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++: #include <iostream>
#include <algorithm>
#include <numeric>
#include <vector>
#include <cassert>
#include <string>
#include <memory.h>
#include <queue>
#include <cstdio>
#include <cstdlib>
#include <set>
#include <map>
#include <cctype>
#include <iomanip>
#include <sstream>
#include <cctype>
#include <fstream>
#include <cmath>
using namespace std;

#define REP2(i, m, n) for(int i = (int)(m); i < (int)(n); i++)
#define REP(i, n) REP2(i, 0, n)
#define ALL(c) (c).begin(), (c).end()
#define ITER(c) __typeof((c).begin())
#define PB(e) push_back(e)
#define FOREACH(i, c) for(ITER(c) i = (c).begin(); i != (c).end(); ++i)
#define MP(a, b) make_pair(a, b)
#define PARITY(n) ((n) & 1)

typedef long long ll;
typedef pair<ll, ll> P;
const int INF = 1000 * 1000 * 1000 + 7;
const double EPS = 1e-10;

class random_bst{
  struct node_t{
    int val;
    int cnt;
    int min;    
    node_t *chl, *chr;
    node_t(int v) : val(v), cnt(1), min(v), chl(NULL), chr(NULL) {}    
    ~node_t(){
      if(this->chl) delete this->chl;
      if(this->chr) delete this->chr;
    }
  };

  node_t *root;
  
  int min(node_t *t)  { return t ? t->min : INF; }
  int count(node_t *t){ return t ? t->cnt   : 0; }
  int value(node_t *t){ return t ? t->val   : 0; }
  
  node_t *update(node_t *t){
    t->cnt = count(t->chl) + count(t->chr) + 1;
    t->min = std::min(std::min(min(t->chl), min(t->chr)), t->val);
    return t;
  }
  
  node_t *merge(node_t *l, node_t *r){
    if(!l || !r) return l ? l : r;
    
    if(rand() % (count(l) + count(r)) <= count(l)){
      // lを新しい根に
      l->chr = merge(l->chr, r);
      return update(l);
    }else{
      // rを新しい根に
      r->chl = merge(l, r->chl);
      return update(r);
    }
  }
  
  pair<node_t*, node_t*> split(node_t *t, int k){
    if(!t) return make_pair<node_t*, node_t*>(NULL, NULL);
    
    if(k <= count(t->chl)){
      
      pair<node_t *, node_t *> s = split(t->chl, k);
      t->chl = s.second;
      return make_pair(s.first, update(t));
    }else{
      
      pair<node_t *, node_t *> s = split(t->chr, k - count(t->chl) - 1);
      t->chr = s.first;
      return make_pair(update(t), s.second);
    }
  }


public:
  random_bst() : root(NULL) {}
  ~random_bst(){ delete root; }
  
  void erase(int pos){
    pair<node_t*, node_t*> pr = split(root, pos);
    pair<node_t*, node_t*> pl = split(pr.first, pos - 1);
    root = update(merge(pl.first, pr.second));
  }

  void insert(int pos, int val){
    pair<node_t*, node_t*> s = split(root, pos);
    root = update(merge(merge(s.first, new node_t(val)), s.second));
  }
  
  void shift(int l, int r){
    pair<node_t*, node_t*> pr = split(root, r); 
    pair<node_t*, node_t*> pm = split(pr.first, r - 1);
    pair<node_t*, node_t*> pl = split(pm.first, l);
    root = merge(merge(pl.first, pm.second),
                 merge(pl.second,pr.second));
  }
  
  int query(int l, int r){
    pair<node_t*, node_t*> pr = split(root, r);
    pair<node_t*, node_t*> pl = split(pr.first, l);
    int res = min(pl.second);
    root = merge(pl.first, pl.second);
    root = merge(root, pr.second);
    return res;
  }
};

int main(){
  int n, q, x, y, z;
  cin >> n >> q;
  vector<int>A(n);
  random_bst t;
  
  REP(i, n) cin >> A[i];
  REP(i, n) t.insert(i, A[i]);
  
  
  REP(i, q){
    cin >> x >> y >> z;
    switch(x){
    case 0:
      t.shift(y, z + 1);
      break;
      
    case 1:
      cout << t.query(y, z + 1) << endl;
      break;
    case 2:
      t.erase(y);
      t.insert(y, z);
      break;
    }
  }
  return 0;
}