binary search misc

Author: zarif98sjs

Algorithm/42 Binary Search.cpp

@@ -0,0 +1,193 @@
+
+/** Which of the favors of your Lord will you deny ? **/
+
+#include<bits/stdc++.h>
+using namespace std;
+
+#define LL long long
+#define PII pair<int,int>
+#define PLL pair<LL,LL>
+#define MP make_pair
+#define F first
+#define S second
+
+#define ALL(x) (x).begin(), (x).end()
+#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
+#define READ        freopen("alu.txt", "r", stdin)
+#define WRITE       freopen("vorta.txt", "w", stdout)
+
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+using namespace __gnu_pbds;
+
+template<class TIn>using indexed_set = tree<TIn, null_type, less<TIn>,rb_tree_tag, tree_order_statistics_node_update>;
+
+/**
+
+PBDS
+-------------------------------------------------
+1) insert(value)
+2) erase(value)
+3) order_of_key(value) // 0 based indexing
+4) *find_by_order(position) // 0 based indexing
+
+**/
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p);
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v);
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v);
+
+inline void optimizeIO()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+}
+
+const int nmax = 2e5+7;
+const LL LINF = 1e17;
+
+template <class T>
+string to_str(T x)
+{
+    stringstream ss;
+    ss<<x;
+    return ss.str();
+}
+
+//bool cmp(const PII &A,const PII &B)
+//{
+//
+//}
+
+int ara[nmax];
+
+int binarySearch(int lo,int hi,int key)
+{
+    while(lo<=hi)
+    {
+        int mid = lo + (hi-lo)/2;
+
+        if(ara[mid]<key) lo = mid + 1;
+        else if (ara[mid]>key) hi = mid - 1;
+        else return mid;
+    }
+
+    return -1;
+}
+
+int lowerBound(int lo,int hi,int key)
+{
+    while(lo!=hi)
+    {
+        int mid = lo + (hi-lo)/2;
+
+        if(ara[mid]<key) lo = mid + 1;
+        else hi = mid;
+    }
+
+    return lo;
+
+}
+
+int upperBound(int lo,int hi,int key)
+{
+    while(lo!=hi)
+    {
+        int mid = lo + (hi-lo)/2;
+
+        if(ara[mid]<=key) lo = mid + 1;
+        else hi = mid;
+    }
+
+    return lo;
+}
+
+int main()
+{
+    optimizeIO();
+
+    int n;
+    cin>>n;
+
+    for(int i=1;i<=n;i++)
+        cin>>ara[i];
+
+    sort(ara+1,ara+n+1);
+
+    for(int i=1;i<=n;i++)
+        cout<<ara[i]<<" ";
+    cout<<endl;
+
+    while(1)
+    {
+        int val;
+        cin>>val;
+        int idx = binarySearch(1,n,val);
+        if(idx!=-1) cout<<val<<" present at : "<<idx<<endl;
+        else cout<<val<<" absent"<<endl;
+    }
+
+    /// for 1 based indexing with n elements , set lo = 1 , hi = n+1
+
+    while(1)
+    {
+        int val;
+        cin>>val;
+        int idx = lowerBound(1,n+1,val);
+        if(idx>n) cout<<"lower_bound doesn't exist"<<endl;
+        else cout<<"lower_bound of "<<val<<" : "<<idx<<endl;
+    }
+
+    while(1)
+    {
+        int val;
+        cin>>val;
+        int idx = upperBound(1,n+1,val);
+        if(idx>n) cout<<"upper_bound doesn't exist"<<endl;
+        else cout<<"upper_bound of "<<val<<" : "<<idx<<endl;
+    }
+
+    return 0;
+}
+
+/**
+
+10
+10 2 2 8 5 6 4 5 4 4
+
+**/
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p)
+{
+    os<<"{"<<p.first<<", "<<p.second<<"} ";
+    return os;
+}
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v)
+{
+    os<<"[ ";
+    for(int i=0; i<v.size(); i++)
+    {
+        os<<v[i]<<" " ;
+    }
+    os<<" ]";
+    return os;
+}
+
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v)
+{
+    os<<"[ ";
+    for(T i:v)
+    {
+        os<<i<<" ";
+    }
+    os<<" ]";
+    return os;
+}
+
+

Data Structure/01 BIT (POINT update , RANGE query).cpp

@@ -55,13 +55,13 @@ string to_str(LL x)
 //
 //}
 
-int ara[nmax];
+LL ara[nmax];
 
 /** BIT / FENWICK TREE **/
 /*** 1 based indexing ***/
 
 LL BIT[nmax];
-void update(int index,int val,int len) /** POINT update , adds to the current value **/
+void update(int index,LL val,int len) /** POINT update , adds to the current value **/
 {
     while(index<=len)
     {
@@ -81,6 +81,67 @@ LL query(int index) /** RANGE query **/
     return sum;
 }
 
+
+///===================================================================================\\\
+
+
+/** binary search on BIT : lower_bound and upper_bound **/
+
+/// for 1 based indexing with n elements , set lo = 1 , hi = n+1
+
+int lowerBound_BIT(int lo,int hi,int key) /** O( (logN)^2 ) **/
+{
+    while(lo!=hi)
+    {
+        int mid = lo + (hi-lo)/2;
+
+        if(query(mid)<key) lo = mid + 1;
+        else hi = mid;
+    }
+
+    return lo;
+}
+
+int upperBound_BIT(int lo,int hi,int key) /** O( (logN)^2 ) **/
+{
+    while(lo!=hi)
+    {
+        int mid = lo + (hi-lo)/2;
+
+        if(query(mid)<=key) lo = mid + 1;
+        else hi = mid;
+    }
+
+    return lo;
+}
+
+/** binary search on BIT : lower_bound and upper_bound [OPTIMIZED] using Binary Lifting **/
+
+int lowerBound_BIT_efficient(LL v,int N) /** O( logN ) **/
+{
+	LL sum = 0;
+	LL pos = 0;
+
+	int k = 0;
+    while (1 << (k + 1) <= N)
+        k++;
+
+    /** k = log(N) **/
+
+	for(int i=k; i>=0; i--)
+	{
+	    int next_idx = pos + (1 << i);
+
+		if( next_idx < N && sum + BIT[next_idx] < v) /// For upper_bound change to "BIT[next_idx] < v" to "BIT[next_idx] <= v"
+		{
+			sum += BIT[next_idx];
+			pos = next_idx;
+		}
+	}
+
+	return pos + 1; /// +1 because 'pos' will have position of largest value less than 'v'
+}
+
 int main()
 {
     //optimizeIO();