ds-algo-study

<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Document</title> <link rel="stylesheet" href="./../../../assets/style.css" /> <link rel="stylesheet" href="./../../../assets/prism.css" /> <script async src="./../../../assets/prism.js"></script> </head> <body> // Recursive Boolean <div id="> pre data-role="codeBlock" data-info="js" class="language-javascript" ><code><a title="1">function recurBSearch(array, target) {</a> <a title="2"> // Our base case:</a> <a title="3"> // If our array is empty, we do not have the target</a> <a title="4"> if (array.length === 0) {</a> <a title="5"> return false;</a> <a id=-6" title="6"> }</a> <a title="7"></a> <a title="8"> // Get a reference to the middle index, and middle element</a> <a title="9"> const midIdx = Math.floor(array.length / 2);</a> <a id=-10" title="10"> const midEl = array[midIdx]</a> <a title="11"> // We get a subarray that represents our left half by slicing up to but not</a> <a id=-12" title="12"> // including our midIdx.</a> <a id=-13" title="13"> const leftHalf = array.slice(0, midIdx);</a> <a id=-14" title="14"> // We get a subarray that represents our right half by slicing from the</a> <a id=-15" title="15"> // midIdx + 1 all the way to the end of our array (no second argument needed).</a> <a id=-16" title="16"> const rightHalf = array.slice(midIdx + 1);</a> <a id=-17" title="17"> // If our target is smaller than the middle element, repeat this process with</a> <a id=-18" title="18"> // the left half of our array.</a> <a id=-19" title="19"> if (target < midEl) {</a> <a id=-20" title="20"> return recurBSearch(leftHalf, target);</a> <a id=-21" title="21"> }</a> <a id=-22" title="22"> // If our target is larger than the middle element, repeat this process with</a> <a id=-23" title="23"> // the right half of our array.</a> <a id=-24" title="24"> else if (target > midEl) {</a> <a id=-25" title="25"> return recurBSearch(rightHalf, target);</a> <a id=-26" title="26"> }</a> <a id=-27" title="27"> // If neither of these occurred, we found our element and return true.</a> <a id=-28" title="28"> else {</a> <a id=-29" title="29"> return true;</a> <a id=-30" title="30"> }</a> <a id=-31" title="31">}</a></code></pre> </div> // Iterative Boolean <div id="> pre data-role="codeBlock" data-info="js" class="language-javascript" ><code><a title="1">function iterBSearch(array, target) {</a> <a id=-2" title="2"> // Get a reference to our lower and upper bounds that we would like to search</a> <a id=-3" title="3"> // within our array. At the start, this is the entire array, so the indices are</a> <a id=-4" title="4"> // 0 and our length - 1.</a> <a id=-5" title="5"> let lowerIdx = 0;</a> <a id=-6" title="6"> let upperIdx = array.length - 1;</a> <a id=-7" title="7"> // We also create a midIdx variable because we will reassign it at each iteration</a> <a id=-8" title="8"> let midIdx;</a> <a id=-9" title="9"></a> <a id=-10" title="10"> // While our lowerIdx <= upperIdx, we still have elements that we haven't ruled</a> <a id=-11" title="11"> // out as being our target, so we want our iteration to continue.</a> <a id=-12" title="12"> while (lowerIdx <= upperIdx) {</a> <a id=-13" title="13"> // Get a reference to the middle element within our current bounds.</a> <a id=-14" title="14"> // We are using Math.floor in order to get an integer/valid index.</a> <a id=-15" title="15"> // (If we used ceiling, we would have to do some subtraction in order to get</a> <a id=-16" title="16"> // our first element. For example, [14] has a length 1, so</a> <a id=-17" title="17"> // Math.ceil((0 + 1)/2)) = 1, which is outside our bounds.</a> <a id=-18" title="18"> midIdx = Math.floor((lowerIdx + upperIdx) / 2);</a> <a id=-19" title="19"> // If our target is larger than our current middle element, our lower bound</a> <a id=-20" title="20"> // needs to be moved up past our midIdx so that we look at the right half.</a> <a id=-21" title="21"> if (array[midIdx] < target) {</a> <a id=-22" title="22"> lowerIdx = midIdx + 1;</a> <a id=-23" title="23"> // If our target is smaller than our current middle element, our upper bound</a> <a id=-24" title="24"> // needs to be moved down past our midIdx so that we look at the left half.</a> <a id=-25" title="25"> } else if (array[midIdx] > target) {</a> <a id=-26" title="26"> upperIdx = midIdx - 1;</a> <a id=-27" title="27"> // Otherwise, we have found our target at the midIdx and can return true.</a> <a id=-28" title="28"> } else {</a> <a id=-29" title="29"> return true;</a> <a id=-30" title="30"> }</a> <a id=-31" title="31"> }</a> <a id=-32" title="32"></a> <a id=-33" title="33"> // If we made it outside of our loop without returning, our target is not in</a> <a id=-34" title="34"> // the array, so we can return false.</a> <a id=-35" title="35"> return false;</a> <a id=-36" title="36">}</a></code></pre> </div> // Recursive Index <div id="> pre data-role="codeBlock" data-info="js" class="language-javascript" ><code><a title="1">function recurBSearchIdx(array, target) {</a> <a title="2"> // Our base case</a> <a title="3"> // This is another way of checking if the length is 0</a> <a id=-4" title="4"> // Since 0 is a falsey value, !0 would be truthy, meaning our array is empty</a> <a id=-5" title="5"> // -1 here indicates that the value is not found (very common for -1 to be used</a> <a id=-6" title="6"> // in these situations so that all return values are numbers)</a> <a id=-7" title="7"> if (!array.length) return -1;</a> <a id=-8" title="8"></a> <a id=-9" title="9"> // Getting a reference to our middle element for our comparisons</a> <a id=-10" title="10"> const midIdx = Math.floor(array.length / 2);</a> <a id=-11" title="11"> const midEl = array[midIdx];</a> <a id=-12" title="12"></a> <a id=-13" title="13"> // We get a subarray that represents our left half by slicing up to but not</a> <a id=-14" title="14"> // including our midIdx.</a> <a id=-15" title="15"> const leftHalf = array.slice(0, midIdx);</a> <a id=-16" title="16"> // We get a subarray that represents our right half by slicing from the</a> <a id=-17" title="17"> // midIdx + 1 all the way to the end of our array (no second argument needed).</a> <a id=-18" title="18"> const rightHalf = array.slice(midIdx + 1);</a> <a id=-19" title="19"></a> <a id=-20" title="20"> // If our target is less than our current middle element, we can recursively</a> <a id=-21" title="21"> // call our function with the left half of the array and return that value.</a> <a id=-22" title="22"> if (target < midEl) {</a> <a id=-23" title="23"> return recurBSearchIdx(leftHalf, target);</a> <a id=-24" title="24"> // If our target is greater than our current middle element we have two scenarios</a> <a id=-25" title="25"> // The first scenario, we did not find our target in the subarray (right side).</a> <a id=-26" title="26"> // In this case, we also want to return -1 to indicate that the value isn't</a> <a id=-27" title="27"> // in our array.</a> <a id=-28" title="28"> // The second scenario is that we find our element in the subarray.</a> <a id=-29" title="29"> // In this case, the return value is going to be the index IN THE SUBARRAY.</a> <a id=-30" title="30"> // In order for us to be able to return what index that corresponds to in</a> <a id=-31" title="31"> // our larger original array, we need to shift this value by where this</a> <a id=-32" title="32"> // subarray starts in our larger array.</a> <a id=-33" title="33"> // Ultimately this means taking our return value and adding on our midIdx + 1</a> <a id=-34" title="34"> // Take a look at the comments below this function for an example</a> <a id=-35" title="35"> } else if (target > midEl) {</a> <a id=-36" title="36"> const idxShift = recurBSearchIdx(rightHalf, target)</a> <a id=-37" title="37"> if (idxShift === -1) {</a> <a id=-38" title="38"> return -1</a> <a id=-39" title="39"> }</a> <a id=-40" title="40"> else {</a> <a id=-41" title="41"> return idxShift + midIdx + 1</a> <a id=-42" title="42"> }</a> <a id=-43" title="43"> // If neither of the above cases are true, we found our element and return that</a> <a id=-44" title="44"> // index (the midIdx that we compared)</a> <a id=-45" title="45"> } else {</a> <a id=-46" title="46"> return midIdx;</a> <a id=-47" title="47"> }</a> <a id=-48" title="48">}</a></code></pre> </div> // Using the right-side shift example: // Array: [1, 2, 3, 4, 5], Target: 5 // The first index that we are going to compare is Math.floor(array.length/2) = 2, // which is our element 3. // Our target is greater than this value, so we need to check the right subarray. // The new array is [4, 5] with the same target of 5. // In this recursive call, the index that we are checking is Math.floor(array.length/2) = 1, // which is our element 5. // Since we found our element, we are hitting our last case of the conditional, // return our index of 1 to where our recursive function was called. // This value of 1 does not line up with the index of our original array, though, // it was the index of our subarray. // In order to convert this into an index that aligns with our current, larger // array, we need to add on the amount that the indices were shifted. Our slicing // of the subarray was acheived by taking the first three elements off. We know // this intuitively, but it can be calculated by adding on our midIdx + 1 that // we originally passed to our slice method. // We end up getting our returned index from the recursion (1) added on to our // midIdx + 1 (2 + 1), getting a final index of 4, which corresponds to where // our element is in the larger array. // This shifting didn't have to take place on the left side because the indices // of the subarrays are the same as the indices of our larger array (index 1 of // the left subarray is the same element as index 1 of the larger original). // Recursive Index v2 <div id="> pre data-role="codeBlock" data-info="js" class="language-javascript" ><code><a title="1">function recurBSearchIdxV2(array, target, lo = 0, hi = array.length - 1) {</a> <a id=-2" title="2"> // I'm adding a second condition to this base case that Alvin doesn't do. It's</a> <a id=-3" title="3"> // possible that our last element of the array is the target, which would mean</a> <a id=-4" title="4"> // that lo === hi, but we haven't checked that element yet.</a> <a id=-5" title="5"> // This second part of the condition will only ever be evaluated when the first</a> <a id=-6" title="6"> // is true, making that final check.</a> <a id=-7" title="7"> // (This is an edge case that I don't think Alvin accounts for)</a> <a id=-8" title="8"> if (lo === hi && array[lo] !== target) {</a> <a id=-9" title="9"> return -1;</a> <a id=-10" title="10"> }</a> <a id=-11" title="11"></a> <a id=-12" title="12"> let midIdx = Math.floor((lo + hi) / 2);</a> <a id=-13" title="13"></a> <a id=-14" title="14"> if (target < array[midIdx]) {</a> <a id=-15" title="15"> return recurBSearchIdxV2(array, target, lo, midIdx);</a> <a id=-16" title="16"> } else if (target > array[midIdx]) {</a> <a id=-17" title="17"> return recurBSearchIdxV2(array, target, midIdx + 1, hi);</a> <a id=-18" title="18"> } else {</a> <a id=-19" title="19"> return midIdx;</a> <a id=-20" title="20"> }</a> <a id=-21" title="21">}</a></code></pre> </div> // Iterative Index <div > pre data-role="codeBlock" data-info="js" class="language-javascript" ><code><a title="1">function iterBSearchIdx(array, target) {</a> <a id=-2" title="2"> // The implementation of this function is exactly the same as returning a boolean</a> <a id=-3" title="3"> // Instead of returning true/false, we return the midIdx.</a> <a id=-4" title="4"> // No index shifting needs to take place like in the right-side scenario above</a> <a id=-5" title="5"> // because we are never making subarrays; we are only dealing with the indices</a> <a id=-6" title="6"> // as they relate to the original array.</a> <a id=-7" title="7"> let lowerIdx = 0;</a> <a id=-8" title="8"> let upperIdx = array.length - 1;</a> <a id=-9" title="9"> let midIdx;</a> <a id=-10" title="10"></a> <a id=-11" title="11"> while (lowerIdx <= upperIdx) {</a> <a id=-12" title="12"> midIdx = Math.floor((lowerIdx + upperIdx) / 2);</a> <a id=-13" title="13"> if (array[midIdx] < target) {</a> <a id=-14" title="14"> lowerIdx = midIdx + 1;</a> <a id=-15" title="15"> } else if (array[midIdx] > target) {</a> <a id=-16" title="16"> upperIdx = midIdx - 1;</a> <a id=-17" title="17"> } else {</a> <a id=-18" title="18"> return midIdx;</a> <a id=-19" title="19"> }</a> <a id=-20" title="20"> }</a> <a id=-21" title="21"></a> <a id=-22" title="22"> return -1;</a> <a id=-23" title="23">}</a></code></pre> </div> <div id="> pre data-role="codeBlock" data-info="js" class="language-javascript" ><code><a title="1">module.exports = {</a> <a id=-2" title="2"> recurBSearch,</a> <a id=-3" title="3"> iterBSearch,</a> <a id=-4" title="4"> recurBSearchIdx,</a> <a id=-5" title="5"> recurBSearchIdxV2,</a> <a id=-6" title="6"> iterBSearchIdx</a> <a id=-7" title="7">}</a></code></pre> </div> </body> </html>