Problem:
Range Minimum Query (RMQ)

Write a program which manipulates a sequence A = {a0, a1, . . . , an-1} with the following operations:

find(s, t): report the minimum element in as, as+1, . . . ,at.

update(i, x): change ai to x.

Note that the initial values of ai (i = 0, 1, . . . , n−1) are 231-1.

Input

n q
com0 x0 y0
com1 x1 y1
...
comq−1 xq−1 yq−1

In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes update(xi, yi) and '1' denotes find(xi, yi).

Output

For each find operation, print the minimum element.

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

If comi is 0, then 0 ≤ xi < n, 0 ≤ yi < 231-1.

If comi is 1, then 0 ≤ xi < n, 0 ≤ yi < n.

Sample Input 1

3 5
0 0 1
0 1 2
0 2 3
1 0 2
1 1 2

Sample Output 1

1
2

Sample Input 2

1 3
1 0 0
0 0 5
1 0 0

Sample Output 2

2147483647
5

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        //static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();

        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            var cin = new Scanner();
            var input = cin.ReadSplit();
            int n = input[0];
            int q = input[1];

            var st = new SegmentTree<long>(n, Min, (1L << 31) - 1, (1L << 31) - 1);
            for(var i = 0; i < q; i++)
            {
                var p = cin.ReadSplitL();
                if (p[0] == 0)
                {
                    st.UpdateQuery((int)p[1], p[2]);
                }
                else
                {
                    Console.WriteLine(st.AnswerQuery((int)p[1], (int)p[2] + 1));
                }
            }


            Console.Out.Flush();
        }

        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
        struct Pair<T, U> : IComparable<Pair<T, U>>
        where T : IComparable<T>
        where U : IComparable<U>
        {
            public T first;
            public U second;
            private readonly bool CompWithFirst;

            public Pair(T f, U s, int comp)
            {
                first = f;
                second = s;
                CompWithFirst = comp == 1;
            }
            public Pair(T f, U s)
            {
                first = f;
                second = s;
                CompWithFirst = true;
            }

            public int CompareTo(Pair<T, U> other)
            {
                return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
            }
        }
    }

    public class PriorityQueue<T> where T : IComparable<T>
    {

        public readonly List<T> Q;
        private readonly int r;

        public PriorityQueue(bool ascending)
        {
            if (ascending)
            {
                r = 1;
            }
            else
            {
                r = -1;
            }
            Q = new List<T>();
        }


        private void PushHeap(List<T> list, T item)
        {
            int n = list.Count();
            list.Add(item);

            while (n != 0)
            {
                int pIndex = (n - 1) / 2;

                if (list[n].CompareTo(list[pIndex]) * r > 0)
                {
                    Swap(Q, n, pIndex);
                }
                else { break; }

                n = pIndex;
            }
        }

        private void PopHeap(List<T> list)
        {
            int n = list.Count() - 1;
            list[0] = list[n];
            list.RemoveAt(n);

            int cur = 0;
            int comp;

            while (2 * cur + 1 <= n - 1)
            {
                int c1 = 2 * cur + 1;
                int c2 = 2 * (cur + 1);
                if (c1 == n - 1)
                {
                    comp = c1;
                }
                else
                {
                    comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                }

                if (list[cur].CompareTo(list[comp]) * r < 0)
                {
                    Swap(Q, cur, comp);
                }
                else { break; }

                cur = comp;
            }
        }

        private void Swap(List<T> list, int a, int b)
        {
            T keep = list[a];
            list[a] = list[b];
            list[b] = keep;
        }



        public void Enqueue(T value)
        {
            PushHeap(Q, value);
        }

        public T Dequeue()
        {
            T ret = Q[0];
            PopHeap(Q);
            return ret;
        }

        public T Peek()
        {
            return Q[0];
        }

        public int Count()
        {
            return Q.Count();
        }

        public bool Contains(T obj)
        {
            return Q.Contains(obj);
        }
    }
    public class Scanner
    {
        public int[] ReadSplit()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] ReadSplitL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

    }

    public class SegmentTree<T>
    {
        int n;
        T[] Tree;
        Func<T, T, T> f;
        T ex;
        public SegmentTree(int size, Func<T, T, T> fun, T exvalue)
        {
            f = fun;
            ex = exvalue;
            n = 1;
            while (n < size) n <<= 1;
            Tree = new T[(n << 1) - 1];
            for (var i = 0; i < Tree.Length; i++) Tree[i] = ex;
        }
        public SegmentTree(int size, Func<T, T, T> f, T exvalue, T initial) : this(size, f, exvalue)
        {
            for (var i = 0; i < size; i++) Tree[i + n - 1] = initial;
            Set_All();
        }

        public void Set_All()
        {
            for(var i = n - 2; i >= 0; i--)
            {
                Tree[i] = f(Tree[(i << 1) + 1], Tree[(i << 1) + 2]);
            }
        }

        public void Assign(int ind, T val)
        {
            Tree[ind + n - 1] = val;
        }
        public void Update(int ind)
        {
            int i = ind + n - 1;
            while (i > 0)
            {
                i = (i - 1) >> 1;
                Tree[i] = f(Tree[(i << 1) + 1], Tree[(i << 1) + 2]);
            }
        }

        public void UpdateQuery(int ind,T val)
        {
            Assign(ind, val);
            Update(ind);
        }
        public T AnswerQuery(int l,int r) //[l,r)
        {
            return Scanning(l, r, 0, 0, n);
        }
        private T Scanning(int l, int r, int ind, int ind_l, int ind_r)
        {
            if (ind_r <= l || r <= ind_l) { return ex; }
            if (l <= ind_l && ind_r <= r) { return Tree[ind]; }
            return f(Scanning(l, r, (ind << 1) + 1, ind_l, (ind_l + ind_r) >> 1), Scanning(l, r, (ind << 1) + 2, (ind_l + ind_r) >> 1, ind_r));
        }

        public T Debug_Look(int ind)
        {
            return Tree[ind + n - 1];
        }
        public void Debug_Display_All()
        {
            for (var i = 0; i < n; i++) Console.Write($"{Tree[i + n - 1]} ");
            Console.WriteLine();
        }
    }
}