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 <cstdio>
#include <algorithm>
#include <cassert>
using namespace std;

const int INF = int(1.05e9); 

class Random {
private:
	unsigned int x, y, z, w, t;
public:
	unsigned int rand(){
		t = x ^ (x << 11);
		x = y; y = z; z = w;
		return w = ( (w ^ (w>>19)) ^ (t ^ (t>>8)));
	}

};

Random rnd;

typedef unsigned int uint;

template<class T>
struct Node {
	T value, mini;
	Node *child[2];
	uint priority;
	int size;

	Node(){}
	Node(T val, uint pri):
		value(val), mini(val), priority(pri), size(1)
	{
		child[0] = child[1] = 0;
	}
};

template<class T>
inline Node<T> *allocateNode(T value, uint priority) {
	return new Node<T>(value, priority);
}

template<class T>
inline void freeNode(Node<T> *node) {
	free(node);
}

template<class T>
inline int getSize(Node<T> *r) {
	return !r ? 0 : r->size;
}

template<class T>
inline Node<T> *getNode(Node<T>* r, int k) {
	assert(r && 0 <= k && k < r->size);
	int left = getSize(r->child[0]), which = (k > left);
	if (left == k) {
		return r;
	}
	return getNode(r->child[which], k - (which ? (left + 1) : 0));
}

template<class T>
inline Node<T> *update(Node<T> *r) {
	r->size = getSize(r->child[0]) + getSize(r->child[1]) + 1;
	r->mini = r->value;
	for (int i = 0; i < 2; ++i) if (r->child[i]) {
		r->mini = min(r->mini, r->child[i]->mini);
	}
	return r;
}

template<class T>
inline Node<T> *updateValue(Node<T> *r, int k, T val) {
	assert(r && 0 <= k && k < getSize(r));
	int left = getSize(r->child[0]), which = (k > left);
	if (left == k) {
		r->value = val;
		return update(r);
	}
	if (r->child[which]) {
		r->child[which] = updateValue(r->child[which], k - (which ? (left + 1) : 0), val);
	}
	return update(r);
}

template<class T>
inline T queryValue(Node<T> *r, int from, int to) {
	if (to <= from) {
		return INF;
	}
	assert(r && 0 <= from && to <= getSize(r));
	if (to - from == getSize(r)) {
		return r->mini;
	}
	int left = getSize(r->child[0]);
	if (to <= left) {
		return queryValue(r->child[0], from, to);
	}
	if (left < from) {
		return queryValue(r->child[1], from - left - 1, to - left - 1);
	}
	return min(r->value,
			min(queryValue(r->child[0], from ,left),
				queryValue(r->child[1], 0, to - left - 1)));
}

template<class T>
inline Node<T> *rotate(Node<T> *r, int which) { 
	assert(which == 0 || which == 1);
	Node<T> *opposite = r->child[which^1];
	r->child[which^1] = opposite->child[which];
	opposite->child[which] = r;
	update(r);
	update(opposite);
	return opposite;
}

template<class T>
inline Node<T> *insert(Node<T> *r, int k, T value, uint priority) {
	if (!r) {
		assert(k == 0);
		return allocateNode(value, priority);
	}
	assert(0 <= k && k <= r->size);
	int left = getSize(r->child[0]), which = (k > left);
	r->child[which] = insert(r->child[which], k - (which ? (left + 1) : 0), value, priority);
	update(r);
	if (r->priority > r->child[which]->priority) {
		r = rotate(r, which^1);
	}
	return r;
}

template<class T>
inline Node<T> *insert(Node<T> *r, int k, T value) {
	return insert(r, k, value, rnd.rand());
}

template<class T>
inline Node<T> *erase(Node<T> *r, int k) {
	assert(r);
	if (r->size == 1) {
		assert(k == 0);
		freeNode(r);
		return 0;
	}
	int left = getSize(r->child[0]), which = (k > left);
	if (left == k) {
		r = rotate(r, left > 0);
		return erase(r, k);
	}
	r->child[which] = erase(r->child[which], k - (which ? (left + 1) : 0));
	update(r);
	return r;
}



const int MAX_NODE = 400000;
Node<int> nodes__[MAX_NODE];
int freeNodeStack__[MAX_NODE], *lastStack__;

void initNode(int n = MAX_NODE) {
	for (int i = 0; i < n; ++i) {
		freeNodeStack__[i] = n - 1 - i;
	}
	lastStack__ = freeNodeStack__ + n;
}

template<>
inline Node<int> *allocateNode(int value, uint priority) {
	return &(nodes__[*--lastStack__] = Node<int>(value, priority));
}

template<>
inline void freeNode(Node<int> *node) {
	assert(node);
	if (node) {
		*lastStack__ = int(node - nodes__);
		++lastStack__;
	}
}

int main() {
	initNode();
	rnd.rand();
	for (int n, q, x, y, z; scanf("%d%d", &n, &q) == 2;) {
		Node<int> *tp = 0;
		for (int i = 0; i < n; ++i) {
			int a; scanf("%d", &a);
			tp = insert(tp, i, a);
		}
		for (int _ = 0; _ < q; ++_) {
			scanf("%d%d%d", &x, &y, &z);
			if (x == 0) {
				int tmp = getNode(tp, z)->value;
				tp = erase(tp, z);
				tp = insert(tp, y, tmp);
			}
			else if (x == 1) {
				printf("%d\n", queryValue(tp, y, z+1));
			}
			else if (x == 2) {
				tp = updateValue(tp, y, z);
			}
		}
		break;
	}
	return 0;
}