Add segment tree.

Algorithms/dynamic_programming/LongestIncreasingSub - nLogn.cpp

@@ -0,0 +1,26 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+#define INF 1e9
+
+/* Finds longest increasing subsequence in O(N logN) time, using binary search */
+
+int main(){
+	int n;
+	cin >> n;
+
+	vector<int> A(n);
+	vector<int> lis(n+1, INF);
+
+	for(int i=0;i<n;i++) cin >> A[i];
+
+	/* for non-decreasing subsequence, change lower_bound to upper_bound */
+	for(int i=0;i<n;i++) *lower_bound(lis.begin(), lis.end(), A[i]) = A[i];
+
+	for(int i=0;i<=n;i++) 
+		if(lis[i] == INF) { 
+			cout << i ; 
+			break;
+		}
+
+}

Data Structures/trees/segment-tree.cpp

@@ -0,0 +1,84 @@
+#include<bits/stdc++.h>
+using namespace std;
+#define INF 1e9
+
+/* Perform range operations in O(logN) with segment trees */
+
+/* This implementation finds the minimum element in an subarray in O(logN) as opposed to the simple for loop approach which does it in O(N) */
+
+
+int tree[5000];
+int A[5000];
+
+int build(int node, int start, int end){
+	if(start == end){
+		tree[node] = A[start];	
+	}
+	else{
+		int mid = (start + end)>>1;
+		build(node<<1, start, mid);
+		build(node<<1|1, mid+1, end);
+
+		tree[node] = min(tree[node<<1], tree[node<<1|1]);
+	}
+}
+
+int query(int node, int start, int end, int l, int r){
+	if(start>r||end<l)return INF;
+	if(l<=start && end<=r)return tree[node];
+	else{
+		int mid = (start+end)>>1;
+		int a = query(node<<1, start, mid, l, r);
+		int b = query(node<<1|1, mid+1, end, l, r);
+		return min(a,b);	
+	}
+}
+
+int update(int node, int start, int end, int idx, int val){
+	if(start == end && start == idx){
+		tree[node] = val;
+		A[idx] = val;
+	}
+	else{
+		int mid = (start + end)>>1;
+		if(idx<=mid) update(node<<1, start, mid, idx, val);
+		else update(node<<1|1, mid+1, end, idx, val);
+		tree[node] = min(tree[node<<1], tree[node<<1|1]);
+	}
+}
+
+int main(){
+
+	int n, q;
+	cin >> n >> q; // read in number of elements and number of queries
+
+	for(int i=0;i<n;i++) cin >> A[i]; // read in array
+
+	build(1, 0, n-1); // build segment tree
+
+	while(q--){
+		// each query is of two types - type 1 (update an index) OR type 2 (query a subarray)
+
+		int type;
+		cin >> type; // whether query or update	on array
+
+		if(type == 1){ // if update an index
+			int idx, val;
+			cin >> idx >> val;
+			idx--; // remove 1-based indexing
+			update(1, 0, n-1, idx, val);
+		}
+
+		else if(type == 2){	// if to query the minimum of a subarray
+			int l, r;
+			cin >> l >> r;
+			l--, r--;
+			cout << "Minimum element from index "<<l<<" to index "<<r<<" is "<< query(1, 0, n-1, l, r) <<"\n";
+		}
+	}
+
+	/* Total complexity = O( n + qLogn )
+}
+
+
+