題目描述

FJ‘s N (1 ≤ N ≤ 10,000) cows conveniently indexed 1..N are standing in a line. Each cow has a positive integer height (which is a bit of secret). You are told only the height H (1 ≤ H ≤ 1,000,000) of the tallest cow along with the index I of that cow.

FJ has made a list of R (0 ≤ R ≤ 10,000) lines of the form "cow 17 sees cow 34". This means that cow 34 is at least as tall as cow 17, and that every cow between 17 and 34 has a height that is strictly smaller than that of cow 17.

For each cow from 1..N, determine its maximum possible height, such that all of the information given is still correct. It is guaranteed that it is possible to satisfy all the constraints.

有n頭牛給定最高身高H和它的位置I，n頭牛站成一列給定R個關系A，B 即A能看到B所以A------B之間所有牛小於AB且B的身高大於等於A

輸入輸出格式

輸入格式：

Line 1: Four space-separated integers: N, I, H and R

Lines 2..R+1: Two distinct space-separated integers A and B (1 ≤ A, B ≤ N), indicating that cow A can see cow B.

輸出格式：

Lines 1..N: Line i contains the maximum possible height of cow i.

輸入輸出樣例

9 3 5 5
1 3
5 3
4 3
3 7
9 8

5
4
5
3
4
4
5
5
5



分析：
　　由題意可知在給定區間（A,B）中A,B除外所有元素均小於A,B所以可知各區間僅能包含或覆蓋不能相交
　　——————————————————————
　　　　———————————
　　反證法可證明：若區間(C,D)和區間（A,B)相交
　　——————————————————————
　　C                     D
　　　　　　——————————————————————
　　　     A 　　　　　　　　　　　　B
　　由題意可得D高度小於A，B因而若C向右看一定先看到A>B與已知情況矛盾所以不成立
　　因此區間僅能相互覆蓋所以問題轉化為統計每個位置上區間覆蓋次數
　　可用差分數組實現對於區間(A,B)　　ch[A+1]--;ch[B]++;
　　最後差分+最高高度H就是答案
 

[USACO07JAN] Tallest Cow