Prefix sum

algos/range_queries/PrefixSum/soln/IshanRajSingh/Solution3.py

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+# Submission Link: https://codeforces.com/contest/1605/submission/356614528
+# Approach: find all 1s that should be 0 (from left) and all 0s that should be 1 (from right), if any mismatches do one operation
+# Runtime: O(n) per test
+import sys
+input=sys.stdin.readline
+t=int(input().strip())
+for _ in range(t):
+    n=int(input().strip())
+    s=list(input().strip())
+    zeros=sorted([i for i in range(n) if s[i]=='0'])
+    ones=sorted([i for i in range(n) if s[i]=='1'])
+    l, r=0,len(zeros)-1
+    i, j=0,len(ones)-1
+    left=0
+    right=n-1
+    badL=[]
+    badR=[]
+    # two pointers: from left find 1 before a zero that should be left
+    lptr=0
+    rptr=n-1
+    while lptr<rptr:
+        while lptr<n and s[lptr]=='0':
+            lptr+=1
+        while rptr>=0 and s[rptr]=='1':
+            rptr-=1
+        if lptr<rptr:
+            badL.append(lptr+1)
+            badR.append(rptr+1)
+            lptr+=1
+            rptr-=1
+    if not badL:
+        print(0)
+    else:
+        ops=badL+badR[::-1]
+        print(1)
+        print(len(ops),*ops)

algos/range_queries/PrefixSum/soln/IshanRajSingh/Solution4.py

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+# Submission Link: https://codeforces.com/problemset/submission/1843/356614985
+# Approach: binary search on first query index such that any segment has > half ones using prefix sums
+# Runtime: O((n+m) log q)
+import sys
+input=sys.stdin.readline
+
+def check(mid, n, segs, ord):
+    arr=[0]*n
+    for i in range(mid):
+        arr[ord[i]] = 1
+    pref=[0]*(n+1)
+    for i in range(n):
+        pref[i+1]=pref[i]+arr[i]
+    for l,r in segs:
+        if pref[r+1]-pref[l] > (r-l+1)//2:
+            return True
+    return False
+
+t=int(input().strip())
+for _ in range(t):
+    n,m=map(int,input().split())
+    segs=[tuple(map(lambda x: int(x)-1, input().split())) for _ in range(m)]
+    q=int(input().strip())
+    ord=[int(input().strip())-1 for _ in range(q)]
+    lo,hi=0,q+1
+    while hi-lo>1:
+        mid=(lo+hi)//2
+        if check(mid,n,segs,ord):
+            hi=mid
+        else:
+            lo=mid
+    ans = hi if hi<=q else -1
+    print(ans)