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: Time Limit Exceeded)

#include <stdio.h>

#define INF 2147483647
#define RMQ_SIZE 262144

#define min(a, b) a<b?a:b

void update(int pos, int value);
int getMin(int right, int left);
int dfs(int a,int b,int k,int l,int r);

int tree[RMQ_SIZE];

int main()
{
    int n, q, i, tmp, a, b;

    scanf("%d %d", &n, &q);

    for (i = 0; i <= n; i++) {
        update(i, INF);
    }
    for (i = 0; i < q; i++) {
        scanf("%d %d %d", &tmp, &a, &b);
        if (tmp) {
            printf("%d\n", getMin(a, b+1));
        } else {
            update(a, b);
        }
    }
            
    return 0;
}


int dfs(int a,int b,int k,int l,int r)
{
    //* ????±????????????????????????¬???????????¢?´¢.
    if (r <= a || b <= l) {
        return INF;
    }
    //* ??¨?????¬?????????????±?????????\???????????????.
    if (a <= l && r <= b) {
        return tree[k];
    }
    int m = (l+r)/2;
    return min(dfs(a, b, k*2+1, l, m), dfs(a, b, k*2+2, m, r));
}

int getMin(int right, int left)
{
    return dfs(right, left, 0, 0, RMQ_SIZE/2);
}

void update(int pos, int value)
{
    pos += (RMQ_SIZE/2 -1);
    tree[pos] = value;
    while (pos) {
        pos = (pos-1)/2;
        tree[pos] = min(tree[pos*2+1], tree[pos*2+2]);
    }
}