feat: Add comments of implementation details

changicho · changicho · commit cd57889645f2 · 2022-10-15T00:27:14.000+09:00
diff --git a/Data-Structures/Tree/SegmentTree.js b/Data-Structures/Tree/SegmentTree.js
@@ -14,50 +14,78 @@ class SegmentTree {
   size
   tree
   constructor (arr) {
+    // we define tree like this
+    // tree[1] : root node of tree
+    // tree[i] : i'th node
+    // tree[i * 2] : i'th left child
+    // tree[i * 2 + 1] : i'th right child
+    // and we use bit, shift operation for index
     this.size = arr.length
     this.tree = new Array(2 * arr.length)
     this.tree.fill(0)
 
     this.build(arr)
   }
 
+  // function to build the tree
   build (arr) {
     const { size, tree } = this
     // insert leaf nodes in tree
+    // leaf nodes will start from index N
+    // in this array and will go up to index (2 * N – 1)
     for (let i = 0; i < size; i++) {
       tree[size + i] = arr[i]
     }
 
     // build the tree by calculating parents
+    // tree's root node will contain all leaf node's sum
     for (let i = size - 1; i > 0; --i) {
-      tree[i] = tree[i << 1] + tree[(i << 1) | 1]
+      // current node's value is the sum of left child, right child
+      // tree[i] = tree[i * 2] + tree[i * 2 + 1]
+      tree[i] = tree[i * 2] + tree[i * 2 + 1]
     }
   }
 
-  update (p, value) {
+  update (index, value) {
     const { size, tree } = this
 
-    // set value at position p
-    tree[p + size] = value
-    p += size
+    // only update values in the parents of the given node being changed.
+    // to get the parent move to parent node (index / 2)
+
+    // set value at position index
+    index += size
+    // tree[index] is leaf node and index's value of array
+    tree[index] = value
 
     // move upward and update parents
-    for (let i = p; i > 1; i >>= 1) {
+    for (let i = index; i > 1; i >>= 1) {
+      // i ^ 1 turns (2 * i) to (2 * i + 1)
+      // i ^ 1 is second child
       tree[i >> 1] = tree[i] + tree[i ^ 1]
     }
   }
 
+  // interval [L,R) with left index(L) included and right (R) excluded.
   query (left, right) {
     const { size, tree } = this
+    // cause R is excluded, increase right for convenient
     right++
     let res = 0
 
     // loop to find the sum in the range
     for (left += size, right += size; left < right; left >>= 1, right >>= 1) {
+      // L is the left border of an query interval
+
+      // if L is odd it means that it is the right child of its parent and our interval includes only L and not the parent.
+      // So we will simply include this node to sum and move to the parent of its next node by doing L = (L + 1) / 2.
+
+      // if L is even it is the left child of its parent
+      // and the interval includes its parent also unless the right borders interfere.
       if ((left & 1) > 0) {
         res += tree[left++]
       }
 
+      // same in R (the right border of an query interval)
       if ((right & 1) > 0) {
         res += tree[--right]
       }
