We‘ll call an array of n non-negative integers a[1], a[2], ..., a[n] interesting, if it meets m constraints. The i-th of the m constraints consists of three integers li, ri, qi (1 ≤ li ≤ ri ≤ n) meaning that value should be equal to qi.
Your task is to find any interesting array of n elements or state that such array doesn‘t exist.
Expression x&y means the bitwise AND of numbers x and y. In programming languages C++, Java and Python this operation is represented as "&", in Pascal — as "and".
Input
The first line contains two integers n, m (1 ≤ n ≤ 105, 1 ≤ m ≤ 105) — the number of elements in the array and the number of limits.
Each of the next m lines contains three integers li, ri, qi (1 ≤ li ≤ ri ≤ n, 0 ≤ qi < 230) describing the i-th limit.
Output
If the interesting array exists, in the first line print "YES" (without the quotes) and in the second line print n integers a[1], a[2], ..., a[n](0 ≤ a[i] < 230) decribing the interesting array. If there are multiple answers, print any of them.
If the interesting array doesn‘t exist, print "NO" (without the quotes) in the single line.
Examples
input
3 1 1 3 3
output
YES 3 3 3
input
3 2 1 3 3 1 3 2
output
NO
算法:线段树
题解:直接用线段树版子,更新用按位或来修改,用按位与来向上更新,要快点可以打个lazy数组。
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <set>
#include <map>
#include <vector>
usingnamespace std;
#define INF 0x3f3f3f3f
typedef longlong ll;
constint maxn = 1e5+7;
struct node {
int l, r, s;
}tree[maxn << 2];
struct queue {
int l, r, w;
}Q[maxn];
int n, m;
int lazy[maxn << 2];
void build(int root, int l, int r) {
tree[root].l = l;
tree[root].r = r;
tree[root].s = 0;
if(l == r) {
return;
}
int mid = (l + r) >> 1;
build(root << 1, l, mid);
build(root << 1 | 1, mid + 1, r);
}
void pushup(int root) {
tree[root].s = tree[root << 1].s & tree[root << 1 | 1].s;
}
void pushdown(int root) {
if(lazy[root]) {
tree[root << 1].s |= lazy[root];
tree[root << 1 | 1].s |= lazy[root];
lazy[root << 1] |= lazy[root];
lazy[root << 1 | 1] |= lazy[root];
lazy[root] = 0;
}
}
void update(int root, int x, int y, int val) {
int l = tree[root].l;
int r = tree[root].r;
if(x <= l && r <= y) {
tree[root].s |= val;
lazy[root] |= val;
return;
}
pushdown(root);
int mid = (l + r) >> 1;
if(x <= mid) {
update(root << 1, x, y, val);
}
if(y > mid) {
update(root << 1 | 1, x, y, val);
}
pushup(root);
}
int queue(int root, int x, int y) {
int l = tree[root].l;
int r = tree[root].r;
if(x <= l && r <= y) {
return tree[root].s;
}
pushdown(root);
int mid = (l + r) >> 1;
int ans = (1 << 30) - 1;
if(x <= mid) {
ans &= queue(root << 1, x, y);
}
if(y > mid) {
ans &= queue(root << 1 | 1, x, y);
}
pushdown(root);
return ans;
}
int main() {
scanf("%d %d", &n, &m);
build(1, 1, n);
for(int i = 1; i <= m; i++) {
scanf("%d %d %d", &Q[i].l, &Q[i].r, &Q[i].w);
update(1, Q[i].l, Q[i].r, Q[i].w);
}
for(int i = 1; i <= m; i++) {
if(queue(1, Q[i].l, Q[i].r) != Q[i].w) { //如果其中有一个不满足条件的话,就输出NO
printf("NO\n");
return0;
}
}
printf("YES\n");
for(int i = 1; i <= n; i++) {
printf("%d%c", queue(1, i, i), " \n"[i == n]);
}
return0;
}