;
let rows = matrix.length;
let left = 0;
let right = cols*rows - 1;
while(left <= right) {
let midIndex = left + Math.floor((right-left)/2);
let midValue = matrix[Math.floor(midIndex/cols)][Math.floor(midIndex%cols)];
console.log(midValue);
if(midValue === target) {
return true;
}
else if(midValue < target) {
left = midIndex + 1;
} else {
right = midIndex - 1;
}
}
return false;
};
Solution 2:
var searchMatrix = function(matrix, target) {
let arr = []
for(let row of matrix) {
arr = [...arr,...row];
}
let left = 0;
let right = arr.length - 1;
while(left <= right) {
let middle = left + Math.floor((right-left)/2);
if(arr[middle] === target) {
return true;
} else if(arr[middle] < target) {
left = middle + 1;
} else {
right = middle - 1;
}
}
return false;
};
In Solution 2, our major alteration involves converting the matrix into a standard Array. Does this adjustment escalate the algorithm's complexity to O(n), considering we must iterate over and add every element to the new array?
By contrast, Solution 1 operates sans the necessity of forming a new array; thus, we maintain constant space, correct? Elucidating why the first solution excels in terms of time/space efficiency eludes me.