Create readme.md

Author: geekykant

Tree/Segment-Tree/readme.md

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+### Segment Trees
+
+- A Segment Tree is a data structure that stores information about array intervals as a tree.
+- This allows answering range queries over an array efficiently, while still being flexible enough to allow quick modification of the array. 
+
+> Segment Tree is useful when the array has many "update" operations in intervals. [Read more](https://cp-algorithms.com/data_structures/segment_tree.html)
+
+Video Tutorial - https://www.youtube.com/watch?v=2bSS8rtFym4&ab_channel=TECHDOSE
+
+#### C++ Code
+<img width="820" src="https://user-images.githubusercontent.com/27401142/182177229-6db97527-7130-403a-ae90-0032b5e4f39c.png">
+
+```cpp
+void updateValue(vector<int>& st, int start, int end, int updatingIdx, int diff, int idx) {
+    // To be updated idx is outside range
+    if (updatingIdx < start || updatingIdx > end)
+        return;
+
+    //Idx is in the range of this node, update the value
+    // of this node and its children
+    st[idx] += diff;
+    if (start != end) {
+        int mid = start + (end - start) / 2;
+        updateValue(st, start, mid, updatingIdx, diff, 2 * idx + 1);
+        updateValue(st, mid + 1, end, updatingIdx, diff, 2 * idx + 2);
+    }
+}
+
+int getSum(vector<int>& st, int start, int end, int searchStartIdx, int searchEndIdx, int idx) {
+    // Case 1: Full overlaping condition
+    // Segment of the node is part of the range
+    // --searchStartIdx-- start ---- end ---searchEndIdx---
+    if (searchStartIdx <= start && searchEndIdx >= end)
+        return st[idx];
+
+    // Case 2: NO-overlap condition
+    // ---end -- searchStartIdx--
+    // ---searchEndIdx -- start--
+    if (end < searchStartIdx || start > searchEndIdx)
+        return 0;
+
+    // Case 3: Partial Overlap
+    int mid = start + (end - start) / 2;
+    return getSum(st, start, mid, searchStartIdx, searchEndIdx, 2 * idx + 1) +
+           getSum(st, mid + 1, end, searchStartIdx, searchEndIdx, 2 * idx + 2);
+}
+
+int fillSTValues(vector<int>& nums, vector<int>& st, int start, int end, int idx) {
+    // If there is only single element in array, store in st
+    // and return it
+    if (start == end) {
+        st[idx] = nums[start];
+        return nums[start];
+    }
+
+    // Split at any pivot into left and right subtrees
+    // and store their sum into current node
+    int mid = start + (end - start) / 2;
+    st[idx] = fillSTValues(nums, st, start, mid, 2 * idx + 1) +
+              fillSTValues(nums, st, mid + 1, end, 2 * idx + 2);
+
+    return st[idx];
+}
+
+void buildST(vector<int>& nums, vector<int>& st) {
+    //allocate memory for segement tree
+    int n = nums.size();
+    int x = (int)(ceil(log2(n)));
+
+    //Maximum size of segment tree
+    int max_size = 2 * (int)pow(2, x) - 1;
+
+    st.resize(max_size);
+    fillSTValues(nums, st, 0, n - 1, 0);
+}
+
+int main() {
+    vector<int> nums = {1, 3, 5, 7, 9, 11};
+    int n = nums.size();
+
+    //build segment tree
+    vector<int> st;
+    buildST(nums, st);
+
+    //Find sum in range - output = 32
+    int searchStartIdx = 2, searchEndIdx = 5;
+    cout << getSum(st, 0, n - 1, searchStartIdx, searchEndIdx, 0) << endl;
+
+    //Update value
+    int newValue = 7, updatingIdx = 2;
+    int diff = newValue - nums[updatingIdx];
+    updateValue(st, 0, n - 1, diff, updatingIdx, 0);
+
+    //Find sum range again - output = 34
+    cout << getSum(st, 0, n - 1, searchStartIdx, searchEndIdx, 0) << endl;
+
+    return 0;
+}
+```