Go: package main

// packed from [splaytree.go main.rmq.go splaytree_debug.go] with goone.

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
	"strings"
)

type SplayTreeNode struct {
	parent, left, right *SplayTreeNode

	size    int
	value   int
	minimum int
}

func newSplayTreeNode(v int) *SplayTreeNode {
	return &SplayTreeNode{value: v}
}

func (node *SplayTreeNode) rotate() {
	var pp, p, c *SplayTreeNode
	p = node.parent
	pp = p.parent
	if pp != nil && pp.left == p {
		pp.left = node
	}
	if pp != nil && pp.right == p {
		pp.right = node
	}
	node.parent = pp
	if p.left == node {
		c = node.right
		node.right = p
		p.left = c
	} else {
		c = node.left
		node.left = p
		p.right = c
	}
	p.parent = node
	if c != nil {
		c.parent = p
	}
	p.update()
	node.update()
}

func (node *SplayTreeNode) state() int {
	if node.parent == nil {
		return 0
	}
	if node.parent.left == node {
		return -1
	} else if node.parent.right == node {
		return 1
	}
	return 0
}

func (node *SplayTreeNode) splay() {
	for node.state() != 0 {
		if node.parent.state() == 0 {
			node.rotate()
			return
		}
		if node.state() == node.parent.state() {
			node.parent.rotate()
			node.rotate()
		} else {
			node.rotate()
			node.rotate()
		}
	}
}

func (node *SplayTreeNode) update() {
	node.size = 1
	node.minimum = node.value
	if node.left != nil {
		node.size += node.left.size
		node.minimum = min(node.minimum, node.left.minimum)
	}
	if node.right != nil {
		node.size += node.right.size
		node.minimum = min(node.minimum, node.right.minimum)
	}
}
func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func (node *SplayTreeNode) Get(idx int) *SplayTreeNode {
	cur := node
	for true {
		lSize := 0
		if cur.left != nil {
			lSize = cur.left.size
		}
		if idx < lSize {
			cur = cur.left
		}
		if lSize == idx {
			cur.splay()
			return cur
		}
		if idx > lSize {
			cur = cur.right
			idx = idx - lSize - 1
		}
	}
	return nil
}

func mergeSplayNode(l, r *SplayTreeNode) (root *SplayTreeNode) {
	if l == nil {
		return r
	}
	if r == nil {
		return l
	}
	root = l.Get(l.size - 1)
	root.right = r
	r.parent = root
	root.update()
	return root
}

func (node *SplayTreeNode) Split(leftCount int) (left *SplayTreeNode, right *SplayTreeNode) {
	root := node.Get(leftCount)
	lRoot, rRoot := root.left, root

	rRoot.left = nil
	if lRoot != nil {
		lRoot.parent = nil
	}
	rRoot.update()
	return lRoot, rRoot
}

func splayTreeInsert(t *SplayTreeNode, idx int, node *SplayTreeNode) (root *SplayTreeNode) {
	l, r := t.Split(idx)
	return mergeSplayNode(
		mergeSplayNode(l, node),
		r,
	)
}

func removeSplayTree(t *SplayTreeNode, idx int) (root *SplayTreeNode, removed *SplayTreeNode) {
	target := t.Get(idx)
	l, r := target.left, target.right
	if l != nil {
		l.parent = nil
	}
	if r != nil {
		r.parent = nil
	}
	target.left = nil
	target.right = nil
	target.update()
	return mergeSplayNode(l, r), target
}

const (
	initialBufSize = 100000
	maxBufSize     = 1000000
)

var sc *bufio.Scanner

func initScanner(r io.Reader) *bufio.Scanner {
	buf := make([]byte, initialBufSize)

	sc := bufio.NewScanner(r)
	sc.Buffer(buf, maxBufSize)
	sc.Split(bufio.ScanWords)
	return sc
}

func main() {
	sc = initScanner(os.Stdin)
	resolve()
}

func resolve() {
	n := scanInt(sc)
	q := scanInt(sc)
	table := newDebugNodeSlice(200001)
	for i := 0; i < n; i++ {
		table.l[i].parent = &table.l[i+1]
		table.l[i+1].left = &table.l[i]
		table.l[i].update()
		table.l[i+1].update()
	}
	var root *SplayTreeNode = &table.l[n]
	for i := 0; i < n; i++ {
		table.l[i].value = scanInt(sc)
		table.l[i].update()
	}
	table.l[n].update()
	for i := 0; i < q; i++ {
		switch scanInt(sc) {
		case 0:
			root = shift(root, scanInt(sc), scanInt(sc))
		case 1:
			l := scanInt(sc)
			r := scanInt(sc)
			tmp, rRoot := root.Split(r + 1)
			lRoot, cRoot := tmp.Split(l)
			fmt.Println(cRoot.minimum)
			root = mergeSplayNode(mergeSplayNode(lRoot, cRoot), rRoot)
		case 2:
			root = root.Get(scanInt(sc))
			root.value = scanInt(sc)
			root.update()
		}
	}
}


C++: #define _USE_MATH_DEFINES
#define INF 0x3f3f3f3f

#include <iostream>
#include <cstdio>
#include <sstream>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <stack>
#include <limits>
#include <map>
#include <string>
#include <cstring>
#include <set>
#include <deque>
#include <bitset>
#include <list>
#include <cctype>
#include <utility>
#include <assert.h>

using namespace std;

typedef long long ll;

static const double EPS = 1e-8;

static const int tx[] = {0,1,0,-1};
static const int ty[] = {-1,0,1,0};

struct Node {
  int val;
  Node* children[2];
  double priority;
  int size;
  int range_min;
  Node(int val,double priority)
    : val(val), priority(priority),size(1),range_min(val){
    children[0] = children[1] = NULL;
  }
};

class Treap {
private:
  Node* root;

  int compute_size(Node *current) {
    return (current == NULL ? 0 : current->size);
  }

  int compute_range_min(Node *current) {
    return (current == NULL ? INF : current->range_min);
  }

  Node* update(Node *current) {
    current->size
      = compute_size(current->children[0])
      + compute_size(current->children[1]) + 1;
    current->range_min
      = min(min(compute_range_min(current->children[0]),current->val),
            min(compute_range_min(current->children[1]),current->val));
    return current;
  }

  Node* merge(Node* lhs, Node* rhs) {
    if (lhs == NULL || rhs == NULL) {
        return (lhs == NULL ? rhs : lhs);
    }

    if (lhs->priority > rhs->priority) {
      lhs->children[1] = merge(lhs->children[1], rhs);
      return update(lhs);
    } else {
      rhs->children[0] = merge(lhs, rhs->children[0]);
      return update(rhs);
    }
  }

  pair<Node*, Node*> split(Node* current, int k) { // [0,k), [k,n)
    if(current == NULL) {
      Node* dummy = NULL;
      return make_pair(dummy, dummy);
    }
    
    if (k <= compute_size(current->children[0])) {
      pair<Node*, Node*> s = split(current->children[0], k);
      current->children[0] = s.second;
      return make_pair(s.first, update(current));
    }
    else {
      pair<Node*, Node*> s = split(current->children[1],
                                   k - compute_size(current->children[0]) - 1);
      current->children[1] = s.first;
      return make_pair(update(current), s.second);
    }
  }

  Node* insert(Node* current, int k, int v) {
    pair<Node*, Node*> splitted = split(current, k);
    double priority = (double)rand() / (double)RAND_MAX;
    current = merge(splitted.first, new Node(v, priority));
    current = merge(current, splitted.second);
    return update(current);
  }

  Node* erase(Node* current, int k) {
    // lhs: [0,k+1) [k+1,n) == [0,k] [k+1,n)
    // rhs: [0,k) [k,n) == [0,k-1] [k,n)
    // [0,k-1] [k+1,n) == rhs.first lhs.second
    pair<Node*, Node*> lhs = split(current, k + 1);
    pair<Node*, Node*> rhs = split(lhs.first, k);
    return merge(rhs.first, lhs.second);
  }

  Node* find(Node* current, int k) {
    if(current == NULL) return NULL;
    int lhs_size = compute_size(current->children[0]);
    if(k < lhs_size) {
      return find(current->children[0], k);
    }
    else if(k == lhs_size) {
      return current;
    }
    else {
      return find(current->children[1], k - lhs_size - 1);
    }
  }
  
  Node* shift(Node* current, int left_i, int right_i) { // [left_i,right_i]
    pair<Node*, Node*> rhs = split(current, right_i + 1); // 1st:[0,right_i] 2nd:[right_i + 1,n)
    pair<Node*, Node*> lhs = split(rhs.first, right_i); // 1st:[0,right_i-1] 2nd:[right_i,right_i]
    pair<Node*, Node*> mid = split(lhs.first, left_i); // 1st:[0,left_i-1] 2nd:[left_i,right_i-1]

    //[0,left_i-1] [right_i] [left_i,right_i-1] [right_i+1,n)
    return merge(merge(merge(mid.first,lhs.second),mid.second),rhs.second);
  }
  
  int query(Node* current, int left_i, int right_i) {
    pair<Node*, Node*> rhs = split(current, right_i + 1); // 1st:[0,right_i+1) 2nd:[right_i+1,n)
    pair<Node*, Node*> lhs = split(rhs.first, left_i); // 1st:[0,left_i) 2nd:[left_i,right_i]
    int res = compute_range_min(lhs.second);
    current = merge(merge(lhs.first,lhs.second),rhs.second);
    return res;
  }

public:
  Treap() {
    root = NULL;
  }

  void insert(int k, int v) {
    root = insert(root, k, v);
  }

  void erase(int k) {
    root = erase(root, k); 
  }

  int find(int k) {
    Node* node = find(root, k);
    return node->val;
  }

  void shift(int left_i, int right_i) {
    root = shift(root, left_i, right_i);
  }

  int query(int left_i, int right_i) {
    return query(root, left_i, right_i);
  }

  void disp() {
    int idx = 0;
    Node* node;
    printf("---------------\n");
    while((node = find(root, idx)) != NULL) {
      printf("%d: %d\n",idx,node->val);
      idx++;
    }
  }
};

int main(){
  int sequence_length;
  int total_queries;

  while(~scanf("%d %d",&sequence_length,&total_queries)){
    vector<int> sequence;
    Treap treap;
    for(int seq_i = 0; seq_i < sequence_length; seq_i++){
      int num;
      scanf("%d",&num);
      treap.insert(seq_i,num);
    }

    for(int query_i = 0; query_i < total_queries; query_i++){
      int command;
      int left_i;
      int right_i;
      scanf("%d %d %d",&command,&left_i,&right_i);
      if(command == 0) {
        treap.shift(left_i, right_i);
      }
      else if(command == 1) {
        printf("%d\n",treap.query(left_i, right_i));
      }
      else if(command == 2) {
        treap.erase(left_i);
        treap.insert(left_i,right_i);
      }
    }
  }
}