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 <algorithm>
#include <cstdlib>
#include <iostream>
#include <memory>
#include <numeric>
#include <vector>
using namespace std;

unsigned seed128[4];
void seed(unsigned s){
	for(int i=1; i<=4; i++)
		seed128[i-1] = s = 1812433253U * (s^(s>>30)) + i;
}

unsigned xor_shift() {
	unsigned t;
	t=(seed128[0]^(seed128[0]<<11));
	seed128[0]=seed128[1];
	seed128[1]=seed128[2];
	seed128[2]=seed128[3];
	return seed128[3]=(seed128[3]^(seed128[3]>>19))^(t^(t>>8));
}

// Randomized Binary Search Tree
// infix, 0-based

typedef int type;
constexpr int INF = (1 << 29);
constexpr type INIT = INF;
constexpr int MAX_N = 200000;

// update function
inline type func(type a, type b) {
	return min(a, b);
}

struct RBST {
	type value, res;
	int size;
	RBST *left, *right;

	RBST(int v = 0):value(v), res(v), size(1), left(nullptr), right(nullptr) {}

	void update() {
		size = 1;
		res = value;

		if(left) {
			size += left->size;
			res = func(res, left->res);
		}

		if(right) {
			size += right->size;
			res = func(res, right->res);
		}
	}
};

RBST nodes[MAX_N];
vector<int> pool(MAX_N);

inline int node_size(const RBST *x) {
	return x ? x->size : 0;
}

inline RBST *make_node(type value = 0) {
	const int v = pool.back();
	nodes[v].value = nodes[v].res = value;
	nodes[v].size = 1;
	nodes[v].left = nodes[v].right = nullptr;
	pool.pop_back();
	return nodes + v;
}

inline void free_node(RBST *x) {
	pool.emplace_back(x - nodes);
}

RBST *merge(RBST *x, RBST *y) {
	if(!x) return y;
	if(!y) return x;

	if(xor_shift() % (x->size + y->size) < x->size) {
		x->right = merge(x->right, y);
		x->update();
		return x;
	}
	else {
		y->left = merge(x, y->left);
		y->update();
		return y;
	}
}

typedef pair<RBST *, RBST *> P;

P split(RBST *x, int num) {
	if(!x) return P(nullptr, nullptr);

	const int l_size = node_size(x->left);
	if(l_size < num) {
		const P tmp = split(x->right, num - l_size - 1);
		x->right = tmp.first;
		x->update();
		return P(x, tmp.second);
	}
	else {
		const P tmp = split(x->left, num);
		x->left = tmp.second;
		x->update();
		return P(tmp.first, x);
	}
}

RBST *insert(RBST *x, int pos, type value) {
	RBST *new_node = make_node(value);
	const P tmp = split(x, pos);
	return merge(merge(tmp.first, new_node), tmp.second);
}

RBST *erase(RBST *x, int pos) {
	P tmp = split(x, pos);
	RBST *left = tmp.first;
	tmp = split(tmp.second, 1);
	free_node(tmp.first);
	return merge(left, tmp.second);
}

// [l, r)
type query(RBST *x, int l, int r) {
	if(!x) return INIT;
	if(r <= 0 || x->size <= l) return INIT;
	if(l <= 0 && x->size <= r) return x->res;

	const int l_size = node_size(x->left);
	const type res = (l <= l_size && l_size < r ? x->value : INIT);
	const type vl = query(x->left, l, r);
	const type vr = query(x->right, l - l_size - 1, r - l_size - 1);
	return func(res, func(vl, vr));
}

enum { SHIFT, QUERY, UPDATE };

int main() {
	cin.tie(nullptr);
	ios::sync_with_stdio(false);

	iota(begin(pool), end(pool), 0);
	seed(time(NULL));

	int n, q;
	cin >> n >> q;

	RBST *root = nullptr;
	for(int i = 0; i < n; ++i) {
		int a;
		cin >> a;
		root = insert(root, i, a);
	}

	while(q--) {
		int x, y, z;
		cin >> x >> y >> z;
		switch(x) {
		case SHIFT:
		{
			const auto value = query(root, z, z + 1);
			root = erase(root, z);
			root = insert(root, y, value);
			break;
		}
		case QUERY:
		{
			cout << query(root, y, z + 1) << '\n';
			break;
		}
		case UPDATE:
		{
			root = erase(root, y);
			root = insert(root, y, z);
			break;
		}
		}
	}

	return EXIT_SUCCESS;
}