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 <bits/stdc++.h>

using namespace std;

#define L 250

#define INF 1000000000

struct RMQ {
	vector< vector<int> > v;
	vector<int> m;
	void shift(int l, int r) {
		int pos = 0;
		int rv = -1;
		for (int i = 0; i < v.size(); ++i) {
			int np = pos+v[i].size();
			if (pos <= r && r < np) {
				int j = r-pos;
				rv = v[i][j];
				v[i].erase(v[i].begin()+j);
				updateMin(i);
				break;
			}
			pos = np;
		}

		pos = 0;
		for (int i = 0; i < v.size(); ++i) {
			int np = pos+v[i].size();
			if (pos <= l && l < np) {
				int j = l-pos;
				v[i].insert(v[i].begin()+j, rv);
				updateMin(i);
			}
			pos = np;
		}
	}
	int get(int l, int r) {
		int ret = INF;
		int pos = 0;
		for (int i = 0; i < v.size(); ++i) {
			int np = pos+v[i].size();
			if (l <= pos && np-1 <= r) {
				ret = min(ret, m[i]);
			}
			else if (pos <= r && l < np) {
				for (int j = 0; j < v[i].size(); ++j) {
					if (l <= pos+j && pos+j <= r) {
						ret = min(ret, v[i][j]);
					}
				}
			}
			pos = np;
		}
		return ret;
	}
	void update(int x, int val) {
		int pos = 0;
		for (int i = 0; i < v.size(); ++i) {
			int np = pos+v[i].size();
			if (pos <= x && x < np) {
				v[i][x-pos] = val;
				updateMin(i);
				break;
			}
			pos = np;
		}
	}
	void updateMin(int pos) {
		m[pos] = INF;
		for (int i = 0; i < v[pos].size(); ++i) {
			m[pos] = min(m[pos], v[pos][i]);
		}
	}
	void smooth() {
		vector<int> a;
		for (int i = 0; i < v.size(); ++i) {
			for (int j = 0; j < v[i].size(); ++j) {
				a.push_back(v[i][j]);
			}
		}
		init(a);
	}
	void init(vector<int> a) {
		int N = a.size();
		v.clear(); v.resize((N-1)/L+2); // N > 0
		m = vector<int>(v.size(), INF);

		int pos = 0;
		for (int i = 0; i < v.size(); ++i) {
			for (int j = 0; j < L; ++j) {
				if (pos+j < N) {
					v[i].push_back(a[pos+j]);
				}
			}
			updateMin(i);
			pos += L;
		}
	}
};

int main() {
	RMQ rmq;
	int N, Q; cin >> N >> Q;
	vector<int> v(N);
	for (int i = 0; i < N; ++i) {
		cin >> v[i];
	}
	rmq.init(v);
	for (int t = 0; t < Q; ++t) {
		int x, y, z; cin >> x >> y >> z;
		switch (x) {
			case 0:
				rmq.shift(y, z);
				break;

			case 1:
				cout << rmq.get(y, z) << endl;
				break;

			case 2:
				rmq.update(y, z);
				break;
		}
		if (t % L == 0) {
			rmq.smooth();
		}
	}
}